
Citation 
 Permanent Link:
 http://ufdc.ufl.edu/AA00026405/00001
Material Information
 Title:
 Learning disability subtypes a cluster analytic study
 Creator:
 Johnston, Carol Sue, 1952
 Publication Date:
 1986
 Language:
 English
 Physical Description:
 viii, 177 leaves : ill. ; 29 cm.
Subjects
 Subjects / Keywords:
 Arithmetic ( jstor )
Cluster analysis ( jstor ) Disabilities ( jstor ) Grade levels ( jstor ) Intelligence quotient ( jstor ) Learning disabilities ( jstor ) Neuropsychological tests ( jstor ) Reading comprehension ( jstor ) Reading difficulties ( jstor ) Standardization ( jstor ) Child ( mesh ) Clinical and Health Psychology thesis Ph.D ( mesh ) Dissertations, Academic  Clinical and Health Psychology  UF ( mesh ) Evaluation Studies ( mesh ) Infant ( mesh ) Learning Disorders ( mesh )
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 bibliography ( marcgt )
theses ( marcgt ) nonfiction ( marcgt )
Notes
 Thesis:
 Thesis (Ph. D.)University of Florida, 1986.
 Bibliography:
 Includes bibliographical references (leaves 169175).
 Additional Physical Form:
 Also available online.
 General Note:
 Typescript.
 General Note:
 Vita.
 Statement of Responsibility:
 by Carol Sue Johnston.
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 University of Florida
 Holding Location:
 University of Florida
 Rights Management:
 Copyright Carol Sue Johnston. Permission granted to the University of Florida to digitize, archive and distribute this item for nonprofit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
 Resource Identifier:
 022096710 ( ALEPH )
17865024 ( OCLC )

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Full Text 
LEARNING DISABILTY SUBTYPES:
A CLUSTER ANALYTIC STUDY
By
CAROL SUE JOHNSTON
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA 1986
ACKNOWLEDGEMENTS
I would like to thank Paul Satz for providing the inspiration that got me started on this project, and Robin Morris for helping me to begin to make sense of what I had found. Special thanks are also due to Eileen Fennell for her support and encouragement that kept me going, as well as to the rest of my committee for their patience.
I am indebted to the PennTrafford School District for their cooperation, without which this research would not have been possible. In particular, I am grateful to Carl Bruno, Superintendent, and Alice Giglio, Director of Pupil Personnel Services, for their support and facilitation of the project.
Closer to home, I would like to thank my husband and
daughter for their tolerance of a parttime wife and mother during the long struggle toward completion. Finally I would like to acknowledge my appreciation of Hope McGee, whose excellent child care, in the truest sense, allowed me to focus my attention on my work.
ii
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ............ ..... ii
LIST OF TABLES . . . . iv
LIST OF FIGURES . . . . vi
ABSTRACT ......... .. .. . V 1ii
CHAPTERS
I INTRODUCTION . . * 1
Research on Learning Disability Subtypes .. 5 Conclusions and Hypotheses ....... 28
II METHOD ............. ...... 31
Subjects ..... .... .... 31
Measures ..... ............ 32
Procedure . . . .. 36
III RESULTS ................... 44
Phase I: Cluster Analysis of Achievement
Variables .. .... .. .... 44
Phase II: Cluster Analysis of Neuropsychological Variables .. 106
IV DISCUSSION ................. 128
Discussion of Hypotheses .......... 128
Conclusions and Directions for Future
Research ...... . ....... 163
BIBLIOGRAPHY . . . . .. .168
BIOGRAPHICAL SKETCH ................ 176
iii
LIST OF TABLES
Table Page
1 Mean Grade Equivalent Discrepancy Scores for Male Achievement Subgroups Based on WRAT
Clustering Variables . . . 46
2 OLMAT IQ Scores, CA, and ISP SES Ratings for Male Achievement Subgroups Based on WRAT
Clustering Variables . . . 51
3 Mean Grade Equivalent Discrepancy Scores for Male Achievement Subgroups Based on WRAT and
GMRT Clustering Variables ........ .. 54
4 Mean OLMAT IQ Scores, CA, and ISP SES Ratings for Male Achievement Subgroups for Male
Achievement Subgroups Based on WRAT and GMRT
Clustering Variables . ... .. . 59
5 Variable Correlations for Male Sample ... 61
6 Mean Grade Equivalent Discrepancy Scores for Female Achievement Subgroups based
on WRAT Clustering Variables .... .. 64
7 Mean OLMAT IQ Scores for Female Achievement Subgroups Based on WRAT Clustering Variables. 70
8 Mean Grade Equivalent Discrepancy Scores for Female Achievement Subgroups Based on WRAT
and GMRT Clustering Variables .... 73
9 Mean OLMAT IQ Scores for Female Achievement Subgroups Based on WRAT and GMRT Clustering
Variables . . . . 79
10 Variable Correlations for Female Sample . 82
11 Mean Grade Equivalent Discrepancy Scores for
Combined Sex Achievement Subgroups Based on
WRAT Clustering Variables ...... . 6
12 Mean OLMAT IQ Scores, CA, and ISP SES Ratings
for Combined Sex Achievement Subgroups Based
on WRAT Clustering Variables ....... 90
iv
Table Page
13 Mean Grade Equivalent Discrepancy Scores
for Combined Sex Achievement Subgroups Based
on WRAT and GMRT Clustering Variables .... 92
14 Mean OLMAT IQ Scores, CA, and ISP SES Ratings
for Combined Sex Achievement Groups Based on
WRAT and GMRT Clustering Variables . 99
15 Gender Distribution for Combined Sex
Achievement Subgroups Based on WRAT and GMRT
Clustering Variables .. ....... 101
16 Variable Correlations for Total Sample. ... 105
17 Mean Neuropsychological Test Scores for Male
Learning Disability Subtypes. .... . 108
18 Mean OLMAT IQ Scores and CA for Male Learning
Disability Subtypes ...... ........ 113
19 Mean Neuropsychological Test Scores for Female
Learning Disability Subtypes ....... 116
20 Mean OLMAT Scores for Female Learning
Disability Subtypes ....... . 119
21 Mean Neuropsychological Test Scores for
Combined Sex Learning Disability Subtypes 123
22 Mean OLMAT IQ Scores for Combined Sex
Learning Disability Subtypes ..... 126
v
LIST OF FIGURES
Figure Page
1 Schematic representation of cluster analysis 40
2 Male achievement subgroups based on WRAT clustering variables; mean based on local
population . . ... . 48
3 Male achievement subgroups based on GMRT and WRAT clustering variables; mean based on
local population . . . . 57
4 Female achievement subgroups based on WRAT clustering variables; mean based on local
population ...... ... ......... 67
5 Female achievement subgroups based on GMRT and WRAT clustering variables; mean based
on local population . .. .. 76
6 Combined sex achievement subgroups based on WRAT clustering variables; mean based on
local population . . . . 88
7 Combined sex achievement subgroups based on GMRT and WRAT clustering variables; mean
based on local population .... . .. 95
8 Male learning disability subtypes based on neuropsychological test clustering variables;
mean based on standardization norms .... 110
9 Female learning disability subtypes based on neuropsychological clustering variables;
mean based on standardization norms ... 117
10 Combined sex learning disability subtypes
based on neuropsychological test clustering
variables; mean based on standardization norms 124
vi
Abstract of Dissertation Presented to the Graduate
School of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of Doctor of Philosophy
LEARNING DISABILITY SUBTYPES: A CLUSTER ANALYTIC STUDY
By
Carol Sue Johnston
May, 1986
Chairman: Eileen B. Fennell Major Department: Clinical Psychology
The purpose of this study was to identify naturally
occurring subtypes of learning disabilities in a large and relatively unselected population of fifth grade boys and girls by means of a two stage cluster analysis of achievement and neuropsychological test variables.
In the first stage cluster analytic techniques were
applied to the reading, spelling, and arithmetic test scores of 150 females and 150 males, as well as the combined sex sample of 300 children, in order to establish a preliminary achievement based classification system from which a learning disabled subsample could be drawn. The data yielded 6 distinctive patterns of achievement in the male and combined sex samples and 10 achievement patterns in the female sample. None of the solutions were significantly improved by the addition of a reading comprehension measure to the clustering variables in a subsequent analysis. Two
vii
clusters were found to have at least one area of significant academic impairment, when compared with sample norms in all 3 solutions. These clusters represented a specific reading disability subgroup and a nonspecific learning disability subgroup. In addition a specific arithmetic disability subgroup was identified in the female and combined sex samples.
In the second phase of the investigation the learning disabled subgroups were combined and reclustered according to their performance of 4 measures, which were selected from a neuropsychological test battery because of their high loadings on factors of verbalconceptual and perceptualmotor abilities. A 6 cluster optimal solution emerged from the male data; the combined sex and female data yielded 4 unique clusters, the latter after one outlier cluster was excluded. When interpreted according to standardization norms, subtypes involving specific visualmotor impairment, mixed specific language and global perceptualmotor impairment, and a normal diagnostic profile were common to all three solutions.
Present results were considered to have partially replicated the findings of previous subtyping studies employing similar methodology and sample characteristics. In addition the present evaluation allowed for sex comparisons, the results of which were more notable for their similarities rather than differences. Finally, the need for further validation of the subtyping solution was discussed.
viii
CHAPTER I
INTRODUCTION
The last decade has witnessed the emergence of
considerable interest among developmental neuropsychologists in the identification of subtypes of children with learning disabilities. The search for subtypes has been prompted in large part by dyslexia research, in which there has been a gradual realization that the accumulation of a body of contradictory and inconsistent findings may have been due to the heterogeneity of the population examined (Benton 1975). The traditional assumption that reading disabilities constitute a homogeneous diagnostic entity gave rise to simplistic models which focused on explanation rather than description. Yet, as Applebee (1971) noted, these models did not adequately "fit" the problem. The literature is full of studies in which each of the unitary deficit hypotheses has, in turn, been demonstrated to be inadequate to account for the great diversity among reading disabled children. The resulting controversy has been termed inevitable by Fletcher and Satz (1985) because of the inappropriateness of "applying a research strategy based on univariate contrastinggroups methodology when the experimental group is not homogeneous and the basis for the
1
2
disability is multivariate in nature [p. 40]." Therefore, the delineation of a descriptive typology has been considered a prerequisite to further exploration of the nature and etiology of learning disabilities (Benton, 1975; Fletcher, 1985).
A second factor in the current interest in learning disability subtypes involves the lack of an adequate operational definition of the problem. Rutter (1978) distinguished between general reading backwardness and specific reading retardation, referring to achievement which is below expectation for both age and ability in the latter case, but age alone in the former. Benton (1975) observed that prevalence rates for reading failure in an elementary school population have ranged from 10 to 30% in the literature. Yet he estimated the incidence of developmental dyslexia at only 3.5%. The discrepancy in incidence rates is due to the exclusionary nature of specific developmental dyslexia, as defined by the World Federation of Neurology (Critchley, 1970). This definition, which presumes a constitutional or neurological etiology, excludes those disabled readers who may have inadequate intelligence, sociocultural opportunity, or exposure to conventional instruction. The validity of this concept as a diagnostic entity has been seriously challenged by Taylor et al. (1979), who found no significant differences between dyslexic and nondyslexic disabled readers on a number of academic, medical, familial or neuropsychological dimensions
3
which have traditionally been viewed as specific to dyslexia. Further, the literature in developmental dyslexia does not support a neurological basis for the disorder (Benton, 1975).
Although the definition of specific developmental
dyslexia has been criticized for its ambiguity and circular logic, and pronounced both unsatisfactory and unworkable (Rutter, 1978), it has nonetheless had farreaching implications for public policy as well as research directions (Eisenberg, 1978). Public Law 94142, the Education for All Handicapped Children Act (Office of Education, 1976), defines learning disabilities in a similar manner, expressly excluding children with mental retardation, emotional disturbance, or environmental, cultural or economic disadvantage from eligibility for services. Boder (1973) pointed out that such definitions ignore the possibility that learning problems may coexist and be aggravated by contributory factors. Furthermore, the 2% cap that was put on learning disabilities placements by Congress grossly underserves the population, based on previous incidence estimates of 1015% (Gaddes, 1976). Such an artificial limit encourages misinterpretation or distortion of eligibility requirements. For example, those children who were unable to obtain medical certification of a neurological basis for their learning difficulties were denied placement in the early years of the law's interpretation. In addition, secondary behavioral
4
characteristics of chronic learning failure may be misclassified as primary in nature, switching eligibility to a less populated exceptionality. Finally, overinclusive definitions of exclusionary criteria have frequently resulted in the denial of services to children with low average or borderline ability and/or less advantaged backgrounds. The common use of an achievement ratio rather than regression equation as a means of determining the extent of academic delay further restricts access to lower ability students (Rutter, 1978).
Therefore, the development of a model of learning
disability subtypes, free from a priori theoretical biases, is needed by educators and researchers alike, as well as those children who have been unfortunate enough to suffer from learning difficulties that have somehow been expected to occur. A descriptive typology will aid in the development of a definition of learning disabilities which more accurately reflects the apparently multivariate nature of the disorder. This definition will have to take into account the heterogeneity of the population with regard to the severity and pattern of academic handicap as well as cognitive deficiencies (if any) in information processing. Developmental course, sex differences, prevalence, and ability and sociocultural factors will all need to be addressed. Once a typology has been delineated, it will be very important to establish its usefulness and validity through hypothesis testing of subtype similarities and
5
differences (Fletcher, 1985). One such area of recent focus has been the attempt to differentiate the subtypes on the basis of their response to different teaching methods (Lyon, 1983, 1985). Such studies may help to develop more effective remediation strategies for learning disabled children. It has been suggested that some interventions that have been specifically designed for use with learning disabled children may actually do more harm than good if presented without regard for the diagnostic characteristics of these children (Rourke, 1978). Increasing the efficiency of learning disabilities services may allow more children to be served as well as providing important feedback to the students themselves regarding their academic competency, thus addressing current educational issues involving both the inadequacy of services and prevalence of secondary emotional and behavioral characteristics among learning disabled children. Studies of this kind will help to define the nature of the subtypes and explore their determinants and underlying mechanisms, thereby starting the transition from descriptive to explanatory relevance in the classification process.
Research on Learning Disability Subtypes
Two recent articles (Satz & Morris, 1981; Lyon, 1983) have reviewed the literature in this area. Both reviews have divided classification attempts into clinicalinferential and statisticalempirical studies, based on their methodological approach. Studies in the former group,
by definition, have been plagued by the subjectivity of their procedures. Such studies are faulted not only for a priori theoretical biases, but also for visual inspection methods which attempt to reduce complex, multidimensional data sets into oversimplified, nonoverlapping groups. Both tend to obscure the true, hidden structure of the data and often result in the designation of subgroups with surplus meanings. Samples are often small and biased by referral status, frequently being drawn from a clinic population, so that the majority of subjects may either have a severe academic impairment or, more likely, disturbances in several areas, while less problematic but nevertheless academically impaired children may be underrepresented or absent. Further selection bias often occurs in terms of arbitrary or exclusionary criteria related to the above mentioned definitions of specific developmental dyslexia. In contrast, studies employing a statistical approach to classification make no a priori assumptions regarding either number or type of subgroups in the solution. In addition, they allow the emergence of homogeneous subgroups from complex multidimensional data sets. This method involves the application of descriptive multivariate statistics, either Qtechnique factor analysis or hierarchical cluster analysis, which have the advantage of being able to accommodate much larger data sets than possible with visual inspection methods. Although the same criticisms regarding sample bias apply as above, inasmuch as most studies draw
7
their subjects from a clinic population, one research group (Darby, 1978; Satz, Morris & Darby, 1979; Satz & Morris, 1981, 1983) has used multivariate statistics to identify the learning disabled subsample from an unselected school population. In both the clinicalinferential and statisticalempirical approaches to classification, the characteristics of the resulting subtypes are necessarily determined by the types of variables which form the basis for the subtyping decisions. These classification variables have most often taken the form of achievement or neuropsychological test scores, or a combination of the two.
Several clinical inferential studies have attempted to focus upon the reading process itself as a basis for classification. Monroe (1932) analyzed the reading performance of her subjects and classified their errors into ten types. Although patterns of error types were identified, they did not differentiate among reading disabled, mentally retarded, or behaviordisordered subject groups. Ingram et al. (1970) described three types of reading errors which he used as a basis for classifying reading disabilities into audiophonic, visuospatial, or mixed subtypes. He found that the majority of his reading disabled subjects fell into the last category. Boder (1973) examined the patterns of specific reading and spelling deficits in children who fit the criteria for specific developmental dyslexia. She was able to classify 100 of 107 children into dysphonetic, dyseidetic, or mixed subtypes.
8
In contrast to the results reported above, twothirds of the children evidenced difficulties in phonetic analysis. Twentythree percent made mixed errors, and only 10% demonstrated reading errors which reflected visual processing deficits.
Other clinicalinferential studies have focused on neuropsychologicalpsychometric performance patterns in academically impaired samples. Whereas most examples of this type of investigation have limited their focus to reading disabled subjects, a few have extended classification efforts to specific impairments in arithmetic or generalized academic handicap. For example, Rourke and Finlayson (1978) divided 45 children, ages 9 to 14, into 3 groups depending on their patterns of achievement on the Wide Range Achievement Test and then compared their performance on a battery of neuropsychological tests. Findings were interpreted as indicating somewhat deficient visualperceptualorganizational skills in a specific arithmetic disability group, a pattern which was considerably different from that of two severe nonspecific learning disability groups (one of whose arithmetic mean was relatively more advanced). The two latter groups' performance was virtually indistinguishable and was interpreted as indicating poor verbal and auditoryperceptual skills. Although the sample contained both sexes, no attempt was made to interpret the results accordingly. Rourke argued that because another study in his laboratory
9
(Canning et al., 1980) had found no significant sex differences in two different age groups of retarded readers on the same battery of tests, it was unnecessary to do so. Inasmuch as only the reading criterion was listed for this study, it is not clear if the two samples were comparable, i.e., if the sex differences sample represented either a specific reading disability or a nonspecific learning disability group, or if both disabilities were included. Interestingly, in light of Rourke's assertion, it was reported that the data were reanalyzed according to male scores alone; even so, the small number of female subjects (6/45) makes it unlikely that their omission would significantly affect the results. Secondly, no attempt was made to differentiate neuropsychological subtypes within each of the learning disability groups. Although subsequent studies by the Windsor group (Petrauskas & Rourke, 1979; Fisk & Rourke, 1979) have identified subtypes of nonspecific learning disabilities and retarded readers, no attempt has been made to further investigate the possibility of specific arithmetic disability subtypes. Rather, emphasis has been given to the external validation of the pattern identified by this initial investigation (Strang & Rourke, 1985).
In contrast to the strategy of investigating one
characteristic cognitive pattern for each different pattern of academic impairment, most researchers have concentrated on identifying more than one neuropsychological subtype for one particular category of academic problem. Badian (1983)
10
classified developmental dyscalculia into 4 subtypes on the basis of her analysis of arithmetic errors made by 50 specific arithmetic disabled children. She described a spatial dyscalculia subtype, an anarithmetria subtype (involving extreme confusion regarding arithmetic processes), an attentionalsequential dyscalculia subtype, and a mixed subtype. The majority of children made attentionalsequential errors. A fifth subtype, involving alexia and agraphia for numbers, was hypothesized, but was not supported by the data. Mattis et al. (1975) classified 90% of his dyslexic subjects into monothetic categories of language disorder, articulatory and graphomotor dyscoordination syndrome, and visual perception disorder on the basis of their performance on a battery of neuropsychological tests. The first two subtypes represented almost equal numbers of subjects (39% and 37%, respectively) while the last subtype represented only 16% of the sample. These findings were replicated in a larger crossvalidation sample of younger black and Hispanic children who, in contrast to the first study, were not clinic referred. The same three subtypes emerged, although the language disorder group comprised the vast majority (63%) of the sample, while the articulatory and graphomotor dyscoordination subtype dropped to 10% and visualperceptual subtype fell to 5%. In addition, although no overlap among subtypes was noted in the initial solution, the second study found that 9% of subjects displayed mixed deficits. Denckla (1972) reported
1I
that 70% of her clinical sample either exhibited mixed deficits or could not be classified into her three subgroups of specific language disturbance, visuospatial disability, and dyscontrol syndrome, which were again determined according to neuropsychological test profiles. Cole and Kraft (1964) observed five subgroups in their clinical sample, which can be faulted for its small size: dyslexia with primary language deficit, dyslexia with primary visuospatial deficit, dyslexia with intact language and visuospatial functioning but abnormalities of synthesis, dyslexia with mixed deficits, and a heterogeneous grouping of specific learning disability without dyslexia. Smith (1970) found three WISC patterns specific to his sample of retarded readers: deficient auditory sequencing ability, deficient spatial and perceptual organization, and mixed deficits. He further compared his results according to age and found that the first and last subgroups evidenced an increasing incidence with age, while the middle subgroup showed the opposite trend. The Smith study is somewhat unique in that it utilized a normal control group, enabling the identification of subgroups idiosyncratic to the target sample; the use of control groups of normal and, in the case of selected samples, nondyslexic retarded readers has been infrequent.
Although on the surface there seem to be similarities among the findings of these studies, Satz & Morris (1981) caution that comparisons are inappropriate because of marked
12
differences in methodology and design. It is difficult to compare studies which differ in the characteristics of the subjects involved, the types of data collected, and the methods as well as criteria for determining the results. Surplus meanings inherent in subgroup labels have further confused the issue, so that the investigators themselves have linked different sets of subgroups in apparent comparison attempts. In addition there have been few replication efforts, Mattis (1978) being an exception, and no opportunity for statistical verification. Therefore the conclusions which can be drawn from this research are limited.
Statistical approaches have been applied less
frequently in this research area because of the relatively recent development of specific techniques and computer systems able to handle them. Cluster analysis, which is a generic term encompassing a variety of statistical methods, was created specifically for purposes of classification. As such it enables a basic descriptive search for naturally occurring subgroups among a given population, assigning individuals on the basis of their similarity on specified variables. Hierarchical methods group the two most similar observtions or clusters together through a series of multistage comparisons until one cluster results which contains all subjects. Morris et al. (1981) described three decisions which must be made when using hierarchical agglomerative clustering methods. The first concerns the
13
choice of one of many methods of constructing the initial data matrix. Distance measures are recommended when the elevation of the cluster profile is more important than profile shape. Correctional measures, which are relatively insensitive to elevation, may be particularly contraindicated for research in this area. The second decision involves the selection of a method for defining the similarity between subgroups during the clustering process. Such methods, which are based on different definitions of distance, include single linkage (nearest neighbor), complete linkage (furthest neighbor), average linkage, median, centroid, and minimum variance (Ward's). The single linkage method "may fail to give useful solutions because of (their) sensitivity to the presence of 'noise' points between relatively distinct clusters and the subsequent chaining effects (p. 92)" (Everitt, 1974). However, there appear to be no recognized reasons at present to either recommend or contraindicate the other methods. Everitt states that no one method is best in all circumstances and recommends that several be utilized. The third decision involves the determination of the optimal number of clusters in a data set, thus fixing the stopping point in the clustering process. This decision, which is especially vulnerable to subjective error, can be aided by the examination of clustering results via the hierarchical tree, cluster profiles, and clustering coefficients, the last an indication of the amount of variance accounted for at each
14
step in the clustering process. Finally, because a subject cannot change clusters once he is assigned, even if he is more similar to a subsequently formed subgroup than the one in which he was placed, the use of an iterative partitioning technique is recommended following the determination of optimal number of clusters in a solution. This procedure relocates misassigned subjects into more appropriate clusters and is an indiction of the stablity of the solution.
Qtechnique factor analysis is the most widely used
method of clustering subjects in psychology but differs from other cluster analytic techniques in that individuals are assigned to groups on the basis of their loadings on extracted factors which reflect the similarity in their pattern of responses. The result is a dimensional representation, rather than the categorical one derived from hierarchical methods (Morris et al., 1981). It is not equipped to handle multiple factor loadings, whereas other methods of cluster analysis allow for mixed groups. Because of its reliance on correlation coefficients, it assumes a linear model and is relatively insensitive to elevation. In addition the number of subgroups formed is limited by the number of classification variables; employing a large number of variables is not an acceptable solution because the interpretability of the resulting subgroups is made more complex. Although hierarchical cluster analysis is not limited as to the number of clusters in the solution, is
15
stronger when the assumption of linearity is violated, and can be sensitive to elevation in the data (Lyon, 1983), it has nevertheless been criticized for several areas of limitation (Satz & Morris, 1983). These include the lack of firm statistical foundation as well as critical examination, definition, and validation of clustering methods. It has been noted that different software programs contain different algorithms, producing predictably differing results.
Doehring and Hosko (1977) used a Qtechnique to analyze the results of 31 tests of readingrelated skills in a sample of reading disabled children. For 31 out of 34 subjects classification into one of three subgroups was possible. The first subgroup was characterized by good performance on all visual and several auditoryvisual matching tests but performed poorly in oral word and syllable reading. The second subgroup performed well on visual number and letter scanning, relatively poorly on oral word reading and two auditoryvisual matching tests, and very poorly on the remaining auditoryvisual letter matching tests. Subgroup three showed good visual and auditoryvisual letter matching, poor visual and auditoryvisual matching of words and syllables, and very poor oral syllable, word, and sentence reading skills. A comparison sample of combined nonreading learning disorders, language disorders, and mental retardation also revealed the first two subgroups. Attempts to compare the resulting subgroups
16
with those found by other investigators, a procedure which was previously discussed as inappropriate, was nonetheless attempted but proved unsuccessful because of the complexity of the data. However, Doehring et al. (1979) found that the three subtypes remained stable and continued to be specific to the reading disabled sample when they were compared with a group of normal readers who were matched for age and sex. Doehring et al. (1981) next classified their reading disabled subjects on an extensive battery of language and neuropsychological tests according to Qtype factor analysis. While the results indicated generally poor language development in the reading disabled sample, there was no simple correspondence between reading and nonreading deficits. Three out of five factors identified were considered interpretable, classifying 65% of the sample. The nature of the deficits remains somewhat obscure but appears to involve language repetition and/or naming.
Even more confusing are the results of Petrauskas and Rourke (1979), who classified 160 poor and normal readers, all 7 to 8 years old and clinicreferred, on the basis of 20 neuropsychological tests with the Qtechnique. Six factors emerged, four of which were replicated in a splitsample analysis, and of these one was comprised of normal readers. A description of the three unique and reliable subgroups, which classified only 50% of the subjects, follows. Subgroup one, which comprised 25% of the sample, was characterized by relative strengths in visualspatial and
17
eyehand coordination abilities; average or near average tactilekinesthetic, abstract reasoning, vocabulary, and nonverbal concept formation abilities; mild impairments in word blending, immediate memory for digits, and general information; moderate to severe impairments in verbal fluency and memory for sentences; the largest Verbal/ Performance IQ discrepancies (low VIQ) on the WISC; and lower WRAT scores in reading and spelling than arithmetic. The second subgroup, representing 16% of the sample, was average or near average in kinesthetic, psychomotor, visualspatial construction, vocabulary, nonverbal problemsolving, and abstract reasoning skills; borderline to moderately impaired in immediate memory for digits, sequencing, general information, sound blending, verbal fluency, and verbal concept formation; moderately to severely impaired in finger recognition, immediate visualspatial memory, and memory for sentences; no WISC discrepancy; and uniformly poor reading, spelling and arithmetic skills on the WRAT. Subgroup three comprised 8% of the sample, and showed average or near average finger recognition in the left hand, kinesthetic, visualspatial construction, vocabulary, nonverbal concept formation, and sound blending abilities; borderline to mild impairment in finger recognition in the right hand, immediate memory for digits, speeded eyehand coordination, general information, nonverbal abstraction, and the ability to shift sets; mild to moderate impairment in verbal fluency, memory for
sentences, and immediate visualspatial memory; moderate to severe impairment in verbal concept formation; and a high proportion of normal readers. The overwhelming complexity of these subgroups prohibit interpretation and illustrate the disadvantage of employing a large number of clustering variables. Whereas other techniques allow for consolidation of clustering variables into factors prior to the analysis, Qtechnique prohibits this option since it itself is a factor analytic technique. That onehalf of the data set was lost (i.e., could not be classified) suggests a further limitation of the Qtechnique in disallowing multiple factor loadings, although it is difficult to imagine how mixed categories could heighten the interpretability of such already confusing results.
The same group (Fisk & Rourke, 1979) conducted a
similar study with older (914 years old) children in order to determine the stability of their initial solution. However the two clinic samples were not necessarily comparable, in that the older learning disabled children were uniformly impaired on all three subtests of the Wide Range Achievement Test, whereas only the reading score was reported as a selection criterion for the younger sample. Nevertheless two of the original subtypes were reported to be replicated across three different age ranges (910, 1112, 1314). Subtype A was considered to be similar to the earlier Subtype 2, now termed a sequencing deficit group. Subtype B replicated Subtype 1, referred to as
19
having clear auditoryverbal and languagerelated problems. Subtype C, distinguished by poor fingertip numberwriting perception, was unique to the latter study. In all, 54% of the sample was classified into one of the three identified subtypes. Although both studies employed a mixed sex sample, which was nonetheless predominately male, the gender makeup of the subtypes was reported only for the earlier investigation. The sex ratio was 3:1 in Subtype 1, 12:1 in Subtype 2, and 2:1 in Subtype 3. However, although reported, the possible implications of these findings were not discussed.
Cluster analytic techniques were first applied to a reading disabled sample by Smith and Carrigan (1959). Although the clustering method was not specified, the investigators identified five subgroups in an analysis of 18 neuropsychological variables for their 30 subject sample. Two subgroups were superior on all measures and one presented an unclear pattern. Of the remaining two subgroups one was impaired in both cognitiveassociational and perceptualmetabolic abilities, while the other obtained average scores in all areas except cognitiveperceptual abilities, in which a deficit was found. External validation on physical and physiological measures showed no differences among subgroups, although there was differentiation along an anxiety dimension. Naidoo (1972) employed a singlelinkage method in her cluster analysis of dyslexic males. Because of the tendency toward chaining in
20
this method, the resulting five subgroups showed considerable within group variability and seemed to exist along a continuum. The validity of her results are additionally questioned by lack of classification for onethird of the sample and the size of the resulting clusters (27, 5, 3, 3, and 2). Generally when individuals resist incorporation into existing clusters, they are dismissed as "outliers," i.e., errors of measurement, and are excluded from further consideration; however, the chaining tendency of the method makes it especially sensitive to intermediate points, so that the small sized clusters may not be the true outliers, if any, in the sample. In any event, the inappropriateness of the clustering technique selected obscures any understanding of the data.
Lyon (1983, 1985) attempted to replicate the subtypes which were described by Mattis et al. (1975) through statistical classification methods. He administered a neuropsychological battery of 10 linguistic and visual perception tasks to 100 learning disability students, all of whom demonstrated significant deficits (approximately 3 years below grade level) in both oral reading and reading comprehension, as well as a, group of normal readers who were matched for age (1112 years) and IQ. Both standard and raw scores were submitted to hierarchical agglomerative cluster analysis which employed a Euclidean distance formula and a minimum variance (Ward's method) criterion; addition cluster analyses were performed on data subsets. The results
21
yielded 6 homogeneous subtypes which were reliable regardless of type of data input or variable subset used. A crossvalidation study (Lyon & Watson, 1981), which employed the same design, replicated the results of the previous study. A multivariate analysis of variance yielded a significant effect for subtype on clustering variables. Eightynine percent of learning disability students in the initial study and 94% of those in the followup study were placed in one of the 6 subtypes, which included a global deficit type, a mixed deficit type, a specific language deficiency type, a visualperceptualmotor deficiency type, a global language deficiency type, and a normal diagnostic profile. The visualperceptualmotor impairment subtype had the largest membership. Lyon noted that the results did not replicate the subtypes identified by Mattis et al. (1975), primarily because of the failure to detect a high rate of anomia. A second crossvalidation study (Lyon et al., 1982) attempted to replicate the subtyping results with a younger aged (69 year old) sample. Five subtypes resulted, replicating all but the global deficit subtype. Lyon criticized his own research for methodological flaws, including his failure to use several methods of cluster analysis or an iterative partitioning technique to assess the adequacy of the solution, both of which concern internal validity. Fletcher (1985), in contrast, commended the study for its reliability and internal validity but faulted its external validation on the basis of classification attributes (i.e., component reading skills).
22
The same criticism can be applied to the investigation conducted by Speece & McKinney (1984), which attempted to validate 6 subtypes of disabled readers on the basis of similar external criteria. The sample again was drawn from school learning disabilities classes and screened according to performance on a test of oral reading; additional selection criteria involved age (910 years), IQ, and maternal educational attainment. A control group of normal readers met similar selection criteria. A battery of information processing tasks was administered and cluster analyzed using a hierarchical agglomerative method (Ward's method with a correlation similarity measure). Internal validation was accomplished through split sample replication, reclustering using an average linkage algorithm, and adding additional subjects (normal readers) as well as randomly removing reading disabled subjects from the data set. The results supported the stability of a 6 cluster optimal solution which achieved 100% coverage. A MANOVA revealed a significant difference between the clusters on clustering variables. All subtypes revealed a general deficit in speed of recoding. In addition Cluster 1 was distinguished by a deficit in short term memory capacity, while Cluster 2 demonstrated a deficit in semantic encoding. Cluster 3 had poor sustained attention and Cluster 4 showed deficient phonetic and semantic encoding. Cluster 5 was distinguished from Cluster 3 by poorer sustained attention but less severe speed of recoding.
23
Cluster 6 demonstrated a deficit in memory organization. Although Cluster 2 had the largest membership, subject distribution was relatively even among the 6 subtypes. It was noted that females were overrepresented in Cluster 1, while Cluster 6 was composed exclusively of males.
Satz and associates (Darby, 1978; Satz & Morris, 1981, 1983; Fletcher & Satz, 1985) were the first to utilize cluster analytic techniques as a method of determining the target learning disabled group in a relatively large and unselected school population prior to the search for subgroups, thus avoiding the arbitrary and exclusionary selection criteria utilized in previous studies. Using a hierarchical agglomerative averagelinkage method with squared Euclidean distance, Darby identified nine naturally occurring achievement subgroups, after eliminating three outlier clusters (six subjects), on the basis of the WRAT scores of his sample of 236 fifth grade white males. A multivariate analysis of variance on the clustering variables revealed significant differences in achievement among clusters. Comparisons of IO, SES, neurological status, and neuropsychological variables also revealed significant subgroup effects, with lower achieving subgroups tending to show lower scores on all variables. The two lowest achieving subgroups contained high proportions of children with "soft" neurological signs and lower SES ratings. The mean IQ for the sample was 103; all subgroups had mean IOQ scores of at least 90.
24
Two of the subgroups were considered sufficiently depressed, i.e., mean reading, spelling, and arithmetic scores more than two years below expected levels, to be designated learning disabled and subjected to further study. One subgroup represented a specific arithmetic disability but was not included in subsequent investigations. There were no pure reading disability subgroups identified. The two learning disabled subgroups were combined into an 89 subject sample and reclustered on four neuropsychological variables representing two independent factors of language and perceptualmotor abilities. The clustering technique for this phase was a hierarchical agglomerative minimum variance method with squared Euclidean distance. Five distinct, homogeneous clusters (labeled "subtypes" to avoid confusion with achievement "subgroups") emerged, although one cluster of five subjects was ultimately eliminated because of outlier status. Subtype 1 was designated as the Unexpected Type because of its at least average scores, when compared to sample means, on all clustering variables. Subtype 2 was labeled the Specific Language (Naming) Type because of its selective impairment in verbal fluency. Subtype 3, the VisualPerceptualMotor Type, was impaired on both of this factor's measures. Subtype 4, the Mixed Type, was impaired on all clustering variables. Subtype 4 also had a significantly lower mean IQ score than the other three subtypes, all of which approximated the sample mean. There were no differences among subtypes in achievement, SES, neurological status, or personality variables.
25
Satz, Morris, and Darby (1979) reanalyzed the data from the second phase of the above study, using four different hierarchical techniques (complete linkage, average linkage, median, and minimum variance) with two different similarity coefficients (squared Euclidean distance and error sum of squares). All eight methods resulted in identification of five distinct clusters, the membership of which remained virtually identical across methods, thus providing a measure of replicability. The characteristics of the subtypes were the same as in the previous analysis, with the exception of the emergence of a fifth subtype which showed a global language impairment. Analysis of external validation variables found a significantly higher proportion of neurological "soft" signs and a trend toward lower SES status in the global language, perceptualmotor, and mixed subtypes. The specific language impairment and unexpected subtypes, by contrast, showed lower proportions of members with affected neurological ratings and a trend toward higher SES status. Data on parental achievement competencies indicated that the unexpected and specific language subtypes scored higher not only than the other subtypes, but also than the overall samples means, thus ruling out a familial association with learning failure in these groups. That reanalysis of the same data resulted in a somewhat different solution points out the subjective component in cluster analysis statistical techniques, resulting from the general lack of operationalized decision rules. Along with the
26
choice of methods, the determination of the optimal number of clusters presents a major difficulty. Although Everitt (1974) recommends that both qualitative and quantitative methods be employed in assessing the validity of the cluster solution, he admits that much work is needed to perfect the latter techniques.
Morris, Blashfield & Satz (1981) completed additional internal validation studies by means of statistical measures, data manipulation procedures, and graphical methods. Splitsample analysis, data alteration via the addition of superior achieving and specific arithmetic disability subgroups, and the inclusion of additional clustering variables all supported the results of the clustering procedures. External validation procedures also revealed the subtypes to differ on a large number of variables, including developmental course and parental achievement level. Finally, crosscultural replication (Van der Vlugt & Satz 1985) provided additional external validation for the 9 cluster achievement solution and 3 of the 5 neuropsychological subtypes, despite the fact that the Dutch sample was drawn from a more select (i.e., special school) population. Only the specific language impairment and unexpected subtypes of the Florida studies failed to find counterparts in the Dutch solution.
Satz & Morris (1980) criticized the Florida studies
along with the others in their review of learning disability subtyping research. The sample was faulted for its
27
homogeneity, in terms of age, race and gender, which limited the generalizations which could be drawn from their results. Clustering variables were criticized for their limited number (neuropsychological) and breadth (achievement). Specifically the WRAT was faulted for its restricted measure of reading which relies only on word recognition; the addition of a reading comprehension measure to the achievement battery was recommended. Use of the Peabody Picture Vocabulary Test as a measure of intellectual ability was faulted because of its verbal bias. It was felt that subtype validity could have been strengthened by additional criterion measures, including teacher observations and developmental histories. Although a more sensitive measure of personality functioning was called for, it is possible that results on the Children's Personality Questionnaire (CPQ) were confounded with the learning disabled subjects' inability to read. In addition the SES rating can be faulted for its reliance on teacher judgment. Another criticism concerned the subgroups chosen for the subtype analysis: although a specific arithmetic disability subgroup was identified, only the overall impaired (nonspecific learning disability) subgroups were further investigated. Finally the limitations of cluster analysis as a classification method were acknowledged. Despite these criticisms, however, the Florida studies represent a unique and promising approach to learning disability subtyping research.
28
Conclusions and Hypotheses
In summary, recognition of the heterogeneity of
reading/learning disabilities as a diagnostic entity and the related need to identify descriptive subgroups represents a significant advance in the conceptualization of this area. However, efforts toward delineation of subgroups have resulted in relatively little progress toward this goal. A major obstacle arises in the lack of comparability among studies which prevents integration of results so that conclusions may be drawn. Lack of consistency in the characteristics of the subjects investigated, the measures which form the basis of the comparison, and the methods which (at times inappropriately) determine the construction of the subgroups has characterized the research in this area. Little attention has been paid to sex differences or developmental course. Moreover issues of reliability, validity, and utility have rarely been addressed. What is needed is further investigation and expansion of the beginnings which have been made rather than additional isolated efforts. Therefore the present study attempts to expand upon the efforts which have been made by Satz and associates, while at the same time addressing some of the limitations of the earlier work, in order to further describe naturally occurring subtypes of learning disabilities in a schoolaged population.
Specifically, the purpose of this study is to identify naturally occurring learning disability subtypes in a large
29
and relatively unselected population of fifth grade boys and girls by means of a two stage analysis of achievement and neuropsychological test variables. In the first phase of the investigation, cluster analytic techniques are applied to the reading, spelling and arithmetic scores of 150 females and 150 males, as well as the combined sex sample of 300 children, in order to establish a preliminary achievement based classification system. The data are then reclustered following the addition of a reading comprehension measure to the clustering variables, and the solutions for the two cluster analyses for each sample compared, in order to determine the value of including a measure of comprehension as well as word recognition in the assessment of reading skills. Those subgroups which are found to be significantly impaired in one or more academic skill areas are designated as the learning disabled subsample. In the second phase of the investigation the learning disabled subgroups within each sample are combined and reclustered according to their performance on 4 neuropsychological tests representing verbalconceptual and perceptualmotor abilities. The external validity of the resulting subtyping solutions is assessed through comparisons of the clusters on measures of personality, social, and behavioral functioning. In addition the clusters in both the achievement subgrouping and neuropsychological subtyping solutions are compared according to intelligence, socioeconomic status, chronological age and, where appropriate, gender.
30
The hypotheses for this study are
I. Naturally occurring achievement subgroups will
differ according to pattern and level for
relatively unselected male and female samples.
II. The inclusion of a reading comprehension measure along with previously used measures of reading
word recognition, spelling, and arithmetic
computation will not significantly affect the
composition of the above subgroups.
III. Characteristics of the neuropsychological subtypes
of learning disabled males will be similar to
those found by Satz and associates, but will
differ from the female subtypes.
IV. Subtype characteristics will differ for overall and specific learning impaired subgroups.
V. Learning disability subtypes will differ on
personality, social, and behavioral measures.
CHAPTER It
METHOD
Subjects
Subjects for the present investigation consisted of virtually the entire fifth grade population of the PennTrafford School District in Westmoreland County, Pennsylvania. Selection criteria were avoided, with the result that only children who had previously been identified as mentally retarded were excluded. Two parents chose not to have their children participate, leaving 334 students available for study. However, because of size limitations imposed by the statistical data processing system, which was unable to handle more than a 300 subject matrix, it was necessary to eliminate 16 male and 18 female pupils from the sample. Subjects were dropped on the basis of extremes of age in order to increase the homogeneity of the sample and minimize agerelated confounding factors such as number of years of schooling. The resulting sample consisted of 150 and 150 females. The mean age of the children at the beginning of the study was 125.22 months (SD = 4.60) with a range of 118 to 139 months. There were no nonwhite pupils in the grade.
31
32
The male half of the sample is roughly equivalent to that employed in the Florida studies (Darby, 1978; Satz & Morris, 1981, 1983) in terms of age, grade, and race. Both studies have utilized a large, relatively unselected sample in order to permit a comprehensive investigation of naturally occurring subgroups of learning disabilities in an intermediatelevel school population. The homogeneity of the sample in both studies minimizes the possibility of confounding of the results by such factors as inadequate intelligence, lack of exposure to instruction, or cultural disadvantage. Although the number of subjects in the male subsample is necessarily somewhat fewer than in the Florida sample (N = 236), the inclusion of both sexes in the present investigation permits comparisons not only between the two high risk (male) samples, but also extends a comparison of those results to a low risk (female) sample.
Measures
Achievement Tests
Wide Range Achievement Test (WRAT). The WRAT (Jastak & Jastak, 1965) has been the primary measure of school achievement in the Florida Longitudinal Project. It contains measures of reading, spelling, and arithmetic. Although it has gained widespread acceptance as a reasonably accurate estimate of a child's academic skill levels (Rourke & Finlayson, 1978), it has been criticized for its reliance on word recognition as its sole measure of reading. Therefore a second measure of reading was added to the
33
achievement battery in the present study. Raw scores were converted to gradeequivalent (GE) scores for both achievement tests.
GatesMacGinitie Reading Test (GMRT). This widely used test (MacGinitie, 1978) contains measures of vocabulary and reading comprehension. It utilizes a multiple choice format and is available in several difficulty levels. Level D, intended for use with fourth through sixth grade students, was chosen for the present study; however, Level C, intended for use with third grade students, was available for administration to subjects who scored below norms on Level D. Only scores from the Comprehension subtest were used in the present investigation.
Neuropsychological Measures
The following tests were chosen from a child
neuropsychological battery developed by Satz and associates (1973, 1974, 1978). When the battery was subjected to factor analysis, three factors emerged which were found to be highly predictive of future reading achievement. The first two measures listed below loaded highly on Factor I (sensorimotorperceptual ability) and the last two measures loaded highly on Factor II (verbalconceptual ability). Factor I was found to have less predictive power than Factor II at the fifth grade level.
Developmental Test of VisualMotor Integration (VMI).
The VMI (Beery & Buktenica, 1967) consists of a series of 24 geometric line drawing designs, arranged in order of
34
increasing difficulty, which the child is required to copy. Testing is discontinued after three consecutive failures. The raw score was converted to an ageequivalent score (in months) for the cluster analysis. Standardization norms were obtained from the revised manual (Beery, 1982).
RecognitionDiscrimination Test (RD). The RD (Small,
1968) is a 24 item visual perception task which requires the child to match a geometric stimulus design to one of four test figures, three of which are rotated and/or similar in shape to the stimulus figure. The raw score was used in the cluster analysis. Norms were provided by Taylor (personal communication, 1985).
WISC Similarities (SIM). The Similiarities subtest of the Wechsler Intelligence Scale for Children (Wechsler, 1949) was scored as in the manual. In the present study, scaled scores (mean = 10; SD = 3) were used.
Verbal Fluency (VF). The VF is a modified form of the Verbal Associative Fluency Test developed by Spreen and Benton (1965). The child is asked to name as many words as possible beginning with the letters F, A, and S, allowing one minute per letter. The raw score, representing a total number of words produced across the three trials, was used for clustering. The results were interpreted according to norms published by Gaddes and Crockett (1975). External Validation Measures
OtisLennon Mental Ability Test (OLMAT). The OLMAT (Otis & Lennon, 1967) is a widely used groupadministered
35
intelligence test, which consists of verbal, pictorial, and geometric materials tapping verbal and quantitative concepts, reasoning by analogy, and vocabulary. Rasbury et al. (1979) reported a corrected correlation coefficient of .72 between the OLMAT DIQ and the Full Scale IQ on the Wechsler Intelligence ScaleRevised. The Elementary II Level of the OLMAT was administered by the district at the beginning of the school year following the one in which the present study was conducted.
Children's Personality Questionnaire (CPQ). The CPQ
(Porter & Cattell, 1972) is a 140 item, forced choice ("yes" or "no") measure of fourteen factorially independent dimensions of personality. Following the manual's suggestion for test administration with children and older poor readers, the entire test was read aloud. Testing was accomplished on a small group basis. The raw scores for each factor were converted to "sten" scores (mean = 5.5, SD = 2) for the present study.
Behavior Problem Checklist (BPC). The BPC (Quay &
Peterson, 1967) is a scale for rating 55 problem behavior traits occurring in childhood and adolescence. The results yield scores on four subscales which have been derived from factor analytic studies. The factor scores represent the number of items checked by the rater, which, in the present study, was the child's classroom teacher. Two items, involving enuresis and masturbation, were removed from the checklist at district request.
36
LJ Sociometric Test (LJST). This technique (Long
et al., 1962) provides an index of group status for a child based on his classmates' interpersonal preferences. It is accomplished by asking children to list, in descending order, the three pupils in their classroom whom they like the most and the three pupils that they like the least. A weighted score for the most preferred and least preferred variables is derived from both the number of choices and the rank of those choices for each child.
TwoFactor Index of Social Position (ISP). This technique (Hollingshead, 1957) provides an estimate of socioeconomic status (SES) based on the occupation and educational attainment of the head of the household, which was presumed to be the father except when none was listed on the child's permanent record card. Use of the more recent FourFactor Index of Social Status (Hollingshead, 1975), which utilizes data from both parents, was prevented by school records which list the educational attainment of both the mother and father, but the occupation of only one parent. The ISP SES score, which ranges from 11 to 77, is inversely proportional to social class position.
Procedure
In the first phase of the study, the total sample of 300 children, as well as male and female subsamples, was sorted into subgroups according to achievement test scores. In order to accomplish this objective, the WRAT and GMRT were administered to all subjects. The tests were group
37
administered, with the exception of the WRAT Reading subtest, by the author and two district guidance counselors. The LJST and WRAT Reading were administered during individual testing sessions. Because district personnel preferred not to administer a technique which required them to ask students to identify classmates which they most liked and disliked, sociometric data were collected by the author for only four out of thirteen classrooms. External validation data, including birthdate, parents' occupation and education, and group IQ scores, were obtained from each child's permanent record card. A socioeconomic status rating (ISP) was not able to be computed for three female subjects because of incomplete or missing data. OLMAT IQ scores were unavailable for eight males and twentyone females. However, there were no missing data for any of the achievement variables.
In the second phase of the study children in learning impaired subgroups, as determined by the Phase I analysis, were sorted into learning disability subtypes on the basis of their performance on neuropyschological tests. Although it was originally intended that subgroups identified as having relatively lower mean achievement scores in any or all areas be included in the second phase of the study, the multiplicity of combinations possible from such a criterion resulted in the identification of over half of the sample. Hence practical considerations, involving public relations with the school district as well as the author's
38
availability for data collection, necessitated a decision limiting further investigation to specific subgroups. In the end, neuropsychological test data were collected on 117 out of the original 300 subjects. (Even so, missing data due to children's school absence or withdrawal or scheduling problems do occur in the identified subgroups.) The four neuropsychological measures, the VMI, RD, SIM, and VF, and the personality measure, the CPQ, were administered to the 117 identified subjects by the author. In addition the primary classroom teacher for each of the 117 pupils was asked to complete the BPC. Completed checklists were returned by ten out of thirteen teachers; however, in an apparent effort to insure confidentiality, one teacher removed both the student's name and subject identification number from each checklist. Usable BPC data were obtained for 50 subjects, representing nine out of thirteen classrooms. There were no missing data for neuropsychological or personality measures among the 117 identified subjects.
Statistical Analyses
The classification schemes for both phases of the
present study were generated by means of cluster analysis, defined as a procedure that groups individuals into homogeneous clusters based on their performance on clustering variables. All clustering procedures used were contained in the CLUSTAN 2C Program (Wishart, 1982). Three hierarchical agglomerative techniques were initially
39
employed, including average linkage, complete linkage, and minimum variance (Ward's). With each of these methods, squared Euclidian distance similarity coefficients were used to construct the initial data matrix. Results generated by the three different methods were compared and those produced by the Ward's method were found to be the most easily interpretable. Therefore the Ward's method with squared Euclidian distance was subsequently used for all Phase I and II cluster analyses.
A schematic representation of the cluster analysis is presented in Figure 1. In the first phase of the analysis cluster analytic techniques were applied to WRAT Reading, Spelling, and Arithmetic data, which were in the form of grade equivalent (GE) scores, for the total sample of 300 children as well as the two subsamples of males and females. A determination of the optimum number of clusters present in each data set was made by inspecting the dendrogram, plotting the clustering coefficients, and examining the profiles of individual clusters in order to evaluate the meaningfulness of different solutions. The composition of the clusters within the chosen solution were then subjected to a Kmeans iterative partitioning clustering method in order to clarify and maximize the solution. Solutions which resulted in a large number of subject reassignments, arbitrarily defined as more than 15% of the sample, were rejected as inadequately representating the actual structure of the data. Alternate solutions were then subjected to the
40
Sample N's (I) Clustering Variables (I)
a. Males = 150 _. a. WRAT b. Female = 150 B. WRAT & GMRT c. Combined Sex = 300
Subsample N's (II) Clustering Variables (II)
a. Males = 51 Neuropsychological Tests b. Females = 44 (SIM, VF, VMI, & RD) c. Combined Sex = 112
Cluster Analysis
1. Hierarchical Agglomerative Technique (Ward's minimum variance method with squared Euclidean distance).
2. Determination of Optimum Number of Clusters
3. Iterative Partitioning Technique
I i
Interpretation of Interpretation of Results (II) Results (I) Identification of
1. Identification of Neuropsychological Learning Disabled Subtypes
End of nalysis 2. Comparison of Results from WRATonly and WRAT & GMRT Cluster Analyses
End of Analysis
Figure 1. Schematic Representation of Cluster Analysis.
41
relocation procedure until one was found which appeared to more closely approximate the data structure.
The clusters in the optimum solution following
relocation comprised the achievement subgroups for the Phase I analysis. The subgroups were subjected to a multivariate analysis of variance (MANOVA) using the achievement test scores as the dependent variables. When significant effects were found, individual variables were subjected to univariate analyses (ANOVA). External validation data (chronological age, OLMAT IQ score, ISP socioeconomic status rating) were subjected to univariate analyses as well. Individual means were compared using post hoc Duncan's MultiRange Tests (Winer, 1971). All multivariate and univariate analyses were conducted using the General Linear Models (GLM) procedure of the Statistical Analysis Systems (SAS) program (Barr et al., 1976).
Phase I statistical procedures, outlined above, were repeated for the male, female, and combined sex samples using the Comprehension subtest of the GMRT in addition to the three WRAT subtests as clustering variables. The resulting subgroups were compared with those based on the WRAT alone in order to determine if the inclusion of a reading comprehension variable produced a substantially different solution. Unique subgroups which were also impaired on academic measures were identified for further investigation along with the impaired subgroups of the WRATonly clusterings.
42
In the second phase of the analysis those subgroups
whose mean achievement scores were substantially lower than the others were reanalyzed using the four neuropsychological measures (VMI, VF, SIM, and RD) as clustering variables. Because of the small sample size, if several clusters in a solution were impaired in one or more academic areas, they were combined for the Phase II analysis. The procedure was basically the same as that employed in Phase I. Identified subjects in the total sample, as well as male and female subsamples, were subjected to cluster analytic techniques (Ward's method with squared Euclidian distance) based on their performance on four neuropsychological tests. The clustering variables were in the form of an ageequivalent
(AE) score for the VMI, a standard score for the SIM, and raw scores for the VF and RD tests. Following each cluster analysis, the individual solutions were subjected to a Kmeans iterative partitioning method.
The resulting clusters comprised the learning
disability subtypes for the phase II analysis. A separate MANOVA search for differences between subtypes was made on the basis of achievement as well as neuropsychological test scores. Individual analyses of variance followed by post hoc tests (Duncan's MultiRange Tests) were applied as in Phase I. Additional univariate analyses were conducted on CA, OLMAT IQ and ISP SES ratings. Finally, personality and behavioral data were subjected to multivariate analyses. The fourteen factor scores for the CPQ and the four factor
43
scores for the BPC, and the two weighted scores for the LJST, comprised the dependent variables in two separate analyses.
All procedures were run at the Northeast Regional Data Center, University of Florida, Gainesville.
CHAPTER III
RESULTS
Phase I: Cluster Analysis of Achievement Variables Male Sample Analyses
WRAT cluster analysis. A six cluster solution emerged from the cluster analysis of WRAT reading, spelling, and arithmetic scores. The optimum number of clusters was clearly indicated by the dendrogram and clustering coefficients, which showed a sharp increase in withincluster scatter for every successive fusion following the six cluster solution. In addition only 11 out of 150 (71/3%) subjects changed clusters as a result of the relocation procedure. Therefore the six cluster solution was judged near optimal for this study.
Examination of the individual clusters in the resulting solution revealed a distinctive pattern of achievement in which reading and spelling scores appeared to be arranged in a scalar fashion, while arithmetic scores were more variable. The number of children in each subgroup ranged from 5 to 42. Although the five member cluster is somewhat smaller than the others, it is not sufficiently small to be dismissed as an outlier. Therefore the analysis classified 100% of the children in the sample.
44
45
A multivariate analysis of variance (MANOVA) on WRAT Reading, Spelling, and Arithmetic scores yielded a significant main effect for subgroup (HotellingLawley Trace = 8.93, F approximation 15,422 = 83.72, L <.0001). Individual analyses of variance disclosed significant effects for subgroup on WRAT Reading (F5,144 = 98.31, p <.0001), WRAT Spelling (F5144 = 116.78, p <.0001), and WRAT Arithmetic (F5,144 = 86.87, 2 <.0001).
Mean WRAT subtest scores, converted into discrepancy scores by comparing the grade equivalent score with grade level at the time of testing, for each subgroup are listed in Table 1. Mean achievement scores across subgroups were significantly different from each other in all but one instance for arithmetic and two instances for reading and spelling. Subgroups 1 and 2 obtained virtually identical, superior scores, ranging from 31/2 to 4 years above grade level, in reading and spelling. However their arithmetic scores were significiantly different. Subgroup 1 demonstrated skills in arithmetic which were nearly 11/2 years above grade level, while Subgroup 2 showed slightly below grade level skills in the same area. Subgroups 3 and
4 also obtained high scores in reading and spelling, but not to the degree shown by Subgroups 1 and 2. While their mean spelling scores did not differ significantly at 1/2 to 1 year above grade level, reading scores over 1 and 2 years above grade level were significantly different. Subgroup 3's arithmetic score was close to grade level, but Subgroup
46
TABLE 1
Mean Grade Equivalent Discrepancy Scores for Male Achievement Subgroups Based on WRAT Clustering Variables. Subgroup WRAT WRAT WRAT Number N Reading* Spelling* Arithmetic*
1 5 3.86A 3.92A 1.42A 2 16 4.11A 3.61A 0.32C 3 35 2.26B 1.04B 0.23B 4 42 1.30C 0.63B 0.87D 5 33 0.46D 0.57C 0.54C 6 19 0.94D 1.74D 1.69E TOTAL 150 1.24 0.59 0.51
*Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05).
47
4's score was nearly 1 year below. The pattern of achievement shown by Subgroup 4, that of adequate to relatively high reading and spelling skills but depressed arithmetic skills, may constitute a specific arithmetic disability subgroup. Subgroup 5 evidenced mildly depressed scores, approximately 1/2 year below grade level, in all areas tested, and may represent a mild nonspecific learning disability subgroup. It is interesting that Subgroup 2, which had superior reading and spelling skills, did not differ significantly from Subgroup 5 in arithmetic. Subgroup 5 did not significantly differ from Subgroup 6 in reading. This last subgroup obtained severely low scores, nearly 1 to 2 years below grade level, in all areas, constituting a severe nonspecific learning disability subgroup.
Standard score transformation analysis. The total sample means for the three variables did not closely approximate the WRAT standardization norms (Jastek & Jastek, 1965). The mean reading score was over 1 year and spelling over 1/2 year above the standardization mean. Arithmetic fell 1/2 year below the standardization norm. Because of these differences, it was considered useful to compare the subgroups with each other. Therefore the WRAT profiles were plotted as zscores based on the means and standard deviations for the sample as a whole (Figure 2). The results yielded profiles which were distinctive for both pattern and elevation. Subgroup 1 was significantly high in
48
+1 SD
6
4
4
0
1 SD
Reading Spelling Arithmetic Figure 2. Male achievement subgroups based on WRAT
clustering variables; mean based on local
population.
49
all three areas. Subgroup 2, which also had significantly high reading and spelling scores, had average level arithmetic skills. Subgroup 3 was a high average group whose arithmetic score fell just short of significance. Subgroup 4 was the most nearly average of all, despite it being tentatively labelled as an arithmetic disability group; compared with the rest of the sample, its depressed arithmetic discrepancy score was well within the average range. Subgroup 5 had adequate arithmetic skills but below average reading and spelling scores. Although it was tentatively labelled a mild nonspecific learning disability subgroup, when compared with the sample, it appears to represent a specific reading disability group. Subgroup 6 was significantly impaired in all three areas; the tentative identification of this subgroup as a severe nonspecific learning disability group appears appropriate.
Children in Subgroups 5 and 6 showed evidence of impaired learning in one or more academic skill areas compared with their classmates as well as with national norms. No other subgroup met this double criterion. Both subgroups experienced considerable difficulty in reading, the mean scores for which are not significantly different. When compared with standardization norms, their achievement pattern is relatively flat, while the pattern for Subgroups
1 through 4 is that of reading scores which are at least equal to spelling scores and relatively depressed arithmetic scores. For the most part the elevation of the scores seems
50
to differentiate Subgroups 5 and 6, as well as 1 through 4. These sample profile characteristics hold true for Subgroups 2, 4, and 6 when plotted on the normalized (sample) scale. However, when compared with the sample as a whole, Subgroups 1, 3, and 5 show an opposite pattern of Subgroups 2 and 4, that of arithmetic skills which are relatively superior to reading and spelling scores. When elevation is considered along with pattern, only Subgroups 5 and 6, representing approximately onethird of the sample, are sufficiently depressed to be classified as learning disabled subsample.
OLMAT IQ analysis. An analysis of variance yielded a
significant effect for subgroup on OLMAT IQ (F5,136 = 25.71,
2 <.0001). Mean IQ scores are listed by subgroup in Table
2.
Post hoc comparison of IQ means (Duncan's procedure, 2 <.05) showed a strong ordering effect for the subgroups corresponding with overall achievement level. In only two instances were subgroup means not significantly different from each other. Not surprisingly, Subgroup 1 obtained an IQ mean which was significantly higher than the other subgroups. Subgroups 5 and 6 obtained the lowest IQ means with significant differences between the two scores being in the expected direction. Notably, no subgroup obtained a mean IQ less than 90 and the total sample mean (107.84) fell within the average range according to OLMAT standardization norms.
51
TABLE 2
Mean OLMAT IQ Scores, CA, and ISP SES Ratings for Male Achievement Subgroups Based on WRAT Clustering Variables. Subgroup
Number N** OLMAT IO* CA* ISP SES*
1 5 128.20A 123.60A 26.40A 2 16 113.31BC 124.75AB 44.75BC
3 35 115.41B 125.37AB 37.74B
4 42 108.53C 124.24A 44.93BC 5 33 101.31D 128.00BC 46.58BC
6 19 92.29E 130.53C 50.95C TOTAL 150 107.84 126.16 43.74
*Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05).
** Because of missing data, IQ scores are based on 142 subjects. The correct N for Subgroup 3 is 34, for Subgroup
4 is 38, for Subgroup 5 is 32, and for Subgroup 6 is 17.
52
Demographic variables analyses. Individual ANOVAs yielded significant effects for subgroup on CA (F5,144
6.89, 2 <.0001) and ISP SES (F5,144 = 3.65, 2 <.004). The mean scores for these variables are also listed by subgroup in Table 2. Chronological age also showed an ordered tendency, according to post hoc comparisons of subgroup means. The higher achieving subgroups were generally younger than those at the lower end of the achievement spectrum. Children in Subgroup 6 were significantly older than children in all other subgroups except Subgroup 5.
SES means did not differ significantly among subgroups for the most part. Subgroup 1 obtained an SES mean which was significantly lower corresponding to an upper middle class ISP rating, than the remaining subgroups. The mean SES score for the sample corresponds to the lower end of the middle class range of social position.
Combined WRAT and GMRT cluster analysis. Increasing the number of clustering variables to four by adding the GMRT Comprehension score to the WRAT subtest scores resulted in a seven cluster solution. The optimum number of clusters was less obvious than in the cluster analysis of WRAT variables alone, and several solutions were subjected to the iterative partitioning procedure in order to determine the one which most closely reflected the data structure. The seven cluster solution produced the fewest number of relocations (21/150 = 14%), which nevertheless is almost twice the number obtained from the optimal solution based on
53
the WRAT alone. However, inasmuch as no better solution could be found, the seven cluster solution was accepted as optimal for the cluster analysis of the GMRT and WRAT.
Inspection of the individual clusters in the resulting solution revealed an expectedly more complex array of achievement patterns than that that resulted from the cluster analysis of WRAT variables alone. The number of children in each cluster ranged from 10 to 33, so that the analysis again classified 100% of the sample.
A multivariate analysis of variance (MANOVA) on the four achievement variables yielded an overall significant effect for subgroup (HotellingLawley Trace = 11.02, F approximation 24,554 = 63.58, 2 <.0001). Individual analyses of variance showed significant effects for subgroup on GMRT Comprehension (F5,144 = 69.76, 2 <.0001), WRAT Reading (F5,144 = 82.53, p <.0001), WRAT Spelling (F5,144 79.24, p <.0001), and WRAT Arithmetic (F5,144 = 58.96, p <.0001).
Mean GMRT and WRAT discrepancy scores for each subgroup are listed in Table 3. Tests of significance for differences between means revealed that in only one case for reading and two cases for comprehension, were pairs of means not significantly different from each other. For spelling and arithmetic scores, three pairs of means did not significantly differ.
Examination of cluster profiles reveals considerable
similarity between the solutions based on the three and four
54
TABLE 3
Mean Grade Equivalent Discrepancy Scores for Male Achievement Subgroups Based on WRAT and GMRT Clustering Variables.
GMRT
Subgroup Compre WRAT WRAT WRAT Number N hension* Reading* Spelling* Arithmetic*
1 13 5.04A 4.38A 3.213 0.70A 2 21 3.57A 1.78C 0.92C 0.29B 3 10 0.91C 3.60B 3.80A 0.55C 4 33 0.89C 1.98C 0.87C 0.34C 5 26 0.12D 0.87D 0.38D 1.13D 6 32 1.17E 0.50E 0.62D 0.60C 7 15 1.89E 1.09F 1.94E 1.75E TOTAL 150 0.73 1.24 0.59 0.51
*Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05).
55
achievement variables. In both solutions there are two subgroups which have superior scores in reading and spelling, but differ according to level of arithmetic achievement. In the present clustering it is clear that the differences also extend to comprehension skills. Thus Subgroup 1 obtains scores which are more than 5 years above grade level in comprehension, 4 years above grade level in word recognition, 3 years above grade level in spelling, and 1/2 year above grade level in arithmetic. Subgroup 3 had word recognition and spelling skills more than 31/2 years above grade level, but its comprehension score was less than
1 year above grade level and its arithmetic score fell 1/2 year below. Subgroups 2 and 4 did not differ significantly in terms of reading and spelling scores, which were close to
2 and 1 years above grade level, respectively, and their arithmetic scores were both close to grade level, although one was slightly above and the other slightly below. However, again a considerable difference appeared in terms of comprehension skills: Subgroup 2 scored 31/2 years above grade level, while Subgroup 4 was not significantly different from Subgroup 3 at 1 year above the standardization mean.
At the lower end of the achievement spectrum, Subgroup 5, 6, and 7 profiles appear quite similar to those for Subgroups 4, 5, and 6 in the WRATonly clustering. Subgroup
5 showed a pattern of reading and spelling skills which was nearly 1/2 to 1 year above grade level, but arithmetic was
56
more than 1 year below; comprehension was close to the standardization mean. Subgroup 6 was approximately 1/2 year below grade level on all three WRAT subtests, but more than
1 year below on comprehension. Subgroup 7 fell between 1 and 2 years below grade level in all areas.
Standard score tranformation analysis. Because of the differences between the sample and standardization means, which also extended to the comprehension score, the discrepancy scores for the GMRT and WRAT were again converted to a normalized scale having a population mean of zero and a standard deviation of one (Figure 3). The results show relatively flat profiles for Subgroups 1, 4, and 7, who are distinguished by virtue of elevation into significantly high, average, and significantly low achievement subgroups. Subgroups 2 and 3 exhibit profiles which appear to be the mirror image of each other, in that their comprehension and arithmetic scores, as well as reading and spelling scores, seem highly related. However all skills are average to significantly above average. Subgroup 5 fell somewhat below average in all areas, although its arithmetic score was slightly more depressed. However the discrepancy between the arithmetic and other achievement scores does not appear sufficient to warrant a specific arithmetic disability diagnosis. Subgroup 6 showed adequate arithmetic skills, but below average comprehension, reading and spelling scores. Because its comprehension score did not significantly differ from that of Subgroup 7,
  1 SD
57
1 elation.
 +1 SD
Comprehension Reading Spelling Arithmetic Figure 3. Male achievement subgroups based on WRAT and
GMRT clustering variables; mean based on local
population.
which appears to be a severe nonspecific learning disability group, and because its reading score falls just short of significance, Subgroup 6 may be considered a specific reading disability subgroup.
OLMAT IQ0 analysis. An analysis of variance on OLMAT IQ was significant (F6,135 = 29.09, 2 <.0001). Mean IQ scores are listed by subgroup in Table 4.
Post hoc comparisons of IQ means (Duncan's procedure, p <.05) again showed a strong ordering effect for subgroup corresponding with overall achievement level. In only three instances were pairs of means not significantly different from each other. Subgroups 1 and 2 obtained mean IO scores which were significantly higher than the rest. The lowest IQ scores were shown by Subgroups 6 and 7, which were significantly different from each other in the expected direction. Once again, no subgroups obtained a mean IQ less than 90.
Demographic variables analyses. Individual analyses of variance yielded significant effects for subgroup on CA (F6,143 = 5.27, p <.0001) and ISP SES (F6,143 = 3.14, 2 <.0064). The mean scores for these variables are listed by subgroup in Table 4.
The lower achieving subgroups were distinguished from the higher achieving subgroups on the basis of age as well as IQ. Children in Subgroups 6 and 7 were significantly older than their classmates in Subgroups 1 through 5. An ordering effect was also found for SES, in which adjacent
59
TABLE 4
Mean OLMAT IQ Scores, CA, and ISP SES Ratings for Male Achievement Subgroups Based on WRAT and GMRT Clustering Variables.
Subgroup OLMAT ISP Number N** IQ* CA* SES*
1 13 123.85A 125.31A 31.31A 2 21 119.30A 124.62A 38.33AB 3 10 109.50B 124.50A 49.90C 4 33 109.59B 124.18A 46.64BC 5 26 105.67B 125.46A 42.58BC 6 32 99.47C 129.00B 44.78BC 7 15 91.92D 129.67B 51.40C TOTAL 150 107.84 126.16 43.74
*Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05).
**Because of missing data, IQ scores are based on 142 subjects. The correct N's for Subgroup 2 is 20, for Subgroup 4 is 32, for Subgroup 5 is 24, for Subgroup 6 is 30, and for Subgroup 7 is 13.
60
means were generally not significantly different from each other.
Comparison of achievement cluster analysis.
Examination of subject membership in the learning impaired subgroups revealed little difference between the results of the analysis based on WRAT and GMRT scores and the one based on WRAT alone. All 15 subjects in WRATGMRT Subgroup 7 were members of WRAT Subgroup 6. Twentynine out of 32 children in WRATGMRT Subgroup 6 were members of WRAT Subgroup 5, and 23 out of 26 children in WRATGMRT Subgroup 5 were members of WRAT Subgroup 4. Of the remaining 6 subjects, 4 were members of WRAT Subgroup 6 and 2 were members of WRAT Subgroup 4. Therefore the addition of a reading comprehension score did not result in the identification of a single child not already identified as academically impaired, according to either local or standardization norms, by the cluster analysis of WRAT subtest scores alone.
Correlation analysis. Correlation between the
achievement variables were significantly high not only among WRAT subtests but also between the WRAT and GMRT (Table 5). In fact, the GMRT was almost equally positively correlated with each of the WRAT subtests. Therefore the inclusion of a reading comprehension measure appears to have provided redundant information in the classification of the male sample. Similarly high positive correlations were found between the achievement measures and OLMAT IQ. Socioeconomic status and chronological age were found to be
61
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62
negatively correlated with achievement and IQ in the sample as a whole. Interestingly, the negative correlation involving SES which was most highly significant was with arithmetic rather than reading. Negative correlations involving CA were relatively equal across achievement and IO measures.
Summary. Cluster analysis of WRAT variables resulted in the identification of six achievement subgroups which were significantly differentiated from each other on the basis of IQ, CA, and SES as well as achievement. Cluster analysis of combined WRAT and GMRT variables produced a seven cluster solution; significant effects were again found for subgroup on achievement, IQ, and demographic variables. Both analyses revealed a nonspecific learning disability subgroup and a specific reading disability subgroup, as well as one which showed a nonsignificant tendency toward a specific disability in arithmetic. Examination of subject membership in the learning impaired subgroups revealed little difference between the results of the analysis based on WRAT and GMRT clustering variables and that based on WRAT variables alone.
Female Sample Analyses
WRAT cluster analysis. A ten cluster solution emerged from the cluster analysis of WRAT Reading, Spelling, and Arithmetic scores. Although several smaller solutions were suggested by the dendrogram and clustering coefficients, subjecting those solutions to iterative partitioning
63
resulted in 20 to 30 percent subject reassignment. The ten cluster solution produced the fewest number of relocations (19/150 = 12.67%), and was accepted as optimal. The number of subjects in each subgroup ranged from 4 to 30, classifying 100% of the children in the sample.
A multivariate analysis of variance (MANOVA) on WRAT Reading, Spelling, and Arithmetic scores yielded a significant main effect for subgroups (HotellingLawley Trace = 15.65, F approximation 27,410 = 79.22, 2 <.0000). Individual analyses of variance produced significant effects for subgroups on WRAT Reading (F9,140 = 75.05, 2 <.0001), WRAT Spelling (F9,140 = 96.65, p <.0001), and WRAT Arithmetic (F9,140 = 65.36, p <.0001)
Mean WRAT discrepancy scores are listed by subgroups in Table 6. Post hoc pairwise comparisons of means reveal that individual subgroups are less unique than in the male solutions. The number of instances in which pairs of means were not significantly different rose to 7 for reading and spelling, and 9 for arithmetic. Subgroup 2 was significantly different from other subgroups in reading and spelling, which were 6 and 21/2 years above grade level, respectively. However its arithmetic score, more than 1/2 year below grade level, was not significantly different from 3 other clusters. Subgroups 1, 3, and 6 scored 3 to 4 years above grade level in reading. Subgroups 1 and 3 had virtually identical arithmetic scores which were close to grade level, while Subgroup 6 scored more than 1/2 year
64
TABLE 6
Mean Grade Equivalent Discrepancy Scores for Female Achievement Subgroups Based on WRAT Clustering Variables. Subgroup WRAT WRAT WRAT Number N Reading* Spelling* Arithmetic*
1 9 3.59B 4.51A 0.16AB 2 4 6.00A 2.43B 0.65D 3 9 3.62B 1.49C 0.09B 4 16 1.78C 0.92D 0.36A 5 12 1.56CD 1.88C 0.54D 6 12 3.34B 0.81D 0.74D 7 30 0.99D 0.50D 0.30C 8 19 1.23CD 0.48D 1.14E 9 25 0.18E 0.16E 0.67D 10 14 0.41E 0.89F 1.22E TOTAL 150 1.46 0.79 0.50
*Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05).
65
below grade level in arithmetic. However all 3 subgroups differed significantly in terms of spelling skills, which ranged from less than 1 year above grade level for Subgroup
6 to more than 4 years above grade level for Subgroup 1. Subgroups 4, 5, 7, and 8 had relatively high reading and spelling scores at 1 to 2 years and 1/2 to 2 years above grade level, respectively. However, while Subgroup 4 scored somewhat above grade level in arithmetic, Subgroups 5 and 7 scored somewhat below grade level in the same area. Subgroup 8 obtained an arithmetic mean more than 1 year below grade level. The achievement pattern shown by Subgroup 8, that of adequate to relatively high reading and spelling skills but depressed arithmetic skills, may constitute a specific arithmetic disability subgroup. Subgroup 9 scored close to grade level in reading and spelling, but was not significantly different from Subgroups 2, 5, and 6 in arithmetic, which was more than 1/2 year below grade level. Subgroup 10 was nearly 1/2 to 1 year below grade level in reading and spelling, and more than 1 year below grade level in arithmetic, constituting a nonspecific learning disability group. Subgroup 10 did not differ significantly from Subgroup 9 in reading, or Subgroup
8 in arithmetic.
Standard score transformation analysis. As was found with the male sample, the total sample means for the three variables differed from the WRAT standardization norms (Jastek & Jastek, 1965) for the female sample as well. The
66
mean reading score was 11/2 years and spelling over 1/2 year above the standardization mean. Arithmetic fell 1/2 year below the standardization norm. In order to compare the subgroups with each other, the discrepancy scores were converted to a normalized scale (Figure 4). The results show several patterns of achievement which are differentiated according to elevation. The profiles for Subgroups 1 and 5 show a pattern of advanced spelling skills relative to their reading and arithmetic means, which are fairly even. The two profiles are distinguished by their elevation in that Subgroup 1 has superior skills in all areas, while Subgroup 5's scores all fall within the average range. Subgroup 3 shows the opposite pattern, that of spelling skills which are somewhat depressed relative to even performance in reading and arithmetic. Although the spelling score falls within the average range, reading and arithmetic means are significantly above average. Subgroups
2 and 6 show a pattern of achievement in which reading is advanced relative to spelling, which in turn is advanced relative to arithmetic. Although the average level arithmetic scores of the two subgroups are not significantly different, the elevation of the profiles in reading and spelling distinguish one from the other in that Subgroup 2 is superior to Subgroup 6. Even so, the latter's reading score is significantly above average. The opposite pattern, that of increasing levels of skill competency from reading and spelling to arithmetic, is shown by Subgroup 9. The
67
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Reading Spelling Arithmetic Figure 4. Female achievement subgroups based on WRAT
clustering variables; mean based on local
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68
elevation of the profile, involving average arithmetic, below average spelling, and significantly low reading scores, reveals Subgroup 9 to represent a specific reading disability subgroups.
Subgroups 4 and 7 show a pattern of achievement in which reading and spelling scores are consistent, but arithmetic scores are relatively advanced. Again, the elevation of the profiles distinguish the two subgroups in that Subgroup 4 is superior to Subgroup 7 in all areas (although the difference between their spelling means is not significant). Even so, the two subgroups have average level academic skills with one exception: Subgroup 4's arithmetic score is significantly high. The opposite achievement pattern is show by Subgroup 8, in which arithmetic skills are depressed relative to flat reading and spelling performance. The elevation of the profile, in which reading and spelling scores are average but arithmetic significantly low, reveals Subgroup 8 to represent a specific arithmetic disability subgroups. Subgroup 10, exhibiting a relatively flat profile which is significantly below average in all areas, appears to represent a nonspecific learning disability subgroup.
Children in Subgroups 8 and 10 showed evidence of impaired learning in one or more academic skill areas compared with local as well as standardization norms. In addition children in Subgroup 9, while not severely below grade level, were nevertheless significantly delayed in
69
reading skill acquisition when compared with their classmates. The combination of these three subgroups, representing a specific reading disability subgroup, a specific arithmetic disability subgroup, and a nonspecific learning disability subgroup, may be said to constitute the learning disabled subsample. The number of children in the learning disabled subsample, representing over onethird of the females, is roughly equivalent to the number of children in the male LD subsample based on the cluster analysis of WRAT variables. However the male LD subsample contained only the specific reading disability and nonspecific learning disability subgroups. Therefore the proportion of females in those two subgroups is smaller than in the male sample.
OLMAT IQ analysis. An analysis of variance yielded a significant effect for subgroup on OLMAT IQ (F9,119 = 6.92, 2 <.0001). The mean scores for IQ are listed by subgroup in Table 7. Post hoc comparisons of IQ means (Duncan's procedure, 2 <.05) showed a strong ordering effect in which adjacent means were not significantly different. Not surprisingly, the highest achieving subgroups had the highest IQ scores, while the lowest achieving subgroups had the lowest IQ's. In fact, the IQ means for the three subgroups identified as the learning disabled subsample were both lower than the IQ means for the remaining seven subgroups and not significantly different from each other.
70
TABLE 7
Mean OLMAT IQ Scores for Female Achievement Subgroups Based on WRAT Clustering Variables. Subgroup OLMAT Number N IQ*
1 4 119.25A 2 9 118.11A 3 7 114.71AB 4 7 111.71ABC 5 13 115.15AB 6 11 111.82ABC 7 27 109.11BCD
8 17 103.65DE
9 23 104.91CDE 10 11 101.27E TOTAL 129 109.20
*Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05).
71
Again, no subgroup obtained an IQ mean falling below the average range.
Demographic variables analyses. Individual analyses of variance failed to produce a significant effect for subgroup on either CA (F9,140 = .44, 9 <.9121) or ISP SES (F9,137 1.56, p <.1347). The mean CA for the female sample as a whole was 124.27 months. The mean ISP SES rating was 44.56, corresponding to the upper end of the lower middle class range.
Combined WRAT and GMRT cluster analysis. Reclustering the female sample on the basis of GMRT as well as WRAT clustering variables resulted in an eight cluster solution. Twenty subjects (131/3%) were reassigned as a result of the relocation procedure, which is consistent with the number obtained from the optimal solution based on the WRAT alone. The number of subjects in each subgroup ranged from 7 to 30. In the absence of outlier clusters, the solution classified 100% of the female sample.
A multivariate analysis of variance on the achievement variables disclosed a significant main effect for subgroup (HotellingLawley Trace = 9.93, F approximation 28,550 48.77, p <.0001). Individual ANOVAs yielded significant effects for subgroup on GMRT Comprehension (F7,142 = 47.83, p <.0001), WRAT Reading (F7,142 = 71.06, 2 <.0001), WRAT Spelling (F7,142 = 45.00, p <.0001), and WRAT Arithmetic (F7,142 = 42.90, 2 <.0001).
72
Mean WRAT grade equivalent discrepancy scores are listed by subgroup in Table 8. Tests of significance between pairs of means reveal a more unique solution than that that resulted from the cluster analysis of female WRAT scores alone, but one that is considerably less unique than either male solution. Although pairs of comprehension means were significantly different in all but three instances, the number rose to five for reading and arithmetic. Seven pairs of spelling means did not significantly differ.
Comparison of the solutions based on three and four achievement variables yields more similarities than differences. In both solutions there is one subgroup which had superior reading and spelling skills, 31/2 to 41/2 years above grade level, while arithmetic fell close to the standardization mean. Competence extended to comprehension skills as well, which fell 4 years above grade level. Subgroup 3 did not differ significantly from Subgroup 1 in terms of reading, but its comprehension mean was only 2 years above grade level. Spelling was more than 1 year above grade level, while arithmetic fell over 1/2 year below. Subgroup 2 obtained high scores in reading and spelling, which were more than 2 years above grade level, but its comprehension and arithmetic scores fell close to the norm. Low comprehension relative to reading and spelling scores was also found in Subgroups 5 and 6. Their reading and spelling means did not differ significantly at more than 1 and more than 1/2 year above grade level,
73
TABLE 8
Mean Grade Equivalent Discrepancy Scores for Female Achievement Subgroups Based on WRAT and GMRT Clustering Variables.
GMRT
Subgroup Compre WRAT WRAT WRAT Number N hension* Reading* Spelling* Arithmetic*
1 7 4.14A 4.53A 4.49A 0.10A 2 14 0.43DE 2.72B 2.11B 0.21A 3 10 2.25C 4.58A 1.30C 0.66C 4 20 3.32B 1.76C 1.07CD 0.03A 5 23 0.25E 1.85C 0.89CD 0.90D 6 20 1.00F 1.31C 0.57D 0.22B 7 30 1.00D 0.11D 0.04E 0.60C 8 26 1.10F 0.15D 0.28E 1.11D TOTAL 150 0.76 1.46 0.79 0.50
*Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05).
74
respectively. However Subgroups 5's comprehension score was close to grade level, while Subgroup 6 fell 1 year below. Arithmetic skills were close to grade level for Subgroup 6 but nearly 1 year below grade level for Subgroup 5. In contrast to the above pattern, Subgroups 4 and 7 obtained high scores in comprehension relative to reading and spelling as well as arithmetic. Subgroup 4 obtained mean scores which were more than 3 years above grade level in comprehension, 1 to 2 years above grade level in reading and spelling, and close to the norm in arithmetic. Subgroup 7 was 1 year above grade level in comprehension, close to grade level in reading and spelling, and over 1/2 year below grade level in arithmetic.
The lowest achieving cluster, Subgroup 8, was
nevertheless close to grade level in reading and spelling, on which it did not differ significantly from Subgroup 7. However its comprehension mean, which did not differ significantly from that of Subgroup 6, was more than 1 year below grade level. Subgroup 8's arithmetic mean also fell more than 1 year below grade level and did not differ significantly from the arithmetic mean for Subgroup 5. Subgroup 8 might therefore represent a learning disability subgroup with specific delays in reading comprehension and arithmetic. Subgroup 5 might tentatively be labelled a specific arithmetic disability subgroup. Subgroup 6, while apparently representing a specific reading disability subgroup, does not appear delayed in all aspects of reading.
75
In view of its strong word recognition skills, Subgroup 6 might be labelled a specific reading comprehension disability subgroup.
Standard score transformation analysis. The GMRT and
WRAT discrepancy scores were converted to a normalized scale because of the differences between the sample and standardization means, which extended to the comprehension score as well (Figure 5). The only flat profile was obtained by Subgroup 8, the elevation of which reveals it to be a nonspecific learning disabilities subgroup. Subgroup 1, which showed a pattern of advanced spelling and depressed arithmetic relative to consistent reading and comprehension scores, was the only subgroups with significantly high scores in all areas. Subgroup 3 showed a pattern of advanced reading and depressed arithmetic relative to flat comprehension and spelling scores; only the reading score was significantly high. The elevation of the profiles distinguished Subgroups 4 and 7, which were advanced in comprehension and, to a lesser extent, arithmetic relative to their reading and spelling scores. Subgroup 4 had superior skills in the two advanced areas, while Subgroup 7's scores in the same areas were average. Subgroup 7's scores in reading and spelling, while not significantly low, were far below the average level scores for Subgroup 4. A contrasting pattern, that of depressed arithmetic and, to a lesser degree, comprehension scores relative to flat reading and spelling scores, was obtained by Subgroup 5. All scores
76
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/
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1
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Comprehension Reading Spelling Arithmetic Figure 5. Female achievement subgroups based on WRAT
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77
fell within the average range, even though the arithmetic mean score was not significantly different from that of the uniformly depressed Subgroup 8. Subgroups 2 and 6 showed a depressed comprehension and advanced arithmetic skills relative to their reading and spelling skills. The elevation of the profiles showed Subgroup 2's skills in spelling and arithmetic to be significantly high, but Subgroup 6's comprehension score to fall just short of significance in the opposite direction.
Subgroups 6 and 8 showed evidence of impaired learning in one or more academic areas when compared with their classmates as well as standardization norms. Subgroup 6 was delayed only in comprehension, while Subgroup 8 was delayed in both comprehension and arithmetic. When compared with the rest of the sample, Subgroup 8 was delayed in reading and spelling as well. The arithmetic mean for Subgroup 5 did not differ significantly from that of Subgroup 8, even though it did not fall significantly below average when compared with the sample, or more than 1 year below grade level when compared with standardization norms. Similarly, Subgroup 7 did not differ significantly from Subgroup 8 in terms of reading and spelling means even though the former's scores were not significantly low compared with the sample and actually fell above the standardization norms. The number of children identified as learning disabled represents approximately onethird of the sample when limited to Subgroups 6 and 8. However, when Subgroups 5 and
78
7 are included, the number rises from 46 to 99, representing nearly twothirds of the female sample.
OLMAT IQ analysis. An analysis of variance yielded a significant effect for subgroup on OLMAT IQ (F7,119 = 12.62, p <.0001). The mean IQ scores are listed by subgroup in Table 9. Tests of significance between pairs of means (Duncan's Procedure, p <.05) again revealed a strong ordering effect corresponding with the overall achievement level of the subgroups. The highest achieving cluster, Subgroup 1, had an IQ score which was significantly higher, while the lowest achieving cluster, Subgroup 8, had an IQ score which was significantly lower than the rest. No subgroups obtained an IQ mean lower than 90.
Demographic variables analyses. As was found with the solution based on the WRAT clustering variables alone, individual ANOVA's again failed to produce a significant effect for subgroup on either CA (F7,142 = 1.17, 2 <.3250), or ISP SES (F7,139 = .86, p <.5371).
Comparison of achievement cluster analyses. Comparison of subject membership in the learning disabled subsamples reveals considerable overlap between the cluster analyses based on three and four achievement variables. However, because the nature of the subgroups differed somewhat in the two clusterings, the onetoone correspondence between subgroup memberships that characterized the male results is not found with the females. For example, although all 26 subjects in WRATGMRT Subgroup 8 were already identified in
79
TABLE 9
Mean OLMAT IQ Scores for Female Achievement Subgroups Based on WRAT and GMRT Clustering Variables. Subgroup OLMAT Number N** IQ*
1 7 121.29A 2 14 113.31CD 3 10 116.13AB 4 20 115.00BC 5 23 107.83DE
6 20 109.41CDE
7 30 106.79E 8 26 99.52F TOTAL 150 109.20
*Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05).
**Because of missing data, IQ scores are based on 129 subjects. The correct N for Subgroup 2 is 13, for Subgroup
3 is 8, for Subgroup 4 is 17, for Subgroup 5 is 18, for Subgroup 6 is 17, for Subgroup 7 is 28, and for Subgroup 8 is 21.
80
the WRATonly learning disability subsample, 11 came from WRAT Subgroup 10, 9 came from WRAT Subgroup 9, and 6 came from WRAT Subgroup 8. Twelve out of 23 subjects in WRATGMRT Subgroup 5, whose arithmetic mean was not significantly low, came from WRAT Subgroup 8, which was significantly delayed in arithmetic skill acquisition. Similarly 15 out of 30 subjects in WRATGMRT Subgroup 7, whose reading score fell short of significance, came from the significantly reading disabled WRAT Subgroup 9; an additional four subjects, 3 in WRAT Subgroup 10 and 1 in WRAT Subgroup 8, made a total of 19 out of 30 children in WRATGMRT Subgroup 7 that were already identified by the WRATonly clustering. Interestingly a majority of children (15/20) in WRATGMRT Subgroup 6 were common to WRAT Subgroup 7, which was not identified as learning disabled as a result of the WRATonly analysis. Therefore the reading comprehension measure appears to have added valuable information to the female analysis in that a new group of children was identified that showed evidence of significant learning impairment. At the same time, however, two learning disabled subgroups identified by the WRATonly clustering (the specific reading and arithmetic subgroups) were obscurred by the cluster analysis on the GMRT and WRAT variables. Although their counterparts appear (WRATGMRT Subgroups 5 and 7), they are not significantly below average in their specific area of impairment. Even so, the means for those same areas are not significantly different from those in the lowest achieving
81
subgroups. Inclusion of Subgroups 5, 6, 7, and 8 in the LD subsample, representing a specific arithmetic disability subgroup, two kinds of reading disability subgroups, and a nonspecific learning disability subgroup, results in the identification of nearly twothirds of the female sample. Therefore, while providing valuable information about those children not previously identified, the addition of a reading comprehension measure to the WRAT clustering variables actually resulted in the overidentification of learning disabilities among female subjects.
Correlation analysis. Correlations between the achievement variables, while highly significant, were considerably lower in the female sample than in the male sample, a finding which is consistent with the increased emergence of specific learning disability subgroups. In addition the increased complexity of the underlying data structure was evident in the cluster analyses, which resulted in optimal solutions with larger number of clusters. IQ continued to be highly correlated with achievement, but again at a lower level. In contrast to the results of the male sample analysis, demographic variables, with only one exception, were not significantly correlated with achievement. However, IQ continued to be significantly correlated with chronological age in a negative direction.
Summary. Cluster analysis of WRAT subtests resulted in the identification of 10 achievement subgroups, which were significantly differentiated from each other on the basis of
82
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achievement and IQ, but not age or socioeconomic status. Inspection of clusters which showed evidence of significant academic impairment revealed specific reading and arithmetic disability subgroups, as well as a nonspecific learning disability subgroup. Cluster analysis of combined WRAT and GMRT variables produced an 8 cluster solution; significant effects were again found for subgroup on achievement and IQ, but not demographic variables. The same 3 learning disability subgroups were identified; however the results, for the most part, fell short of significance. In addition a subgroup with a specific disability in reading comprehension emerged. Although the combination of the 4 subgroups identified by the combined clustering resulted in the overidentification of learning disabilities in the female sample, all subjects in the nonspecific subgroup, and between onehalf and twothirds of those in the specific reading and arithmetic disability subgroups, were included in the WRATonly learning disability subsample. The specific comprehension disability subgroup proved unique, in that none of its members were represented in any of the 3 subgroups which were identified as significantly impaired in the analysis of WRAT variables alone. Combined Sex Sample Analyses
Comparison of male and female samples. The male and female samples were combined for the cluster analysis of achievement in the total sample. A multivariate analysis of variance on WRAT Reading, Spelling, and Arithmetic, and GMRT
84
Comprehension, failed to yield a significant effect for sex (HotellingLawley Trace = .01, F approximation 4,295 = .52, p <.7247). Individual analyses of variance were insignificant as well for IQ (F1,269 = 1.09, p <.2965), and SES (F1,295 = .21, 2 <.6483). The only area in which the male and female samples differed significantly was chronological age, with the males being older than the females (F1,298 = 13.10, p <.0003).
WRAT cluster analysis. When clustered on the basis of the WRAT variables, a six cluster solution emerged from the combined sex data. Thirtyseven subjects (121/3%) changed their cluster membership as a result of the relocation procedure. Although the six cluster solution was the one most clearly indicated from the dendrogram and clustering coefficients, a larger solution was also attempted. However, when the alternative solution was subjected to iterative partitioning, an even greater number of subjects was reassigned. Therefore the six cluster solution was accepted as optimal for the data. The number of subjects in each cluster ranged from 29 to 94. In the absence of outliers, the six cluster solution classified 100% of the total sample.
A MANOVA on WRAT Reading, Spelling, and Arithmetic scores yielded a significant overall effect for subgroup (HotellingLawley Trace = 8.14, F approximation 15,872 = 157.71, L <.0001). Individual univariate analyses produced significant effects for subgroup on WRAT Reading (F5,294
85
154.78, 2 <.0001), WRAT Spelling (F5,294 = 215.71, L <.0001), and WRAT Arithmetic (F5,294 = 120.57, 2 <.0001).
Mean WRAT discrepancy scores are listed by subgroup in Table 11. Mean scores were significantly different in all instances for spelling, and all but one instance for reading and spelling (Duncan's MultiRange Test, p <.05). These comparisons confirm the appropriateness of the solution and reveal the uniqueness of the individual clusters.
Subgroup 1 had superior skills in reading and spelling, both of which were approximately 4 years above grade level. However, its arithmetic score fell close to the standardization norm. Subgroup 2 also had high scores in reading and spelling, which fell close to 3 and 11/2 years above grade level, respectively; the arithmetic mean was 1/2 year above grade level. The largest cluster, Subgroup 3, had the same pattern of decreasing scores; reading was close to 2 years and spelling was close to 1 year above grade level, while arithmetic was close to 1/2 year below grade level. Subgroup 4 showed the same pattern at a lower level: reading close to 1 year and spelling close to 1/2 year above grade level, and arithmetic more than 1 year below. Subgroup 5 was approximately 1/2 year below the standardization norm in all three areas. Subgroup 6, the lowest achieving subgroup, was more than 1/2 year delayed in reading, and more than 11/2 years below grade level in spelling and arithmetic.
86
TABLE 11
Mean Grade Equivalent Discrepancy Scores for Combined Sex Achievement Subgroups Based on WRAT Clustering Variables. Subgroup WRAT WRAT WRAT Number N Reading* Spelling* Arithmetic*
1 30 4.23A 3.92A 0.60B 2 36 2.90B 1.428 .49A 3 94 1.78C .91C .37C 4 51 .95C .39D 1.10D 5 60 .35E .39E .51C 6 29 .72E 1.52F 1.55E TOTAL 300 1.35 .69 .50
*Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05).
87
Standard score transformation analysis. The total
sample means for the three variables differed considerably from the standardization means. Therefore the WRAT profiles were plotted as zscores based on the means and standard deviations for the sample as a whole (Figure 6). The results yielded three pairs of patterns, the members of which were distinguished by elevation. Subgroups 1 and 4 had arithmetic scores which were depressed relative to their reading and spelling scores. However, Subgroup l's reading and spelling scores were significantly high, while the same scores for Subgroup 4 fell just short of being significantly low. The pattern of adequate reading and spelling skills, but depressed arithmetic skills, may represent a specific arithmetic disability subgroup. Subgroups 2 and 5 showed a pattern of arithmetic skills which were advanced relative to reading and spelling scores. Subgroup 2 was significantly above average in arithmetic and nearly so in reading. However, although Subgroup 5 had average arithmetic skills, its reading mean was significantly below average. Subgroup 5, with its average arithmetic, below average spelling, and significantly low reading scores constitutes a specific reading disability subgroup. The achievement profiles of Subgroups 3 and 6 were relatively flat. Subgroup 3 obtained average scores, but Subgroup 6's scores were significantly low. Therefore Subgroup 6's profile is consistent with a nonspecific learning disability subgroup.
 + SD
6
b
338
*  1 SD
Reading Spelling Arithmetic
Figure 6. Combined sex achievement subgroups based on
WRAT clustering variables; mean based on
local population.
89
OLMAT IO analysis. An analysis of variance on OLMAT IQ was significant for subgroup (F5,265 = 40.35, p <.0001). The mean IQ scores are listed by subgroup in Table 12.
Post hoc comparisons of IQ means (Duncan's procedure, S(<.05) showed a strong ordering effect for the subgroups corresponding with overall achievement level. In only two instances were means not significantly different from each other. Subgroups 1 and 2 obtained IQ scores which were significantly higher than the remaining subgroups. The IQ mean for Subgroup 6, the nonspecific learning disability subgroup, was significantly lower than the rest, but was nonetheless above 90. The IQ means for the two specific LD subgroups, clusters 4 and 5, did not differ significantly from each other. The sample mean (108.49) falls within the average range, according to OLMAT standardization norms.
Demographic variables analysis. Individual ANOVA's produced significant effects for subgroup on CA (F5,294
4.22, p <.0011) and ISP SES (F5,291 = 2.95, p <.0130). However there were no significant sex differences (X2
9.354, p <.0958). The mean scores for CA and SES are listed by subgroup in Table 12.
Chronological age (CA) was found to be strongly ordered with adjacent means not significantly different from each other. SES means were not significantly different, with the exception of Subgroup 2, whose middle class rating was significantly higher than the rest. The mean SES rating for
90
TABLE 12
Mean OLMAT IQ Scores, CA, and ISP SES Ratings for Combined Sex Achievement Subgroups Based on WRAT Clustering Variables.
Subgroup OLMAT ISP Number N** IQ* CA* SES*
1 30 117.53A 123.83A 43.767B 2 36 118.50A 124.19A 36.629A 3 94 110.96B 124.69AB 44.075B 4 51 104.82C 124.73AB 44.300B 5 60 103.46C 126.53BC 45.383B 6 29 93.75D 127.76C 51.034B TOTAL 300 108.49 125.22 44.15
*Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05).
**Because of missing data, IQ scores are based on 271 subjects and SES ratings on 197 subjects. The correct N for Subgroup 1 is 32 (IQ) and 35 (SES), for Subgroup 3 is 84
(IQ) and 93 (SES), for Subgroup 4 is 45 (IQ) and 50 (SES), for Subgroup 5 is 56 (IQ) and for Subgroup 6 is 24 (IQ).
91
the sample corresponds to the upper end of the lower middle class range of social position.
Combined WRAT and GMRT cluster analysis. Increasing
the number of clustering variables to four by including GMRT Comprehension along with the WRAT subtests resulted in a dramatic increase in the complexity of the underlying data structure. The optimum number of clusters was not clearly indicated by the dendrogram and clustering coefficients. Therefore several solutions were subjected to iterative partitioning, but none resulted in a subject reassignment of less than 15% of the sample. The 13 cluster solution, the largest of those attempted, resulted in the fewest number of relocations (58/300 = 191/3%) and, in the absence of a better fitting solution, was accepted as optimal. The number of children in each cluster ranged from 7 to 42. Therefore the 13 cluster solution classified 100% of the combined sex sample.
A multivariate analysis of variance on GMRT and WRAT subtest scores yielded a significant main effect for subgroup (HotellingLawley Trace = 14.74, F approximation
= 86.73, 2 <.0001). Individual ANOVA's disclosed 48,1130
significant effects for subgroup on GMRT Comprehension (F12,287 = 93.93, 2 <.0001), WRAT Reading (F12,287 = 115.91,
2 <.0001), WRAT Spelling (F12,287 = 91.92, p <.0001), and WRAT Arithmetic (F12,287 = 78.97, 2 <.0001).
Mean discrepancy scores for the four achievement
variables are listed by subgroup in Table 13. Tests of
92
TABLE 13
Mean Grade Equivalent Discrepancy Scores for Combined Sex Achievement Subgroups Based on WRAT and GMRT Clustering Variables.
GMRT
Subgroup Compre WRAT WRAT WRAT Number N hension* Reading* Spelling* Arithmetic*
1 7 4.41B 4.00B 4.11A 1.24A 2 15 3.44C 5.08A 3.46B .25D 3 11 6.22A 3.24C 1.33C .27C 4 21 2.21D 2.23D 1.13CD .55B 5 10 .46E 2.60D 4.37A .34DE 6 19 .52E 3.57BC 1.01CD .33DE 7 42 2.55D 1.39E .78D .38DE 8 31 .75G 1.27E .76D .22D 9 32 .52E .21G .13E .51E 10 36 .99EF 1.65E .90CD .97F 11 27 .26FG .37F .40E 1.37G 12 36 1.65H .49G .59E .75F 13 13 2.19H 1.42H 2.08F 1.75H TOTAL 300 .75 1.35 .69 .50
*Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05).

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LEARNING DISABILTY SUBTYPES: A CLUSTER ANALYTIC STUDY By CAROL SUE JOHNSTON DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1986
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ACKNOWLEDGEME^]TS I would like to thank Paul Satz for providing the inspiration that got me started on this project, and Robin Morris tor helping me to begin to make sense of what I had found. Special thanks are also due to Eileen Fennell for her support and encouragement that kept me going, as well as to the rest of my committee for their patience. I am indebted to the PennTraf f ord School District for their cooperation, without which this research would not have been possible. In particular, I am grateful to Carl Bruno, Superintendent, and Alice Giglio, Director of Pupil Personnel Services, for their support and facilitation of the project. Closer to home, I would like to thank my husband and daughter for their tolerance of a parttime wife and mother during the long struggle toward completion. Finally I would like to acknowledge my appreciation of Hope McGee, whose excellent child care, in the truest sense, allowed me to focus my attention on my work. ii
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TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ii LIST OF TABLES iv LIST OF FIGURES vi ABSTRACT ''^ii CHAPTERS I INTRODUCTION 1Research on Learning Disability Subtypes 5 Conclusions and Hypotheses 28 II METHOD 31 Subjects 31 Measures 32 Procedure 36 III RESULTS 44 Phase I: Cluster Analysis of Achievement Variables 44 Phase II: Cluster Analysis of Neuropsychological Variables 106 IV DISCUSSION 128 Discussion of Hypotheses 128 Conclusions and Directions for Future Research 163 BIBLIOGRAPHY 168 BIOGRAPHICAL SKETCH 176 ill
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LIST OF TABLES Table Page 1 Mean Grade Equivalent Discrepancy Scores for Male Achievement Subgroups Based on WRAT Clustering Variables 46 2 OLMAT 10 Scores, CA, and ISP SES Ratings for Male Achievement Subgroups Based on WRAT Clustering Variables 51 3 Mean Grade Equivalent Discrepancy Scores for Male Achievement Subgroups Based on WRAT and GMRT Clustering Variables 54 4 Mean OLMAT IQ Scores, CA, and ISP SES Ratings for Male Achievement Subgroups for Male Achievement Subgroups Based on WRAT and GMRT Clustering Variables 59 5 Variable Correlations for Male Sample 61 6 Mean Grade Equivalent Discrepancy Scores for Female Achievement Subgroups based on WRAT Clustering Variables 64 7 Mean OLMAT IQ Scores for Female Achievement Subgroups Based on WRAT Clustering Variables. 70 8 Mean Grade Equivalent Discrepancy Scores for Female Achievement Subgroups Based on WRAT and GMRT Clustering Variables 73 9 Mean OLMAT IQ Scores for Female Achievement Subgroups Based on WRAT and GMRT Clustering Variables 79 10 Variable Correlations for Female Sample .... 82 11 Mean Grade Equivalent Discrepancy Scores for Combined Sex Achievement Subgroups Based on WRAT Clustering Variables 12 Mean OLMAT IQ Scores, CA, and ISP SES Ratings for Combined Sex Achievement Subgroups Based on WRAT Clustering Variables 90 iv
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Table Page 13 Mean Grade Equivalent Discrepancy Scores for Combined Sex Achievement Subgroups Based on WRAT and GMRT Clustering Variables 92 14 Mean OLMAT IQ Scores, CA, and ISP SES Ratings for Combined Sex Achievement Groups Based on WRAT and GMRT Clustering Variables 99 15 Gender Distribution for Combined Sex Achievement Subgroups Based on WRAT and GMRT Clustering Variables 101 16 Variable Correlations for Total Sample 105 17 Mean Neuropsychological Test Scores for Male Learning Disability Subtypes 108 18 Mean OLMAT IQ Scores and CA for Male Learning Disability Subtypes 113 19 Mean Neuropsychological Test Scores for Female Learning Disability Subtypes 116 20 Mean OLMAT Scores for Female Learning Disability Subtypes 119 21 Mean Neuropsychological Test Scores for Combined Sex Learning Disability Subtypes 123 22 Mean OLMAT IQ Scores for Combined Sex Learning Disability Subtypes 126 V
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LIST OF FIGURES Figure Page 1 Schematic representation of cluster analysis 40 2 Male achievement subgroups based on WRAT clustering variables; mean based on local population 48 3 Male achievement subgroups based on GMRT and WRAT clustering variables; mean based on local population 57 4 Female achievement subgroups based on WRAT clustering variables; mean based on local population 67 5 Female achievement subgroups based on GMRT and WRAT clustering variables; mean based on local population 76 6 Combined sex achievement subgroups based on WRAT clustering variables; mean based on local population 88 7 Combined sex achievement subgroups based on GMRT and WRAT clustering variables; mean based on local population 95 8 Male learning disability subtypes based on neuropsychological test clustering variables; mean based on standardization norms 110 9 Female learning disability subtypes based on neuropsychological clustering variables; mean based on standardization norms 117 10 Combined sex learning disability subtypes based on neuropsychological test clustering variables; mean based on standardization norms 124 vi
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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy LEARNING DISABILITY SUBTYPES: A CLUSTER ANALYTIC STUDY By Carol Sue Johnston May, 1986 Chairman: Eileen B. Fennell Major Department: Clinical Psychology The purpose of this study was to identify naturally occurring subtypes of learning disabilities in a large and relatively unselected population of fifth grade boys and girls by means of a two stage cluster analysis of achievement and neuropsychological test variables. In the first stage cluster analytic techniques were applied to the reading, spelling, and arithmetic test scores of 150 females and 150 males, as well as the combined sex sample of 300 children, in order to establish a preliminary achievement based classification system from which a learning disabled subsample could be drawn. The data yielded 6 distinctive patterns of achievement in the male and combined sex samples and 10 achievement patterns in the female sample. None of the solutions were significantly improved by the addition of a reading comprehension measure to the clustering variables in a subsequent analysis. Two vii
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clusters were found to have at least one area of significant academic impairment, when compared with sample norms in all 3 solutions. These clusters represented a specific reading disability subgroup and a nonspecific learning disability subgroup. In addition a specific arithmetic disability subgroup was identified in the female and combined sex samples In the second phase of the investigation the learning disabled subgroups were combined and reclustered according to their performance of 4 measures, which were selected from a neuropsychological test battery because of their high loadings on factors of verbalconceptual and perceptualmotor abilities. A 6 cluster optimal solution emerged from the male data; the combined sex and female data yielded 4 unique clusters, the latter after one outlier cluster was excluded. When interpreted according to standardization norms, subtypes involving specific visualmotor impairment, mixed specific language and global perceptualmotor impairment, and a normal diagnostic profile were cotmnon to all three solutions. Present results were considered to have partially replicated the findings of previous subtyping studies employing similar methodology and sample characteristics. In addition the present evaluation allowed for sex comparisons, the results of which were more notable for their similarities rather than differences. Finally, the need for further validation of the subtyping solution was discussed vi i i
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CHAPTER I INTRODUCTION The last decade has witnessed the emergence oE considerable interest among developmental neuropsychologists in the identification of subtypes of children with learning disabilities. The search for subtypes has been prompted in large part by dyslexia research, in which there has been a gradual realization that the accumulation of a body of contradictory and inconsistent findings may have been due to the heterogeneity of the population examined (Benton 1975). The traditional assumption that reading disabilities constitute a homogeneous diagnostic entity gave rise to simplistic models which focused on explanation rather than description. Yet, as Applebee (1971) noted, these models did not adeguately "fit" the problem. The literature is full of studies in which each of the unitary deficit hypotheses has, in turn, been demonstrated to be inadeguate to account for the great diversity among reading disabled children. The resulting controversy has been termed inevitable by Fletcher and Satz (1985) because of the inappropr lateness of "applying a research strategy based on univariate contrastinggroups methodology when the experimental group is not homogeneous and the basis for the .1 1 I
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2 disability is multivariate in nature [p. 40]." Therefore, the delineation of a descriptive typology has been considered a prerequisite to further exploration of the nature and etiology of learning disabilities (Benton, 1975; Fletcher, 1985) A second factor in the current interest in learning disability subtypes involves the lack of an adequate operational definition of the problem. Rutter (1978) distinguished between general reading backwardness and specific reading retardation, referring to achievement which is below expectation for both age and ability in the latter case, but age alone in the former. Benton (1975) observed that prevalence rates for reading failure in an elementary school population have ranged from 10 to 30% in the literature. Yet he estimated the incidence of developmental dyslexia at only 3.5%. The discrepancy in incidence rates is due to the exclusionary nature of specific developmental dyslexia, as defined by the World Federation of Neurology (Critchley, 1970). This definition, which presumes a constitutional or neurological etiology, excludes those disabled readers who may have inadequate intelligence, sociocultural opportunity, or exposure to conventional instruction. The validity of this concept as a diagnostic entity has been seriously challenged by Taylor et al. (1979), who found no significant differences between dyslexic and nondyslexic disabled readers on a number of academic, medical, familial or neuropsychological dimensions
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3 which have traditionally been viewed as specific to dyslexia. Further, the literature in developmental dyslexia does not support a neurological basis for the disorder (Benton, 1975) Although the definition of specific developmental dyslexia has been criticized for its ambiguity and circular logic, and pronounced both unsatisfactory and unworkable (Rutter, 1978), it has nonetheless had farreaching implications for public policy as well as research directions (Eisenberg, 1978). Public Law 94142, the Education for All Handicapped Children Act (Office of Education, 1976), defines learning disabilities in a similar manner, expressly excluding children with mental retardation, emotional disturbance, or environmental, cultural or economic disadvantage from eligibility for services. Boder (1973) pointed out that such definitions ignore the possibility that learning problems may coexist and be aggravated by contributory factors. Furthermore, the 2% cap that was put on learning disabilities placements by Congress grossly underserves the population, based on previous incidence estimates of 1015% (Gaddes, 1976). Such an artificial limit encourages misinterpretation or distortion of eligibility requirements. For example, those children who were unable to obtain medical certification of a neurological basis for their learning difficulties were denied placement in the early years of the law's interpretation. In addition, secondary behavioral
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characteristics of chronic learning failure may be misclassif ied as primary in nature, switching eligibility to a less populated exceptionality. Finally, overinclusive definitions of exclusionary criteria have frequently resulted in the denial of services to children with low average or borderline ability and/or less advantaged backgrounds. The common use of an achievement ratio rather than regression equation as a means of determining the extent of academic delay further restricts access to lower ability students (Rutter, 1978). Therefore, the development of a model of learning disability subtypes, free from a priori theoretical biases, is needed by educators and researchers alike, as well as those children who have been unfortunate enough to suffer from learning difficulties that have somehow been expected to occur. A descriptive typology will aid in the development of a definition of learning disabilities which more accurately reflects the apparently multivariate nature of the disorder. This definition will have to take into account the heterogeneity of the population with regard to the severity and pattern of academic handicap as well as cognitive deficiencies (if any) in information processing. Developmental course, sex differences, prevalence, and ability and sociocultural factors will all need to be addressed. Once a typology has been delineated, it will be very important to establish its usefulness and validity through hypothesis testing of subtype similarities and
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5 differences (Fletcher, 1985). One such area of recent focus has been the attempt to differentiate the subtypes on the basis of their response to different teaching methods (Lyon, 1983, 1985). Such studies may help to develop more effective remediation strategies for learning disabled children. It has been suggested that some interventions that have been specifically designed for use with learning disabled children may actually do more harm than good if presented without regard for the diagnostic characteristics of these children (Rourke, 1978). Increasing the efficiency of learning disabilities services may allow more children to be served as well as providing important feedback to the students themselves regarding their academic competency, thus addressing current educational issues involving both the inadequacy of services and prevalence of secondary emotional and behavioral characteristics among learning disabled children. Studies of this kind will help to define the nature of the subtypes and explore their determinants and underlying mechanisms, thereby starting the transition from descriptive to explanatory relevance in the classification process. Research on Learning Disability Subtypes Two recent articles (Satz & Morris, 1981; Lyon, 1983) have reviewed the literature in this area. Both reviews have divided classification attempts into clinicalinferential and statisticalempirical studies, based on their methodological approach. Studies in the former group.
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o by definition, have been plagued by the subjectivity of their procedures. Such studies are faulted not only for a priori theoretical biases, but also for visual inspection methods which attempt to reduce complex, multidimensional data sets into oversimplified, nonoverlapping groups. Both tend to obscure the true, hidden structure of the data and often result in the designation of subgroups with surplus meanings. Samples are often small and biased by referral status, frequently being drawn from a clinic population, so that the majority of subjects may either have a severe academic impairment or, more likely, disturbances in several areas, while less problematic but nevertheless academically impaired children may be underrepresented or absent. Further selection bias often occurs in terms of arbitrary or exclusionary criteria related to the above mentioned definitions of specific developmental dyslexia. In contrast, studies employing a statistical approach to classification make no a priori assumptions regarding either number or type of subgroups in the solution. In addition, they allow the emergence of homogeneous subgroups from complex multidimensional data sets. This method involves the application of descriptive multivariate statistics, either Qtechnique factor analysis or hierarchical cluster analysis, which have the advantage of being able to accommodate much larger data sets than possible with visual inspection methods. Although the same criticisms regarding sample bias apply as above, inasmuch as most studies draw
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7 their subjects frorn a clinic population, one research group (Darby, 1978; Satz, Morris & Darby, 1979; Satz & Morris, 1981, 1983) has used multivariate statistics to identify the learning disabled subsample from an unselected school population. In both the clinicalinferential and statisticalempirical approaches to classification, the characteristics of the resulting subtypes are necessarily determined by the types of variables which form the basis for the subtyping decisions. These classification variables have most often taken the form of achievement or neuropsychological test scores, or a combination of the two. Several clinical inferential studies have attempted to focus upon the reading process itself as a basis for classification. Monroe (1932) analyzed the reading performance of her subjects and classified their errors into ten types. Although patterns of error types were identified, they did not differentiate among reading disabled, mentally retarded, or behaviordisordered subject groups. Ingram et al. (1970) described three types of reading errors which he used as a basis for classifying reading disabilities into audiophonic, visuospatial or mixed subtypes. He found that the majority of his reading disabled subjects fell into the last category. Boder (1973) examined the patterns of specific reading and spelling deficits in children who fit the criteria for specific developmental dyslexia. She was able to classify 100 of 107 children into dysphonetic, dyseidetic, or mixed subtypes.
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8 In contrast to the results reported above, twothirds of the children evidenced difficulties in phonetic analysis. Twentythree percent made mixed errors, and only 10% demonstrated reading errors which reflected visual processing deficits. Other clinicalinferential studies have focused on neuropsycholog icalpsychometric performance patterns in academically impaired samples. Whereas most examples of this type of investigation have limited their focus to reading disabled subjects, a few have extended classification efforts to specific impairments in arithmetic or generalized academic handicap. For example, Rourke and Finlayson (1978) divided 45 children, ages 9 to 14, into 3 groups depending on their patterns of achievement on the Wide Range Achievement Test and then compared their performance on a battery of neuropsychological tests. Findings were interpreted as indicating somewhat deficient visualperceptualorganizational skills in a specific arithmetic disability group, a pattern which was considerably different from that of two severe nonspecific learning disability groups (one of whose arithmetic mean was relatively more advanced). The two latter groups' performance was virtually indistinguishable and was interpreted as indicating poor verbal and auditoryperceptual skills. Although the sample contained both sexes, no attempt was made to interpret the results accordingly. Rourke argued that because another study in his laboratory
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(Canning et al., 1980) had found no significant sex differences in two different age groups of retarded readers on the same battery of tests, it was unnecessary to do so. Inasmuch as only the reading criterion was listed for this study, it is not clear if the two samples were comparable, i.e., if the sex differences sample represented either a specific reading disability or a nonspecific learning disability group, or if both disabilities were included. Interestingly, in light of Rourke's assertion, it was reported that the data were reanalyzed according to male scores alone; even so, the small number of female subjects (6/45) makes it unlikely that their omission would significantly affect the results. Secondly, no attempt was made to differentiate neuropsychological subtypes within each of the learning disability groups. Although subsequent studies by the Windsor group (Petrauskas & Rourke, 1979; Fisk & Rourke, 1979) have identified subtypes of nonspecific learning disabilities and retarded readers, no attempt has been made to further investigate the possibility of specific arithmetic disability subtypes. Rather, emphasis has been given to the external validation of the pattern identified by this initial investigation (Strang & Rourke, 1985). In contrast to the strategy of investigating one characteristic cognitive pattern for each different pattern of academic impairment, most researchers have concentrated on identifying more than one neuropsychological subtype for one particular category of academic problem. Badian (1983)
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10 classified developmental dyscalculia into 4 subtypes on the basis of her analysis of arithmetic errors made by 50 specific arithmetic disabled children. She described a spatial dyscalculia subtype, an anarithmetria subtype (involving extreme confusion regarding arithmetic processes), an attentionalsequential dyscalculia subtype, and a mixed subtype. The majority of children made attentionalsequential errors. A fifth subtype, involving alexia and agraphia for numbers, was hypothesized, but was not supported by the data. Mattis et al. (1975) classified 90% of his dyslexic subjects into monothetic categories of language disorder, articulatory and graphomotor dyscoord i nat ion syndrome, and visual perception disorder on the basis of their performance on a battery of neuropsychological tests. The first two subtypes represented almost equal numbers of subjects (39% and 37%, respectively) while the last subtype represented only 16% of the sample. These findings were replicated in a larger crossvalidation sample of younger black and Hispanic children who, in contrast to the first study, were not clinic referred. The same three subtypes emerged, although the language disorder group comprised the vast majority (63%) of the sample, while the articulatory and graphomotor dyscoordination subtype dropped to 10% and visualperceptual subtype fell to 5%. In addition, although no overlap among subtypes was noted in the initial solution, the second study found that 9% of subjects displayed mixed deficits. Denckla (1972) reported
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11 that 70% of her clinical sample either exhibited mixed deficits or could not be classified into her three subgroups of specific language disturbance, visuospatial disability, and dyscontrol syndrome, which were again determined according to neuropsychological test profiles. Cole and Kraft (1964) observed five subgroups in their clinical sample, which can be faulted for its small size: dyslexia v\/ith primary language deficit, dyslexia with primary visuospatial deficit, dyslexia with intact language and visuospatial functioning but abnormalities of synthesis, dyslexia with mixed deficits, and a heterogeneous grouping of specific learning disability without dyslexia. Smith (1970) found three WISC patterns specific to his sample of retarded readers: deficient auditory sequencing ability, deficient spatial and perceptual organization, and mixed deficits. He further compared his results according to age and found that the first and last subgroups evidenced an increasing incidence with age, while the middle subgroup showed the opposite trend. The Smith study is somewhat unique in that it utilized a normal control group, enabling the identification of subgroups idiosyncratic to the target sample; the use of control groups of normal and, in the case of selected samples, nondyslexic retarded readers has been infrequent Although on the surface there seem to be similarities among the findings of these studies, Satz & Morris (1981) caution that comparisons are inappropriate because of marked
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12 differences in methodology and design. It is difficult to compare studies which differ in the characteristics of the subjects involved, the types of data collected, and the methods as well as criteria for determining the results. Surplus meanings inherent in subgroup labels have further confused the issue, so that the investigators themselves have linked different sets of subgroups in apparent comparison attempts. In addition there have been few replication efforts, Mattis (1978) being an exception, and no opportunity for statistical verification. Therefore the conclusions which can be drawn from this research are 1 imi ted Statistical approaches have been applied less frequently in this research area because of the relatively recent development of specific techniques and computer systems able to handle them. Cluster analysis, which is a generic term encompassing a variety of statistical methods, was created specifically for purposes of classification. As such it enables a basic descriptive search for naturally occurring subgroups among a given population, assigning individuals on the basis of their similarity on specified variables. Hierarchical methods group the two most similar observtions or clusters together through a series of multistage comparisons until one cluster results which contains all subjects. Morris et al. (1981) described three decisions which must be made when using hierarchical agglomerative clustering methods. The first concerns the
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13 choice of one of many methods of constructing the initial data matrix. Distance measures are recommended when the elevation of the cluster profile is more important than profile shape. Correctional measures, which are relatively insensitive to elevation, may be particularly contraindicated for research in this area. The second decision involves the selection of a method for defining the similarity between subgroups during the clustering process. Such methods, which are based on different definitions of distance, include single linkage (nearest neighbor), complete linkage (furthest neighbor), average linkage, median, centroid, and minimum variance (Ward's). The single linkage method "may fail to give useful solutions because of (their) sensitivity to the presence of 'noise' points between relatively distinct clusters and the subsequent chaining effects (p. 92)" (Everitt, 1974). However, there appear to be no recognized reasons at present to either recommend or contra i nd icate the other methods. Everitt states that no one method is best in all circumstances and recommends that several be utilized. The third decision involves the determination of the optimal number of clusters in a data set, thus fixing the stopping point in the clustering process. This decision, which is especially vulnerable to subjective error, can be aided by the examination of clustering results via the hierarchical tree, cluster profiles, and clustering coefficients, the last an indication of the amount of variance accounted for at each
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14 step in the clustering process. Finally, because a subject cannot change clusters once he is assigned, even if he is more similar to a subsequently formed subgroup than the one in which he was placed, the use of an iterative partitioning technique is recommended following the determination of optimal number of clusters in a solution. This procedure relocates misassigned subjects into more appropriate clusters and is an indiction of the stablity of the solut ion 0technique factor analysis is the most widely used method of clustering subjects in psychology but differs from other cluster analytic techniques in that individuals are assigned to groups on the basis of their loadings on extracted factors which reflect the similarity in their pattern of responses. The result is a dimensional representation, rather than the categorical one derived from hierarchical methods (Morris et al., 1981). It is not equipped to handle multiple factor loadings, whereas other methods of cluster analysis allow for mixed groups. Because of its reliance on correlation coefficients, it assumes a linear model and is relatively insensitive to elevation. In addition the number of subgroups formed is limited by the number of classification variables; employing a large number of variables is not an acceptable solution because the i nterpretabi 1 i ty of the resulting subgroups is made more complex. Although hierarchical cluster analysis is not limited as to the number of clusters in the solution, is
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15 stronger when the assumption of linearity is violated, and can be sensitive to elevation in the data (Lyon, 1983), it has nevertheless been criticized for several areas of limitation (Satz & Morris, 1983). These include the lack of firm statistical foundation as well as critical examination, definition, and validation of clustering methods. It has been noted that different software programs contain different algorithms, producing predictably differing results Doehring and Hosko (1977) used a Qtechnique to analyze the results of 31 tests of readingrelated skills in a sample of reading disabled children. For 31 out of 34 subjects classification into one of three subgroups was possible. The first subgroup was characterized by good performance on all visual and several auditoryvisual matching tests but performed poorly in oral word and syllable reading. The second subgroup performed well on visual number and letter scanning, relatively poorly on oral word reading and two auditoryvisual matching tests, and very poorly on the remaining auditoryvisual letter matching tests. Subgroup three showed good visual and auditoryvisual letter matching, poor visual and auditoryvisual matching of words and syllables, and very poor oral syllable, word, and sentence reading skills. A comparison sample of combined nonreading learning disorders, language disorders, and mental retardation also revealed the first two subgroups. Attempts to compare the resulting subgroups
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16 with those found by other investigators, a procedure which was previously discussed as inappropriate, was nonetheless attempted but proved unsuccessful because of the complexity of the data. However, Doehring et al. (1979) found that the three subtypes remained stable and continued to be specific to the reading disabled sample when they were compared with a group of normal readers who were matched for age and sex. Doehring et al. (1981) next classified their reading disabled subjects on an extensive battery of language and neuropsychological tests according to Qtype factor analysis. While the results indicated generally poor language development in the reading disabled sample, there was no simple correspondence between reading and nonreading deficits. Three out of five factors identified were considered i nterpretable classifying 65% of the sample. The nature of the deficits remains somewhat obscure but appears to involve language repetition and/or naming. Even more confusing are the results of Petrauskas and Rourke (1979), who classified 160 poor and normal readers, all 7 to 8 years old and clinicreferred, on the basis of 20 neuropsychological tests with the Qtechnique. Six factors emerged, four of which were replicated in a splitsample analysis, and of these one was comprised of normal readers. A description of the three unique and reliable subgroups, which classified only 50% of the subjects, follows. Subgroup one, which comprised 25% of the sample, was characterized by relative strengths in visualspatial and
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17 eyehand coordination abilities; average or near average tactilekinesthetic, abstract reasoning, vocabulary, and nonverbal concept formation abilities; mild impairments in word blending, immediate memory for digits, and general information; moderate to severe impairments in verbal fluency and memory for sentences; the largest Verbal/ Performance IQ discrepancies (low VIQ) on the WISC; and lower WRAT scores in reading and spelling than arithmetic. The second subgroup, representing 16% of the sample, was average or near average in kinesthetic, psychomotor, visualspatial construction, vocabulary, nonverbal problemsolving, and abstract reasoning skills; borderline to moderately impaired in immediate memory for digits, sequencing, general information, sound blending, verbal fluency, and verbal concept formation; moderately to severely impaired in finger recognition, immediate visualspatial memory, and memory for sentences; no WISC discrepancy; and uniformly poor reading, spelling and arithmetic skills on the WRAT. Subgroup three comprised 8% of the sample, and showed average or near average finger recognition in the left hand, kinesthetic, visualspatial construction, vocabulary, nonverbal concept formation, and sound blending abilities; borderline to mild impairment in finger recognition in the right hand, immediate memory for digits, speeded eyehand coordination, general information, nonverbal abstraction, and the ability to shift sets; mild to moderate impairment in verbal fluency, memory for
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18 sentences, and immediate visualspatial memory; moderate to severe impairment in verbal concept formation; and a high proportion of normal readers. The overwhelming complexity of these subgroups prohibit interpretation and illustrate the disadvantage of employing a large number of clustering variables. Whereas other techniques allow for consolidation of clustering variables into factors prior to the analysis, Qtechnique prohibits this option since it itself is a factor analytic technique. That onehalf of the data set was lost (i.e., could not be classified) suggests a further limitation of the Qtechnique in disallowing multiple factor loadings, although it is difficult to imagine how mixed categories could heighten the interpretabi 1 ity of such already confusing results. The same group (Fisk & Rourke, 1979) conducted a similar study with older (914 years old) children in order to determine the stability of their initial solution. However the two clinic samples were not necessarily comparable, in that the older learning disabled children were uniformly impaired on all three subtests of the Wide Range Achievement Test, whereas only the reading score was reported as a selection criterion for the younger sample. Nevertheless two of the original subtypes were reported to be replicated across three different age ranges (910, 1112, 1314). Subtype A was considered to be similar to the earlier Subtype 2, now termed a sequencing deficit group. Subtype B replicated Subtype 1, referred to as
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19 having clear aud i toryverbal and languagerelated problems. Subtype C, distinguished by poor fingertip numberwriting perception, was unique to the latter study. In all, 54% of the sample was classified into one of the three identified subtypes. Although both studies employed a mixed sex sample, which was nonetheless predominately male, the gender makeup of the subtypes was reported only for the earlier investigation. The sex ratio was 3:1 in Subtype 1, 12:1 in Subtype 2, and 2:1 in Subtype 3. However, although reported, the possible implications of these findings were not discussed. Cluster analytic techniques were first applied to a reading disabled sample by Smith and Carrigan (1959). Although the clustering method was not specified, the investigators identified five subgroups in an analysis of 18 neuropsychological variables for their 30 subject sample. Two subgroups were superior on all measures and one presented an unclear pattern. Of the remaining two subgroups one was impaired in both cognitiveassociational and perceptualmetabolic abilities, while the other obtained average scores in all areas except cognitiveperceptual abilities, in which a deficit was found. External validation on physical and physiological measures showed no differences among subgroups, although there was differentiation along an anxiety dimension. Naidoo (1972) employed a singlelinkage method in her cluster analysis of dyslexic males. Because of the tendency toward chaining in
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20 this method, the resulting five subgroups showed considerable within group variability and seemed to exist along a continuum. The validity of her results are additionally questioned by lack of classification for onethird of the sample and the size of the resulting clusters (27, 5, 3, 3, and 2). Generally when individuals resist incorporation into existing clusters, they are dismissed as "outliers," i.e., errors of measurement, and are excluded from further consideration; however, the chaining tendency of the method makes it especially sensitive to intermediate points, so that the small sized clusters may not be the true outliers, if any, in the sample. In any event, the inappropr lateness of the clustering technique selected obscures any understanding of the data. Lyon (1983, 1985) attempted to replicate the subtypes which were described by Mattis et al. (1975) through statistical classification methods. He administered a neuropsychological battery of 10 linguistic and visual perception tasks to 100 learning disability students, all of whom demonstrated significant deficits (approximately 3 years below grade level) in both oral reading and reading comprehension, as well as a group of normal readers who were matched for age (1112 years) and IQ. Both standard and raw scores were submitted to hierarchical agg lomerat ive cluster analysis which employed a Euclidean distance formula and a minimum variance (Ward's method) criterion; addition cluster analyses were performed on data subsets. The results
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21 yielded 6 homogeneous subtypes which were reliable regardless of type of data input or variable subset used. A crossvalidation study (Lyon & Watson, 1981), which employed the same design, replicated the results of the previous study. A multivariate analysis of variance yielded a significant effect for subtype on clustering variables. Eightynine percent of learning disability students in the initial study and 94% of those in the followup study were placed in one of the 6 subtypes, which included a global deficit type, a mixed deficit type, a specific language deficiency type, a visualperceptualmotor deficiency type, a global language deficiency type, and a normal diagnostic profile. The visualperceptualraotor impairment subtype had the largest membership. Lyon noted that the results did not replicate the subtypes identified by Mattis et al. (1975), primarily because of the failure to detect a high rate of anomia. A second crossvalidation study (Lyon et al., 1982) attempted to replicate the subtyping results with a younger aged (69 year old) sample. Five subtypes resulted, replicating all but the global deficit subtype. Lyon criticized his own research for methodological flaws, including his failure to use several methods of cluster analysis or an iterative partitioning technique to assess the adequacy of the solution, both of which concern internal validity. Fletcher (1985), in contrast, commended the study for its reliability and internal validity but faulted its external validation on the basis of classification attributes (i.e., component reading skills).
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22 The same criticism can be applied to the investigation conducted by Speece & McKinney (1984), which attempted to validate 6 subtypes of disabled readers on the basis of similar external criteria. The sample again was drawn from school learning disabilities classes and screened according to performance on a test of oral reading; additional selection criteria involved age (910 years), IQ, and maternal educational attainment. A control group of normal readers met similar selection criteria. A battery of information processing tasks was administered and cluster analyzed using a hierarchical agglomerative method (Ward's method with a correlation similarity measure). Internal validation was accomplished through split sample replication, reclustering using an average linkage algorithm, and adding additional subjects (normal readers) as well as randomly removing reading disabled subjects from the data set. The results supported the stability of a 6 cluster optimal solution which achieved 100% coverage. A MANOVA revealed a significant difference between the clusters on clustering variables. All subtypes revealed a general deficit in speed of receding. In addition Cluster 1 was distinguished by a deficit in short term memory capacity, while Cluster 2 demonstrated a deficit in semantic encoding. Cluster 3 had poor sustained attention and Cluster 4 showed deficient phonetic and semantic encoding. Cluster 5 was distinguished from Cluster 3 by poorer sustained attention but less severe speed of recoding.
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23 Cluster 6 demonstrated a deficit in memory organization. Although Cluster 2 had the largest membership, subject distribution was relatively even among the 6 subtypes. It was noted that females were overrepresented in Cluster 1, while Cluster 6 was composed exclusively of males. Satz and associates (Darby, 1978; Satz & Morris, 1981, 1983; Fletcher & Satz, 1985) were the first to utilize cluster analytic techniques as a method of determining the target learning disabled group in a relatively large and unselected school population prior to the search for subgroups, thus avoiding the arbitrary and exclusionary selection criteria utilized in previous studies. Using a hierarchical agg lomerat ive averagelinkage method with squared Euclidean distance, Darby identified nine naturally occurring achievement subgroups, after eliminating three outlier clusters (six subjects), on the basis of the WRAT scores of his sample of 236 fifth grade white males. A multivariate analysis of variance on the clustering variables revealed significant differences in achievement among clusters. Comparisons of 10, SES, neurological status, and neuropsychological variables also revealed significant subgroup effects, with lower achieving subgroups tending to show lower scores on all variables. The two lowest achieving subgroups contained high proportions of children with "soft" neurological signs and lower SES ratings. The mean IQ for the sample was 103; all subgroups had mean IQ scores of at least 90.
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24 Two of the subgroups were considered sufficiently depressed, i.e., mean reading, spelling, and arithmetic scores more than two years below expected levels, to be designated learning disabled and subjected to further study. One subgroup represented a specific arithmetic disability but was not included in subsequent investigations. There were no pure reading disability subgroups identified. The two learning disabled subgroups were combined into an 89 subject sample and reclustered on four neuropsychological variables representing two independent factors of language and perceptualmotor abilities. The clustering technique for this phase was a hierarchical agg lomerat ive minimum variance method with squared Euclidean distance. Five distinct, homogeneous clusters (labeled "subtypes" to avoid confusion with achievement "subgroups") emerged, although one cluster of five subjects was ultimately eliminated because of outlier status. Subtype 1 was designated as the Unexpected Type because of its at least average scores, when compared to sample means, on all clustering variables. Subtype 2 was labeled the Specific Language (Naming) Type because of its selective impairment in verbal fluency. Subtype 3, the VisualPerceptualMotor Type, was impaired on both of this factor's measures. Subtype 4, the Mixed Type, was impaired on all clustering variables. Subtype 4 also had a significantly lower mean IQ score than the other three subtypes, all of which approximated the sample mean. There were no differences among subtypes in achievement, SES, neurological status, or personality variables.
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25 Satz, Morris, and Darby (1979) reanalyzed the data from the second phase of the above study, using four different hierarchical techniques (complete linkage, average linkage, median, and minimum variance) with two different similarity coefficients (squared Euclidean distance and error sum of squares). All eight methods resulted in identification of five distinct clusters, the membership of which remained virtually identical across methods, thus providing a measure of replicability The characteristics of the subtypes were the same as in the previous analysis, with the exception of the emergence of a fifth subtype which showed a global language impairment. Analysis of external validation variables found a significantly higher proportion of neurological "soft" signs and a trend toward lower SES status in the global language, perceptualmotor, and mixed subtypes. The specific language impairment and unexpected subtypes, by contrast, showed lower proportions of members with affected neurological ratings and a trend toward higher SES status. Data on parental achievement competencies indicated that the unexpected and specific language subtypes scored higher not only than the other subtypes, but also than the overall samples means, thus ruling out a familial association with learning failure in these groups. That reanalysis of the same data resulted in a somewhat different solution points out the subjective component in cluster analysis statistical techniques, resulting from the general lack of operationalized decision rules. Along with the
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26 choice of methods, the determination of the optimal number of clusters presents a major difficulty. Although Everitt (1974) recommends that both qualitative and quantitative methods be employed in assessing the validity of the cluster solution, he admits that much work is needed to perfect the latter techniques. Morris, Blashfield & Satz (1981) completed additional internal validation studies by means of statistical measures, data manipulation procedures, and graphical methods. Splitsample analysis, data alteration via the addition of superior achieving and specific arithmetic disability subgroups, and the inclusion of additional clustering variables all supported the results of the clustering procedures. External validation procedures also revealed the subtypes to differ on a large number of variables, including developmental course and parental achievement level. Finally, crosscultural replication (Van der Vlugt & Satz 1985) provided additional external validation for the 9 cluster achievement solution and 3 of the 5 neuropsychological subtypes, despite the fact that the Dutch sample was drawn from a more select (i.e., special school) population. Only the specific language impairment and unexpected subtypes of the Florida studies failed to find counterparts in the Dutch solution. Satz & Morris (1980) criticized the Florida studies along with the others in their review of learning disability subtyping research. The sample was faulted for its
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27 homogeneity, in terms of age, race and gender, which limited the generalizations which could be drawn from their results. Clustering variables were criticized for their limited number (neuropsychological) and breadth (achievement). Specifically the WRAT was faulted for its restricted measure of reading which relies only on word recognition; the addition of a reading comprehension measure to the achievement battery was recommended. Use of the Peabody Picture Vocabulary Test as a measure of intellectual ability was faulted because of its verbal bias. It was felt that subtype validity could have been strengthened by additional criterion measures, including teacher observations and developmental histories. Although a more sensitive measure of personality functioning was called for, it is possible that results on the Children's Personality Questionnaire (CPQ) were confounded with the learning disabled subjects' inability to read. In addition the SES rating can be faulted for its reliance on teacher judgment. Another criticism concerned the subgroups chosen for the subtype analysis: although a specific arithmetic disability subgroup was identified, only the overall impaired (nonspecific learning disability) subgroups were further investigated. Finally the limitations of cluster analysis as a classification method were acknowledged. Despite these criticisms, however, the Florida studies represent a unique and promising approach to learning disability subtyping research
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28 Conclusions and Hypotheses In summary, recognition of the heterogeneity of reading/learning disabilities as a diagnostic entity and the related need to identify descriptive subgroups represents a significant advance in the conceptualization of this area. However, efforts toward delineation of subgroups have resulted in relatively little progress toward this goal. A major obstacle arises in the lack of comparability among studies which prevents integration of results so that conclusions may be drawn. Lack of consistency in the characteristics of the subjects investigated, the measures which form the basis of the comparison, and the methods which (at times inappropriately) determine the construction of the subgroups has characterized the research in this area. Little attention has been paid to sex differences or developmental course. Moreover issues of reliability, validity, and utility have rarely been addressed. What is needed is further investigation and expansion of the beginnings which have been made rather than additional isolated efforts. Therefore the present study attempts to expand upon the efforts which have been made by Satz and associates, while at the same time addressing some of the limitations of the earlier work, in order to further describe naturally occurring subtypes of learning disabilities in a schoolaged population. Specifically, the purpose of this study is to identify naturally occurring learning disability subtypes in a large
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29 and relatively unselected population of fifth grade boys and girls by means of a two stage analysis of achievement and neuropsychological test variables. In the first phase of the investigation, cluster analytic techniques are applied to the reading, spelling and arithmetic scores of 150 females and 150 males, as well as the combined sex sample of 300 children, in order to establish a preliminary achievement based classification system. The data are then reclustered following the addition of a reading comprehension measure to the clustering variables, and the solutions for the two cluster analyses for each sample compared, in order to determine the value of including a measure of comprehension as well as word recognition in the assessment of reading skills. Those subgroups which are found to be significantly impaired in one or more academic skill areas are designated as the learning disabled subsample. In the second phase of the investigation the learning disabled subgroups within each sample are combined and reclustered according to their performance on 4 neuropsychological tests representing verbalconceptual and perceptualmotor abilities. The external validity of the resulting subtyping solutions is assessed through comparisons of the clusters on measures of personality, social, and behavioral functioning. In addition the clusters in both the achievement subgrouping and neuropsychological subtyping solutions are compared according to intelligence, socioeconomic status, chronological age and, where appropriate, gender.
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30 The hypotheses for this study are I. Naturally occurring achievement subgroups will differ according to pattern and level for relatively unselected male and female samples. II. The inclusion of a reading comprehension measure along with previously used measures of reading word recognition, spelling, and arithmetic computation will not significantly affect the composition of the above subgroups. III. Characteristics of the neuropsychological subtypes of learning disabled males will be similar to those found by Satz and associates, but will differ from the female subtypes. IV. Subtype characteristics will differ for overall and specific learning impaired subgroups. V. Learning disability subtypes will differ on personality, social, and behavioral measures.
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CHAPTER ri METHOD Subjects Subjects for the present investigation consisted of virtually the entire fifth grade population of the PennTrafford School District in Westmoreland County, Pennsylvania. Selection criteria were avoided, with the result that only children who had previously been identified as mentally retarded were excluded. Two parents chose not to have their children participate, leaving 334 students available for study. However, because of size limitations imposed by the statistical data processing system, which was unable to handle more than a 300 subject matrix, it was necessary to eliminate 16 male and 18 female pupils from the sample. Subjects were dropped on the basis of extremes of age in order to increase the homogeneity of the sample and minimize agerelated confounding factors such as number of years of schooling. The resulting sample consisted of 150 and 150 females. The mean age of the children at the beginning of the study was 125.22 months (SD = 4.60) with a range of 118 to 139 months. There were no nonwhite pupils in the grade. 31
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32 The male half of the sample is roughly equivalent to that employed in the Florida studies (Darby, 1978; Satz & Morris, 1981, 1983) in terms of age, grade, and race. Both studies have utilized a large, relatively unselected sample in order to permit a comprehensive investigation of naturally occurring subgroups of learning disabilities in an intermediatelevel school population. The homogeneity of the sample in both studies minimizes the possibility of confounding of the results by such factors as inadequate intelligence, lack of exposure to instruction, or cultural disadvantage. Although the number of subjects in the male subsample is necessarily somewhat fewer than in the Florida sample (N = 236), the inclusion of both sexes in the present investigation permits comparisons not only between the two high risk (male) samples, but also extends a comparison of those results to a low risk (female) sample. Measures Achievement Tests Wide Range Achievement Test (WRAT) The WRAT (Jastak & Jastak, 1965) has been the primary measure of school achievement in the Florida Longitudinal Project. It contains measures of reading, spelling, and arithmetic. Although it has gained widespread acceptance as a reasonably accurate estimate of a child's academic skill levels ( Rourke & Finlayson, 1978), it has been criticized for its reliance on word recognition as its sole measure of reading. Therefore a second measure of reading was added to the
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33 achievement battery in the present study. Raw scores were converted to gradeequivalent (GE) scores for both achievement tests. GatesMacGinitie Reading Test (GMRT) This widely used test (MacGinitie, 1978) contains measures of vocabulary and reading comprehension. It utilizes a multiple choice format and is available in several difficulty levels. Level D, intended for use with fourth through sixth grade students, was chosen for the present study; however, Level C, intended for use with third grade students, was available for administration to subjects who scored below norms on Level D. Only scores from the Comprehension subtest were used in the present investigation. Neuropsychological Measures The following tests were chosen from a child neuropsychological battery developed by Satz and associates (1973, 1974, 1978). When the battery was subjected to factor analysis, three factors emerged which were found to be highly predictive of future reading achievement. The first two measures listed below loaded highly on Factor I ( sensorimotorperceptual ability) and the last two measures loaded highly on Factor II (verbalconceptual ability). Factor I was found to have less predictive power than Factor II at the fifth grade level. Developmental Test of VisualMotor Integration (VMI) The VMI (Beery & Buktenica, 1967) consists of a series of 24 geometric line drawing designs, arranged in order of
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34 increasing difficulty, which the child is required to copy. Testing is discontinued after three consecutive failures. The raw score was converted to an ageequivalent score (in months) for the cluster analysis. Standardization norms were obtained from the revised manual (Beery, 1982). RecognitionDiscrimination Test (RD) The RD (Small, 1968) is a 24 item visual perception task which requires the child to match a geometric stimulus design to one of four test figures, three of which are rotated and/or similar in shape to the stimulus figure. The raw score was used in the cluster analysis. Norms were provided by Taylor (personal communication, 1985). Wise Similarities (SIM) The Similiarities subtest of the Wechsler Intelligence Scale for Children (Wechsler, 1949) was scored as in the manual. In the present study, scaled scores (mean = 10; SD = 3) were used. Verbal Fluency (VF) The VF is a modified form of the Verbal Associative Fluency Test developed by Spreen and Benton (1965). The child is asked to name as many words as possible beginning with the letters F, A, and S, allowing one minute per letter. The raw score, representing a total number of words produced across the three trials, was used for clustering. The results were interpreted according to norms published by Gaddes and Crockett (1975). External Validation Measures OtisLennon Mental Ability Test (OLMAT) The OLMAT (Otis & Lennon, 1967) is a widely used groupadministered
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35 intelligence test, which consists of verbal, pictorial, and geometric materials tapping verbal and quantitative concepts, reasoning by analogy, and vocabulary. Rasbury et al. (1978) reported a corrected correlation coefficient of .72 between the OLMAT DIQ and the Full Scale IQ on the Wechsler Intelligence ScaleRevised. The Elementary II Level of the OLMAT was administered by the district at the beginning of the school year following the one in which the present study was conducted. Children's Personality Questionnaire (CPQ) The CPQ (Porter & Cattell, 1972) is a 140 item, forced choice ("yes" or "no") measure of fourteen factorially independent dimensions of personality. Following the manual's suggestion for test administration with children and older poor readers, the entire test was read aloud. Testing was accomplished on a small group basis. The raw scores for each factor were converted to "sten" scores (mean = 5.5, SD = 2) for the present study. Behavior Problem Checklist (BPC) The BPC (Quay & Peterson, 1967) is a scale for rating 55 problem behavior traits occurring in childhood and adolescence. The results yield scores on four subscales which have been derived from factor analytic studies. The factor scores represent the number of items checked by the rater, which, in the present study, was the child's classroom teacher. Two items, involving enuresis and masturbation, were removed from the checklist at district request.
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36 LJ Sociometric Test (LJST) This technique (Long et al., 1962) provides an index of group status for a child based on his classmates' interpersonal preferences. It is accomplished by asking children to list, in descending order, the three pupils in their classroom whom they like the most and the three pupils that they like the least. A weighted score for the most preferred and least preferred variables is derived from both the number of choices and the rank of those choices for each child. TwoFactor Index of Social Position (ISP) This technique ( Hoi 1 i ngshead 1957) provides an estimate of socioeconomic status (SES) based on the occupation and educational attainment of the head of the household, which was presumed to be the father except when none was listed on the child's permanent record card. Use of the more recent FourFactor Index of Social Status ( Hollingshead 1975), which utilizes data from both parents, was prevented by school records which list the educational attainment of both the mother and father, but the occupation of only one parent. The ISP SES score, which ranges from 11 to 77, is inversely proportional to social class position. Procedure In the first phase of the study, the total sample of 300 children, as well as male and female subsamples, was sorted into subgroups according to achievement test scores. In order to accomplish this objective, the WRAT and GMRT were administered to all subjects. The tests were group
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37 administered, with the exception of the WRAT Reading subtest, by the author and two district guidance counselors. The LJST and WRAT Reading were administered during individual testing sessions. Because district personnel preferred not to administer a technique which required them to ask students to identify classmates which they most liked and disliked, sociometric data were collected by the author for only four out of thirteen classrooms. External validation data, including birthdate, parents' occupation and education, and group IQ scores, were obtained from each child's permanent record card. A socioeconomic status rating (ISP) was not able to be computed for three female subjects because of incomplete or missing data. OLMAT IQ scores were unavailable for eight males and twentyone females. However, there were no missing data for any of the achievement variables. In the second phase of the study children in learning impaired subgroups, as determined by the Phase I analysis, were sorted into learning disability subtypes on the basis of their performance on neuropyschological tests. Although it was originally intended that subgroups identified as having relatively lower mean achievement scores in any or all areas be included in the second phase of the study, the multiplicity of combinations possible from such a criterion resulted in the identification of over half of the sample. Hence practical considerations, involving public relations with the school district as well as the author's
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38 availability for data collection, necessitated a decision limiting further investigation to specific subgroups. In the end, neuropsychological test data were collected on 117 out of the original 300 subjects. (Even so, missing data due to children's school absence or withdrawal or scheduling problems do occur in the identified subgroups.) The four neuropsychological measures, the VMI, RD, SIM, and VF and the personality measure, the CPQ, were administered to the 117 identified subjects by the author. In addition the primary classroom teacher for each of the 117 pupils was asked to complete the BPC Completed checklists were returned by ten out of thirteen teachers; however, in an apparent effort to insure confidentiality, one teacher removed both the student's name and subject identification number from each checklist. Usable BPC data were obtained for 50 subjects, representing nine out of thirteen classrooms. There were no missing data for neuropsychological or personality measures among the 117 identified subjects. Statistical Analyses The classification schemes for both phases of the present study were generated by means of cluster analysis, defined as a procedure that groups individuals into homogeneous clusters based on their performance on clustering variables. All clustering procedures used were contained in the CLUSTAN 2C Program (Wishart, 1982). Three hierarchical agglomerative techniques were initially
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39 employed, including average linkage, complete linkage, and minimum variance (Ward's). With each of these methods, squared Euclidian distance similarity coefficients were used to construct the initial data matrix. Results generated by the three different methods were compared and those produced by the Ward's method were found to be the most easily interpretable Therefore the Ward's method with squared Euclidian distance was subsequently used for all Phase I and II cluster analyses. A schematic representation of the cluster analysis is presented in Figure 1. In the first phase of the analysis cluster analytic techniques were applied to WRAT Reading, Spelling, and Arithmetic data, which were in the form of grade equivalent (GE) scores, for the total sample of 300 children as well as the two subsamples of males and females. A determination of the optimum number of clusters present in each data set was made by inspecting the dendrogram, plotting the clustering coefficients, and examining the profiles of individual clusters in order to evaluate the meaningf ulness of different solutions. The composition of the clusters within the chosen solution were then subjected to a Kmeans iterative partitioning clustering method in order to clarify and maximize the solution. Solutions which resulted in a large number of subject reassignments arbitrarily defined as more than 15% of the sample, were rejected as inadequately representat ing the actual structure of the data. Alternate solutions were then subjected to the
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40 Sample N's (I) Clustering Variables (I) a. Males = 150 a. WRAT b. Female = 150 c. Combined Sex = 300 ) B. WRAT & GMRT Sub sample N's (II) a. Males = 51 b. Females = 44 c. Combined Sex = 112 Clustering Variables (II) Neuropsychological Tests (SIM, VF, VMI, & RD) Cluster Analysis 1. Hierarchical Agglomerative Technique (Ward's minimum variance method with squared Euclidean distance) 2. Determination of Optimum Number of Clusters 3. Iterative Partitioning Technique Interpretation of Results (II) Identification of Neuropsychological Subtypes J An End of Analysis Interpretation of Results (I) 1. Identification of Learning Disabled Subsample 2. Comparison of Results from WRATonly and WR.\T & GMRT Cluster Analyses T End of Analysis Figure 1. Schematic Representation of Cluster Analysis.
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41 relocation procedure until one was found which appeared to more closely approximate the data structure. The clusters in the optimum solution following relocation comprised the achievement subgroups for the Phase I analysis. The subgroups were subjected to a multivariate analysis of variance (MANOVA) using the achievement test scores as the dependent variables. When significant effects were found, individual variables were subjected to univariate analyses (ANOVA). External validation data (chronological age, OLMAT IQ score, ISP socioeconomic status rating) were subjected to univariate analyses as well. Individual means were compared using post hoc Duncan's MultiRange Tests (Winer, 1971). All multivariate and univariate analyses were conducted using the General Linear Models (GLM) procedure of the Statistical Analysis Systems (SAS) program (Barr et al., 1976). Phase I statistical procedures, outlined above, were repeated for the male, female, and combined sex samples using the Comprehension subtest of the GMRT in addition to the three WRAT subtests as clustering variables. The resulting subgroups were compared with those based on the WRAT alone in order to determine if the inclusion of a reading comprehension variable produced a substantially different solution. Unique subgroups which were also impaired on academic measures were identified for further investigation along with the impaired subgroups of the WRATonly clusterings.
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42 In the second phase of the analysis those subgroups whose mean achievement scores were substantially lower than the others were reanalyzed using the four neuropsychological measures (VMI, VF SIM, and RD) as clustering variables. Because of the small sample size, if several clusters in a solution were impaired in one or more academic areas, they were combined for the Phase II analysis. The procedure was basically the same as that employed in Phase I. Identified subjects in the total sample, as well as male and female subsamples, were subjected to cluster analytic techniques (Ward's method with squared Euclidian distance) based on their performance on four neuropsychological tests. The clustering variables were in the form of an ageequivalent (AE) score for the VMI, a standard score for the SIM, and raw scores for the VF and RD tests. Following each cluster analysis, the individual solutions were subjected to a Kmeans iterative partitioning method. The resulting clusters comprised the learning disability subtypes for the phase II analysis. A separate MANOVA search for differences between subtypes was made on the basis of achievement as well as neuropsychological test scores. Individual analyses of variance followed by post hoc tests (Duncan's MultiRange Tests) were applied as in Phase I. Additional univariate analyses were conducted on CA, OLMAT IQ and ISP SES ratings. Finally, personality and behavioral data were subjected to multivariate analyses. The fourteen factor scores for the CPQ and the four factor
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43 scores for the BPC and the two weighted scores for the LJST, comprised the dependent variables in two separate analyses All procedures were run at the Northeast Regional Data Center, University of Florida, Gainesville.
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I CHAPTER III RESULTS Phase I; Cluster Analysis of Achievement Variables Male Sample Analyses WRAT cluster analysis A six cluster solution emerged from the cluster analysis of WRAT reading, spelling, and arithmetic scores. The optimum number of clusters was clearly indicated by the dendrogram and clustering coefficients, which showed a sharp increase in withincluster scatter for every successive fusion following the six cluster solution. In addition only 11 out of 150 (71/3%) subjects changed clusters as a result of the relocation procedure. Therefore the six cluster solution was judged near optimal for this study. Examination of the individual clusters in the resulting solution revealed a distinctive pattern of achievement in which reading and spelling scores appeared to be arranged in a scalar fashion, while arithmetic scores were more variable. The number of children in each subgroup ranged from 5 to 42. Although the five member cluster is somewhat smaller than the others, it is not sufficiently small to be dismissed as an outlier. Therefore the analysis classified 100% of the children in the sample. 44
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45 A multivariate analysis of variance (MANOVA) on WRAT Reading, Spelling, and Arithmetic scores yielded a significant main effect for subgroup ( Hote 1 1 i ngLawley Trace = 8.93, F approximation ~ 83.72, p <.0001). Individual analyses of variance disclosed significant effects for subgroup on WRAT Reading (F^ = 98.31, p <.0001), WRAT Spelling ( F^ = 116.78, g <.0001), and WRAT Arithmetic (F^ = 86.87, g <.0001). Mean WRAT subtest scores, converted into discrepancy scores by comparing the grade equivalent score with grade level at the time of testing, for each subgroup are listed in Table 1. Mean achievement scores across subgroups were significantly different from each other in all but one instance for arithmetic and two instances for reading and spelling. Subgroups 1 and 2 obtained virtually identical, superior scores, ranging from 31/2 to 4 years above grade level, in reading and spelling. However their arithmetic scores were signif iciantly different. Subgroup 1 demonstrated skills in arithmetic which were nearly 11/2 years above grade level, while Subgroup 2 showed slightly below grade level skills in the same area. Subgroups 3 and 4 also obtained high scores in reading and spelling, but not to the degree shown by Subgroups 1 and 2. While their mean spelling scores did not differ significantly at 1/2 to 1 year above grade level, reading scores over 1 and 2 years above grade level were significantly different. Subgroup 3's arithmetic score was close to grade level, but Subgroup
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46 TABLE 1 Mean Grade Equivalent Discrepancy Scores for Male Achievement Subgroups Based on WRAT Clustering Variables. Subgroup WRAT WRAT WRAT Number N Reading* Spell ing* Arithmetic* 1 5 3 .86A 3.92A 1 .42A 2 16 4 .llA 3 .61A 0 .32C 3 35 2 26B 1 .04B 0.23B 4 42 1 .30C 0 .638 0.87D 5 33 0.46D 0 .57C 0.54C 6 19 0 .94D 1 .74D 1 .69E TOTAL 150 1 .24 0 .59 0.51 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05)
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47 4's score was nearly 1 year below. The pattern of achievement shown by Subgroup 4, that of adequate to relatively high reading and spelling skills but depressed arithmetic skills, may constitute a specific arithmetic disability subgroup. Subgroup 5 evidenced mildly depressed scores, approximately 1/2 year below grade level, in all areas tested, and may represent a mild nonspecific learning disability subgroup. It is interesting that Subgroup 2, which had superior reading and spelling skills, did not differ significantly from Subgroup 5 in arithmetic. Subgroup 5 did not significantly differ from Subgroup 6 in reading. This last subgroup obtained severely low scores, nearly 1 to 2 years below grade level, in all areas, constituting a severe nonspecific learning disability subgroup Standard score transformation analysis The total sample means for the three variables did not closely approximate the WRAT standardization norms (Jastek & Jastek, 1965). The mean reading score was over 1 year and spelling over 1/2 year above the standardization mean. Arithmetic fell 1/2 year below the standardization norm. Because of these differences, it was considered useful to compare the subgroups with each other. Therefore the WRAT profiles were plotted as zscores based on the means and standard deviations for the sample as a whole (Figure 2). The results yielded profiles which were distinctive for both pattern and elevation. Subgroup 1 was significantly high in
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48 Ã‚Â£3 Reading Spelling Arithmetic Figure 2. Male achievement subgroups based on WRAT clustering variables; mean based on local populat ion
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49 all three areas. Subgroup 2, which also had significantly high reading and spelling scores, had average level arithmetic skills. Subgroup 3 was a high average group whose arithmetic score fell just short of significance. Subgroup 4 was the most nearly average of all, despite it being tentatively labelled as an arithmetic disability group; compared with the rest of the sample, its depressed arithmetic discrepancy score was well within the average range. Subgroup 5 had adequate arithmetic skills but below average reading and spelling scores. Although it was tentatively labelled a mild nonspecific learning disability subgroup, when compared with the sample, it appears to represent a specific reading disability group. Subgroup 6 was significantly impaired in all three areas; the tentative identification of this subgroup as a severe nonspecific learning disability group appears appropriate. Children in Subgroups 5 and 6 showed evidence of impaired learning in one or more academic skill areas compared with their classmates as well as with national norms. No other subgroup met this double criterion. Both subgroups experienced considerable difficulty in reading, the mean scores for which are not significantly different. When compared with standardization norms, their achievement pattern is relatively flat, while the pattern for Subgroups 1 through 4 is that of reading scores which are at least equal to spelling scores and relatively depressed arithmetic scores. For the most part the elevation of the scores seems
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50 to differentiate Subgroups 5 and 6, as well as 1 through 4. These sample profile characteristics hold true for Subgroups 2, 4, and 6 when plotted on the normalized (sample) scale. However, when compared with the sample as a whole, Subgroups 1, 3, and 5 show an opposite pattern of Subgroups 2 and 4, that of arithmetic skills which are relatively superior to reading and spelling scores. When elevation is considered along with pattern, only Subgroups 5 and 6, representing approximately onethird of the sample, are sufficiently depressed to be classified as learning disabled subsample. OLMAT IQ analysis An analysis of variance yielded a significant effect for subgroup on OLMAT IQ (F^ = 25.71, g <.0001). Mean IQ scores are listed by subgroup in Table 2. Post hoc comparison of IQ means (Duncan's procedure, g <.05) showed a strong ordering effect for the subgroups corresponding with overall achievement level. In only two instances were subgroup means not significantly different from each other. Not surprisingly. Subgroup 1 obtained an IQ mean which was significantly higher than the other subgroups. Subgroups 5 and 6 obtained the lowest IQ means with significant differences between the two scores being in the expected direction. Notably, no subgroup obtained a mean IQ less than 90 and the total sample mean (107.84) fell within the average range according to OLMAT standardization norms
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51 TABLE 2 Mean OLMAT IQ Scores, CA, and ISP SES Ratings for Male Achievement Subgroups Based on WRAT Clustering Variables. Subgroup Number N** OLMAT 10* CA* ISP SES* 1 5 128 .20A 123 .60A 26.40A 2 16 113 .31BC 124 .75AB 44 .75BC 3 35 115 .41B 125.37AB 37.74B 4 42 108 .53C 124 .24A 44 .93BC 5 33 101 .31D 128 .OOBC 46 .58BC 6 19 92.29E 130 .530 50.95C TOTAL 150 107 .84 126 .16 43 .74 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05 ) ** Because of missing data, IQ scores are based on 142 subjects. The correct N for Subgroup 3 is 34, for Subgroup 4 is 38, for Subgroup 5 is 32, and for Subgroup 6 is 17.
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52 Demographic variables analyses Individual ANOVAs yielded significant effects for subgroup on CA (F^ = 6.89, p <.0001) and ISP SES (F^ = 3.65, p <.004). The '3,144 *mean scores for these variables are also listed by subgroup in Table 2. Chronological age also showed an ordered tendency, according to post hoc comparisons of subgroup means. The higher achieving subgroups were generally younger than those at the lower end of the achievement spectrum. Children in Subgroup 6 were significantly older than children in all other subgroups except Subgroup 5. SES means did not differ significantly among subgroups for the most part. Subgroup 1 obtained an SES mean which was significantly lower corresponding to an upper middle class ISP rating, than the remaining subgroups. The mean SES score for the sample corresponds to the lower end of the middle class range of social position. Combined WRAT and GMRT cluster analysis Increasing the number of clustering variables to four by adding the GMRT Comprehension score to the WRAT subtest scores resulted in a seven cluster solution. The optimum number of clusters was less obvious than in the cluster analysis of WRAT variables alone, and several solutions were subjected to the iterative partitioning procedure in order to determine the one which most closely reflected the data structure. The seven cluster solution produced the fewest number of relocations (21/150 = 14%), which nevertheless is almost twice the number obtained from the optimal solution based on
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I 53 the WRAT alone. However, inasmuch as no better solution could be found, the seven cluster solution was accepted as optimal for the cluster analysis of the GMRT and WRAT. Inspection of the individual clusters in the resulting ; solution revealed an expectedly more complex array of achievement patterns than that that resulted from the cluster analysis of WRAT variables alone. The number of children in each cluster ranged from 10 to 33, so that the analysis again classified 100% of the sample. A multivariate analysis of variance (MANOVA) on the four achievement variables yielded an overall significant effect for subgroup ( Hotel 1 ingLawley Trace = 11.02, F approximation ^4 554 = 63.58, g <.0001). Individual analyses of variance showed significant effects for subgroup on GMRT Comprehension ( = 69.76, g <.0001), WRAT Reading (F^ = 82.53, p <.0001), WRAT Spelling (F^ = 79.24, g <.0001), and WRAT Arithmetic (F^ = 58.96, g <.0001) Mean GMRT and WRAT discrepancy scores for each subgroup are listed in Table 3. Tests of significance for differences between means revealed that in only one case for reading and two cases for comprehension, were pairs of means not significantly different from each other. For spelling and arithmetic scores, three pairs of means did not significantly differ. Examination of cluster profiles reveals considerable similarity between the solutions based on the three and four
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54 TABLE 3 Mean Grade Equivalent Discrepancy Scores for Male Achievement Subgroups Based on WRAT and GMRT Clustering Variables GMRT Subgroup CompreWRAT WRAT WRAT Number N hension* Reading* Spelling* Arithmetic* 1 13 5.04A 4.38A 3.21B 0.70A 2 21 3.57A 1.78C 0.92C 0.29B 3 10 0.91C 3.60B 3.80A 0.55C 4 33 0.89C 1.98C 0.87C 0.34C 5 26 0.12D 0.87D 0.38D 1.13D 6 32 1.17E 0.50E 0.62D 0.60C 7 15 1.89E 1.09F 1.94E 1.75E TOTAL 150 0.73 1.24 0.59 0.51 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05 )
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1 55 achievement variables. In both solutions there are two subgroups which have superior scores in reading and spelling, but differ according to level of arithmetic achievement. In the present clustering it is clear that the differences also extend to comprehension skills. Thus Subgroup 1 obtains scores which are more than 5 years above grade level in comprehension, 4 years above grade level in word recognition, 3 years above grade level in spelling, and 1/2 year above grade level in arithmetic. Subgroup 3 had word recognition and spelling skills more than 31/2 years above grade level, but its comprehension score was less than 1 year above grade level and its arithmetic score fell 1/2 year below. Subgroups 2 and 4 did not differ significantly in terras of reading and spelling scores, which were close to 2 and 1 years above grade level, respectively, and their arithmetic scores were both close to grade level, although one was slightly above and the other slightly below. However, again a considerable difference appeared in terms of comprehension skills: Subgroup 2 scored 31/2 years above grade level, while Subgroup 4 was not significantly different from Subgroup 3 at 1 year above the standardization mean. At the lower end of the achievement spectrum. Subgroup 5, 6, and 7 profiles appear quite similar to those for Subgroups 4, 5, and 6 in the WRATonly clustering. Subgroup 5 showed a pattern of reading and spelling skills which was nearly 1/2 to 1 year above grade level, but arithmetic was
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I 56 more than 1 year below; comprehension was close to the standardization mean. Subgroup 6 was approximately 1/2 year below grade level on all three WRAT subtests, but more than 1 year below on comprehension. Subgroup 7 fell between 1 and 2 years below grade level in all areas. Standard score tranf ormat ion analysis Because of the differences between the sample and standardization means, which also extended to the comprehension score, the discrepancy scores for the GMRT and WRAT were again converted to a normalized scale having a population mean of zero and a standard deviation of one (Figure 3). The results show relatively flat profiles for Subgroups 1, 4, and 7, who are distinguished by virtue of elevation into significantly high, average, and significantly low achievement subgroups. Subgroups 2 and 3 exhibit profiles which appear to be the mirror image of each other, in that their comprehension and arithmetic scores, as well as reading and spelling scores, seem highly related. However all skills are average to significantly above average. Subgroup 5 fell somewhat below average in all areas, although its arithmetic score was slightly more depressed. However the discrepancy between the arithmetic and other achievement scores does not appear sufficient to warrant a specific arithmetic disability diagnosis. Subgroup 6 showed adequate arithmetic skills, but below average comprehension, reading and spelling scores. Because its comprehension score did not significantly differ from that of Subgroup 7,
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57 Comprehension Reading Spelling Arithmetic Figure 3. Male achievement subgroups based on WRAT and GMRT clustering variables; mean based on local population
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58 which appears to be a severe nonspecific learning disability group, and because its reading score falls just short of significance, Subgroup 6 may be considered a specific reading disability subgroup. OLMAT IQ analysis An analysis of variance on OLMAT IQ was significant ( = 29.09, p <.0001). Mean IQ scores are listed by subgroup in Table 4. Post hoc comparisons of IQ means (Duncan's procedure, 2 <.05) again showed a strong ordering effect for subgroup corresponding with overall achievement level. In only three instances were pairs of means not significantly different from each other. Subgroups 1 and 2 obtained mean IQ scores which were significantly higher than the rest. The lowest IQ scores were shown by Subgroups 6 and 7, which were significantly different from each other in the expected direction. Once again, no subgroups obtained a mean IQ less than 90. Demographic variables analyses Individual analyses of variance yielded significant effects for subgroup on CA (Fg = 5.27, 2 <.0001) and ISP SES (^5^143 = 3.14, g <.0064). The mean scores for these variables are listed by subgroup in Table 4. The lower achieving subgroups were distinguished from the higher achieving subgroups on the basis of age as well as IQ. Children in Subgroups 6 and 7 were significantly older than their classmates in Subgroups 1 through 5. An ordering effect was also found for SES, in which adjacent
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59 TABLE 4 Mean OLMAT IQ Scores, CA, and ISP SES Ratings for Male Achievement Subgroups Based on WRAT and GMRT Clustering Variables Subgroup OLMAT ISP Number N** 10 CA SES 1 13 123. O C 8 5 A 125 31A 31 31A 2 21 119. 30A 124 62A 38 33AB 3 10 109. 508 124 50A 49. 90C 4 33 109 59B 124 18A 46. 64BC 5 26 105 67B 125 46A 42. 58BC 6 32 99 47C 129. OOB 44. 78BC 7 15 91 92D 129 67B 51 40C TOTAL 150 107 .84 126 .16 43 .74 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = 05 ) **Because of missing data, IQ scores are based on 142 subjects. The correct N's for Subgroup 2 is 20, for Subgroup 4 is 32, for Subgroup 5 is 24, for Subgroup 6 is 30, and for Subgroup 7 is 13.
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60 means were generally not significantly different from each other Comparison of achievement cluster analysis. Examination of subject membership in the learning impaired subgroups revealed little difference between the results of the analysis based on WRAT and GMRT scores and the one based on WRAT alone. All 15 subjects in WRATGMRT Subgroup 7 were members of WRAT Subgroup 6. Twentynine out of 32 children in WRATGMRT Subgroup 6 were members of WRAT Subgroup 5, and 23 out of 26 children in WRATGMRT Subgroup 5 were members of WRAT Subgroup 4. Of the remaining 6 subjects, 4 were members of WRAT Subgroup 6 and 2 were members of WRAT Subgroup 4. Therefore the addition of a reading comprehension score did not result in the identification of a single child not already identified as academically impaired, according to either local or standardization norms, by the cluster analysis of WRAT subtest scores alone. Correlation analysis Correlation between the achievement variables were significantly high not only among WRAT subtests but also between the WRAT and GMRT (Table 5). In fact, the GMRT was almost equally positively correlated with each of the WRAT subtests. Therefore the inclusion of a reading comprehension measure appears to have provided redundant information in the classification of the male sample. Similarly high positive correlations were found between the achievement measures and OLMAT 10 Ã‚â€¢ Socioeconomic status and chronological age were found to be
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61 ID 0) IÃ‚â€” I XI (T3 Eh e (0 D U3 s 0 ui 05 C o Ã‚â€¢H 4) (B 1Ã‚â€” ( 0 O u (U rH (0 r^ > (X CO 11 !L0 < S J O O iH I c Q) O Eh a CO a: e c s: 0
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62 negatively correlated with achievement and IQ in the sample as a whole. Interestingly, the negative correlation involving SES which was most highly significant was with arithmetic rather than reading. Negative correlations involving CA were relatively equal across achievement and 10 measures Summary Cluster analysis of WRAT variables resulted in the identification of six achievement subgroups which were significantly differentiated from each other on the basis of 10, CA, and SES as well as achievement. Cluster analysis of combined WRAT and GMRT variables produced a seven cluster solution; significant effects were again found for subgroup on achievement, 10 f and demographic variables. Both analyses revealed a nonspecific learning disability subgroup and a specific reading disability subgroup, as well as one which showed a nonsignificant tendency toward a specific disability in arithmetic. Examination of subject membership in the learning impaired subgroups revealed little difference between the results of the analysis based on WRAT and GMRT clustering variables and that based on WRAT variables alone. Female Sample Analyses WRAT cluster analysis A ten cluster solution emerged from the cluster analysis of WRAT Reading, Spelling, and Arithmetic scores. Although several smaller solutions were suggested by the dendrogram and clustering coefficients, subjecting those solutions to iterative partitioning
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63 resulted in 20 to 30 percent subject reassignment. The ten cluster solution produced the fewest number of relocations (19/150 = 12.67%), and was accepted as optimal. The number of subjects in each subgroup ranged from 4 to 30 classifying 100% of the children in the sample. A multivariate analysis of variance (MANOVA) on WRAT Reading, Spelling, and Arithmetic scores yielded a significant main effect for subgroups ( Hotel 1 ingLawley Trace = 15.65, F approximation ^^ = 79 .22 g <.0000). Individual analyses of variance produced significant effects for subgroups on WRAT Reading ( Fg = 75.05, g <0001), WRAT Spelling ( Fg = 96.65, g <.0001), and WRAT Arithmetic (Fg = 65.36, p <.0001). Mean WRAT discrepancy scores are listed by subgroups in Table 6. Post hoc pairwise comparisons of means reveal that individual subgroups are less unique than in the male solutions. The number of instances in which pairs of means were not significantly different rose to 7 for reading and spelling, and 9 for arithmetic. Subgroup 2 was significantly different from other subgroups in reading and spelling, which were 6 and 21/2 years above grade level, respectively. However its arithmetic score, more than 1/2 year below grade level, was not significantly different from 3 other clusters. Subgroups 1, 3, and 6 scored 3 to 4 years above grade level in reading. Subgroups 1 and 3 had virtually identical arithmetic scores which were close to grade level, while Subgroup 6 scored more than 1/2 year
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64 TABLE 6 Mean Grade Equivalent Discrepancy Scores for Female Achievement Subgroups Based on WRAT Clustering Variables. Subgroup WRAT WRAT WRAT Number N Read ing* Spell ing* Ar ithmet 1 9 3 598 4 51 A 0 16AB 2 4 6 OOA 2 .43B 0 65D 3 9 3 .62B 1 49C 0.09b 4 16 1 .78C 0 .92D 0 36A 5 12 1 .56CD 1 .88C O .54D 6 12 3.34B 0.81D 0.74D 7 30 0.99D 0 .50D 0.30C 8 19 1 .23CD 0 .48D 1 .14E 9 25 0.18E 0.16E 0.67D 10 14 0.41E 0.89F 1 .22E TOTAL 150 1.46 0.79 0 .50 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05 )
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i 65 below grade level in arithmetic. However all 3 subgroups differed significantly in terras of spelling skills, which ranged from less than 1 year above grade level for Subgroup 6 to more than 4 years above grade level for Subgroup 1. Subgroups 4, 5, 7, and 8 had relatively high reading and spelling scores at 1 to 2 years and 1/2 to 2 years above grade level, respectively. However, while Subgroup 4 scored somewhat above grade level in arithmetic. Subgroups 5 and 7 scored somewhat below grade level in the same area. Subgroup 8 obtained an arithmetic mean more than 1 year below grade level. The achievement pattern shown by Subgroup 8, that of adequate to relatively high reading and spelling skills but depressed arithmetic skills, may constitute a specific arithmetic disability subgroup. Subgroup 9 scored close to grade level in reading and spelling, but was not significantly different from Subgroups 2, 5, and 6 in arithmetic, which was more than 1/2 year below grade level. Subgroup 10 was nearly 1/2 to 1 year below grade level in reading and spelling, and more than 1 year below grade level in arithmetic, constituting a nonspecific learning disability group. Subgroup 10 did not differ significantly from Subgroup 9 in reading, or Subgroup 8 in arithmetic. Standard score transformation analysis As was found with the male sample, the total sample means for the three variables differed from the WRAT standardization norms (Jastek & Jastek, 1965) for the female sample as well. The
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66 mean reading score was 11/2 years and spelling over 1/2 year above the standardization mean. Arithmetic fell 1/2 year below the standardization norm. In order to compare the subgroups with each other, the discrepancy scores were converted to a normalized scale (Figure 4). The results show several patterns of achievement which are differentiated according to elevation. The profiles for Subgroups 1 and 5 show a pattern of advanced spelling skills relative to their reading and arithmetic means, which are fairly even. The two profiles are distinguished by their elevation in that Subgroup 1 has superior skills in all areas, while Subgroup 5's scores all fall within the average range. Subgroup 3 shows the opposite pattern, that of spelling skills which are somewhat depressed relative to even performance in reading and arithmetic. Although the spelling score falls within the average range, reading and arithmetic means are significantly above average. Subgroups 2 and 6 show a pattern of achievement in which reading is advanced relative to spelling, which in turn is advanced relative to arithmetic. Although the average level arithmetic scores of the two subgroups are not significantly different, the elevation of the profiles in reading and spelling distinguish one from the other in that Subgroup 2 is superior to Subgroup 6. Even so, the latter' s reading score is significantly above average. The opposite pattern, that of increasing levels of skill competency from reading and spelling to arithmetic, is shown by Subgroup 9. The
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67 Reading Spelling Arithmetic Figure 4. Female achievement subgroups based on WRAT clustering variables; mean based on local population.
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68 elevation of the profile, involving average arithmetic, below average spelling, and significantly low reading scores, reveals Subgroup 9 to represent a specific reading disability subgroups. Subgroups 4 and 7 show a pattern of achievement in which reading and spelling scores are consistent, but arithmetic scores are relatively advanced. Again, the elevation of the profiles distinguish the two subgroups in that Subgroup 4 is superior to Subgroup 7 in all areas (although the difference between their spelling means is not significant). Even so, the two subgroups have average level academic skills with one exception: Subgroup 4's arithmetic score is significantly high. The opposite achievement pattern is show by Subgroup 8, in which arithmetic skills are depressed relative to flat reading and spelling performance. The elevation of the profile, in which reading and spelling scores are average but arithmetic significantly low, reveals Subgroup 8 to represent a specific arithmetic disability subgroups. Subgroup 10, exhibiting a relatively flat profile which is significantly below average in all areas, appears to represent a nonspecific learning disability subgroup. Children in Subgroups 8 and 10 showed evidence of impaired learning in one or more academic skill areas compared with local as well as standardization norms. In addition children in Subgroup 9, while not severely below grade level, were nevertheless significantly delayed in
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69 reading skill acquisition when compared with their classmates. The combination of these three subgroups, representing a specific reading disability subgroup, a specific arithmetic disability subgroup, and a nonspecific learning disability subgroup, may be said to constitute the learning disabled subsample. The number of children in the learning disabled subsample, representing over onethird of the females, is roughly equivalent to the number of children in the male LD subsample based on the cluster analysis of WRAT variables. However the male LD subsample contained only the specific reading disability and nonspecific learning disability subgroups. Therefore the proportion of females in those two subgroups is smaller than in the male sample OLMAT IQ analysis An analysis of variance yielded a significant effect for subgroup on OLMAT IQ ( Fg = 6.92, 2 <.0001). The mean scores for IQ are listed by subgroup in Table 7. Post hoc comparisons of IQ means (Duncan's procedure, q <.05) showed a strong ordering effect in which adjacent means were not significantly different. Not surprisingly, the highest achieving subgroups had the highest IQ scores, while the lowest achieving subgroups had the lowest IQ's. In fact, the IQ means for the three subgroups identified as the learning disabled subsample were both lower than the IQ means for the remaining seven subgroups and not significantly different from each other.
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70 TABLE 7 Mean OLMAT IQ Scores for Female Achievement Subgroups Based on WRAT Clustering Variables. Subgroup OLMAT Numbe r N IQ i A 4 1 1 Q OCA 2 fk 1 1 O 1 T A i IH i 1 A i / i i 4 Ã‚â€¢ / I AB 4 7 TIT TlRnO 111.7 1 ABC 5 13 115.15AB 6 11 111 .82ABC 7 27 109 .IIBCD 8 17 103.65DE 9 23 104 .91CDE 10 11 101 .27E TOTAL 129 109.20 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05 )
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71 Again, no subgroup obtained an IQ mean falling below the average range. Demographic variables analyses Individual analyses of variance failed to produce a significant effect for subgroup on either CA ( Fg = .44, g <.9121) or ISP SES ( Fg = 1.56, g <.1347). The mean CA for the female sample as a whole was 124.27 months. The mean ISP SES rating was 44.56, corresponding to the upper end of the lower middle class range Combined WRAT and GMRT cluster analysis Reclustering the female sample on the basis of GMRT as well as WRAT clustering variables resulted in an eight cluster solution. Twenty subjects (131/3%) were reassigned as a result of the relocation procedure, which is consistent with the number obtained from the optimal solution based on the WRAT alone. The number of subjects in each subgroup ranged from 7 to 30. In the absence of outlier clusters, the solution classified 100% of the female sample. A multivariate analysis of variance on the achievement variables disclosed a significant main effect for subgroup ( Hotell ingLawley Trace = 9.93, F approximation = Zo 5 5 U 48.77, g <.0001). Individual ANOVAs yielded significant effects for subgroup on GMRT Comprehension ( F^ = 47.83, g <.0001), WRAT Reading ( F^ = 71.06, g <.0001), WRAT Spelling (F^^^^2 = 45.00, g <.0001), and WRAT Arithmetic (F^ 142 ^ 42.90, g <.0001)
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72 Mean WRAT grade equivalent discrepancy scores are listed by subgroup in Table 8. Tests of significance between pairs of means reveal a more unique solution than that that resulted from the cluster analysis of female WRAT scores alone, but one that is considerably less unique than either male solution. Although pairs of comprehension means were significantly different in all but three instances, the number rose to five for reading and arithmetic. Seven pairs of spelling means did not significantly differ. Comparison of the solutions based on three and four achievement variables yields more similarities than differences. In both solutions there is one subgroup which had superior reading and spelling skills, 31/2 to 41/2 years above grade level, while arithmetic fell close to the standardization mean. Competence extended to comprehension skills as well, which fell 4 years above grade level. Subgroup 3 did not differ significantly from Subgroup 1 in terms of reading, but its comprehension mean was only 2 years above grade level. Spelling was more than 1 year above grade level, while arithmetic fell over 1/2 year below. Subgroup 2 obtained high scores in reading and spelling, which were more than 2 years above grade level, but its comprehension and arithmetic scores fell close to the norm. Low comprehension relative to reading and spelling scores was also found in Subgroups 5 and 6. Their reading and spelling means did not differ significantly at more than 1 and more than 1/2 year above grade level.
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73 TABLE 8 Mean Grade Equivalent Discrepancy Scores for Female Achievement Subgroups Based on WRAT and GMRT Clustering Variables GMRT Subgroup CompreWRAT WRAT WRAT Number N hension* Reading* Spelling* Arithmetic* 1 7 4.14A 4.53A 4.49A O.lOA 2 14 0.43DE 2.72B 2.11B 0.21A 3 10 2.25C 4.58A 1.30C 0.66C 4 20 3.32B 1.76C 1.07CD 0.03A 5 23 0.25E 1.85C 0.89CD 0.90D 6 20 l.OOF 1.31C 0.57D 0.22B 7 30 l.OOD O.llD 0.04E 0.60C 8 26 I.IOF 0.15D 0.28E l.llD TOTAL 150 0.76 1.46 0.79 0.50 *Means followed by the same different within variables. Alpha level = .05 ) letter are not significantly (Duncan's MultiRange Test,
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74 respectively. However Subgroups 5's comprehension score was close to grade level, while Subgroup 6 fell 1 year below. Arithmetic skills were close to grade level for Subgroup 6 but nearly 1 year below grade level for Subgroup 5. In contrast to the above pattern. Subgroups 4 and 7 obtained high scores in comprehension relative to reading and spelling as well as arithmetic. Subgroup 4 obtained mean scores which were more than 3 years above grade level in comprehension, 1 to 2 years above grade level in reading and spelling, and close to the norm in arithmetic. Subgroup 7 was 1 year above grade level in comprehension, close to grade level in reading and spelling, and over 1/2 year below grade level in arithmetic. The lowest achieving cluster. Subgroup 8, was nevertheless close to grade level in reading and spelling, on which it did not differ significantly from Subgroup 7. However its comprehension mean, which did not differ significantly from that of Subgroup 6, was more than 1 year below grade level. Subgroup 8's arithmetic mean also fell more than 1 year below grade level and did not differ significantly from the arithmetic mean for Subgroup 5. Subgroup 8 might therefore represent a learning disability subgroup with specific delays in reading comprehension and arithmetic. Subgroup 5 might tentatively be labelled a specific arithmetic disability subgroup. Subgroup 6, while apparently representing a specific reading disability subgroup, does not appear delayed in all aspects of reading.
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75 In view oÃ‚Â£ its strong word recognition skills. Subgroup 6 might be labelled a specific reading comprehension disability subgroup. Standard score transformation analysis The GMRT and WRAT discrepancy scores were converted to a normalized scale because of the differences between the sample and standardization means, which extended to the comprehension score as well (Figure 5). The only flat profile was obtained by Subgroup 8, the elevation of which reveals it to be a nonspecific learning disabilities subgroup. Subgroup 1, which showed a pattern of advanced spelling and depressed arithmetic relative to consistent reading and comprehension scores, was the only subgroups with significantly high scores in all areas. Subgroup 3 showed a pattern of advanced reading and depressed arithmetic relative to flat comprehension and spelling scores; only the reading score was significantly high. The elevation of the profiles distinguished Subgroups 4 and 7, which were advanced in comprehension and, to a lesser extent, arithmetic relative to their reading and spelling scores. Subgroup 4 had superior skills in the two advanced areas, while Subgroup 7's scores in the same areas were average. Subgroup 7's scores in reading and spelling, while not significantly low, were far below the average level scores for Subgroup 4. A contrasting pattern, that of depressed arithmetic and, to a lesser degree, comprehension scores relative to flat reading and spelling scores, was obtained by Subgroup 5. All scores
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76 Comprehension Reading Spelling Arithmetic Figure 5. Female achievement subgroups based on WRAT And GMRT clustering variables; mean based on local population.
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77 fell within the average range, even though the arithmetic mean score was not significantly different from that of the uniformly depressed Subgroup 8. Subgroups 2 and 6 showed a depressed comprehension and advanced arithmetic skills relative to their reading and spelling skills. The elevation of the profiles showed Subgroup 2's skills in spelling and arithmetic to be significantly high, but Subgroup 6's comprehension score to fall just short of significance in the opposite direction. Subgroups 6 and 8 showed evidence of impaired learning in one or more academic areas when compared with their classmates as well as standardization norms. Subgroup 6 was delayed only in comprehension, while Subgroup 8 was delayed in both comprehension and arithmetic. When compared with the rest of the sample. Subgroup 8 was delayed in reading and spelling as well. The arithmetic mean for Subgroup 5 did not differ significantly from that of Subgroup 8, even though it did not fall significantly below average when compared with the sample, or more than 1 year below grade level when compared with standardization norms. Similarly, Subgroup 7 did not differ significantly from Subgroup 8 in terms of reading and spelling means even though the former's scores were not significantly low compared with the sample and actually fell above the standardization norms. The number of children identified as learning disabled represents approximately onethird of the sample when limited to Subgroups 6 and 8. However, when Subgroups 5 and
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78 7 are included, the number rises from 46 to 99, representing nearly twothirds of the female sample. QLMAT IQ analysis An analysis of variance yielded a significant effect for subgroup on OLMAT IQ ( F^ = 12.62, g <.0001). The mean IQ scores are listed by subgroup in Table 9. Tests of significance between pairs of means (Duncan's Procedure, p <.05) again revealed a strong ordering effect corresponding with the overall achievement level of the subgroups. The highest achieving cluster. Subgroup 1, had an IQ score which was significantly higher, while the lowest achieving cluster, Subgroup 8, had an IQ score which was significantly lower than the rest. No subgroups obtained an IQ mean lower than 90. Demographic variables analyses As was found with the solution based on the WRAT clustering variables alone, individual ANOVA' s again failed to produce a significant effect for subgroup on either CA ( ~ Q <.3250), or ISP SES (F^ = '^^ 2 <.5371). Comparison of achievement cluster analyses Comparison of subject membership in the learning disabled subsaraples reveals considerable overlap between the cluster analyses based on three and four achievement variables. However, because the nature of the subgroups differed somewhat in the two clusterings, the onetoone correspondence between subgroup memberships that characterized the male results is not found with the females. For example, although all 26 subjects in WRATGMRT Subgroup 8 were already identified in
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79 TABLE 9 Mean OLMAT IQ Scores for Female Achievement Subgroups Based on WRAT and GMRT Clustering Variables. Subgroup Number N** OLMAT 10* 1 7 121 29A 2 14 113 .31CD 3 10 116. 1 3AB 4 20 115.00BC 5 23 107.83DE 6 20 109 .41CDE 7 30 106 .79E 8 26 99 .52F TOTAL 150 109 .20 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05 ) **Because of missing data, IQ scores are based on 129 subjects. The correct N for Subgroup 2 is 13, for Subgroup 3 is 8, for Subgroup 4 is 17, for Subgroup 5 is 18, for Subgroup 6 is 17, for Subgroup 7 is 28, and for Subgroup 8 is 21
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80 the WRATonly learning disability subsample, 11 came from WRAT Subgroup 10, 9 came from WRAT Subgroup 9, and 6 came from WRAT Subgroup 8. Twelve out of 23 subjects in WRATGMRT Subgroup 5, whose arithmetic mean was not significantly low, came from WRAT Subgroup 8, which was significantly delayed in arithmetic skill acguisition. Similarly 15 out of 30 subjects in WRATGMRT Subgroup 7, whose reading score fell short of significance, came from the significantly reading disabled WRAT Subgroup 9; an additional four subjects, 3 in WRAT Subgroup 10 and 1 in WRAT Subgroup 8, made a total of 19 out of 30 children in WRATGMRT Subgroup 7 that were already identified by the WRATonly clustering. Interestingly a majority of children (15/20) in WRATGMRT Subgroup 6 were common to WRAT Subgroup 7, which was not identified as learning disabled as a result of the WRATonly analysis. Therefore the reading comprehension measure appears to have added valuable information to the female analysis in that a new group of children was identified that showed evidence of significant learning impairment. At the same time, however, two learning disabled subgroups identified by the WRATonly clustering (the specific reading and arithmetic subgroups) were obscurred by the cluster analysis on the GMRT and WRAT variables. Although their counterparts appear (WRATGMRT Subgroups 5 and 7), they are not significantly below average in their specific area of impairment. Even so, the means for those same areas are not significantly different from those in the lowest achieving
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81 subgroups. Inclusion of Subgroups 5, 6, 7, and 8 in the LD subsample, representing a specific arithmetic disability subgroup, two kinds of reading disability subgroups, and a nonspecific learning disability subgroup, results in the identification of nearly twothirds of the female sample. Therefore, while providing valuable information about those children not previously identified, the addition of a reading comprehension measure to the WRAT clustering variables actually resulted in the overident i f icat ion of learning disabilities among female subjects. Correlation analysis Correlations between the achievement variables, while highly significant, were considerably lower in the female sample than in the male sample, a finding which is consistent with the increased emergence of specific learning disability subgroups. In addition the increased complexity of the underlying data structure was evident in the cluster analyses, which resulted in optimal solutions with larger number of clusters. IQ continued to be highly correlated with achievement, but again at a lower level. In contrast to the results of the male sample analysis, demographic variables, with only one exception, were not significantly correlated with achievement. However, IQ continued to be significantly correlated with chronological age in a negative direction. Summary Cluster analysis of WRAT subtests resulted in the identification of 10 achievement subgroups, which were significantly differentiated from each other on the basis of
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82 0) iH X! (0 0) iH Oi g m (0 JQ 3 0) rH ra S (1) o <4l 0} c o Ã‚â€¢H m <{ 0) o u 0) ja (0 H > <: J o O M I c CD O U rt Eh a Cfi a e c S O 0 cox: I 2 < c S C/3 c rl < m 2 a + + + + + + 00 c o 11 + + m ID + + CN in + + o + + O in o o rH I in o + + + + + + + + Ã‚â€¢K m (N rÃ‚â€” 1 ro in rÃ‚â€” 1 rl Ã‚â€¢ Ã‚â€¢ Ã‚â€¢ Ã‚â€¢ Ã‚â€¢ Ã‚â€¢ o CO H c 4J
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83 achievement and 10/ but not age or socioeconomic status. Inspection of clusters which showed evidence of significant academic impairment revealed specific reading and arithmetic disability subgroups, as well as a nonspecific learning disability subgroup. Cluster analysis of combined WRAT and GMRT variables produced an 8 cluster solution; significant effects were again found for subgroup on achievement and IQ, but not demographic variables. The same 3 learning disability subgroups were identified; however the results, for the most part, fell short of significance. In addition a subgroup with a specific disability in reading comprehension emerged. Although the combination of the 4 subgroups identified by the combined clustering resulted in the overidentification of learning disabilities in the female sample, all subjects in the nonspecific subgroup, and between onehalf and twothirds of those in the specific reading and arithmetic disability subgroups, were included in the WRATonly learning disability subsample. The specific comprehension disability subgroup proved unique, in that none of its members were represented in any of the 3 subgroups which were identified as significantly impaired in the analysis of WRAT variables alone. Combined Sex Sample Analyses Comparison of male and female samples The male and female samples were combined for the cluster analysis of achievement in the total sample. A multivariate analysis of variance on WRAT Reading, Spelling, and Arithmetic, and GMRT
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84 Comprehension, failed to yield a significant effect for sex ( Hotell ingLawley Trace = .01, F approximation ^ 295 ~ .52, g <.7247). Individual analyses of variance were insignificant as well for IQ (Fj^ ^^q I'O^f 2 <.2965), and SES (F, = .21, p <.6483). The only area in which the male and female samples differed significantly was chronological age, with the males being older than the females (F^ ^ 13.10, 2 <.0003). WRAT cluster analysis When clustered on the basis of the WRAT variables, a six cluster solution emerged from the combined sex data. Thirtyseven subjects (121/3%) changed their cluster membership as a result of the relocation procedure. Although the six cluster solution was the one most clearly indicated from the dendrogram and clustering coefficients, a larger solution was also attempted. However, when the alternative solution was subjected to iterative partitioning, an even greater number of subjects was reassigned. Therefore the six cluster solution was accepted as optimal for the data. The number of subjects in each cluster ranged from 29 to 94. In the absence of outliers, the six cluster solution classified 100% of the total sample. A MANOVA on WRAT Reading, Spelling, and Arithmetic scores yielded a significant overall effect for subgroup ( HotellingLawley Trace = 8.14, F approximation = 157.71, g <.0001). Individual univariate analyses produced significant effects for subgroup on WRAT Reading (F_ _q. =
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85 154.78, 2 <.0001), WRAT Spelling ( 215.71, g <.0001), and WRAT Arithmetic (F^ ^94 = 120.57, 2 <.0001). Mean WRAT discrepancy scores are listed by subgroup in Table 11. Mean scores were significantly different in all instances for spelling, and all but one instance for reading and spelling (Duncan's MultiRange Test, p <.05). These comparisons confirm the appropriateness of the solution and reveal the uniqueness of the individual clusters. Subgroup 1 had superior skills in reading and spelling, both of which were approximately 4 years above grade level. However, its arithmetic score fell close to the standardization norm. Subgroup 2 also had high scores in reading and spelling, which fell close to 3 and 11/2 years above grade level, respectively; the arithmetic mean was 1/2 year above grade level. The largest cluster. Subgroup 3, had the same pattern of decreasing scores; reading was close to 2 years and spelling was close to 1 year above grade level, while arithmetic was close to 1/2 year below grade level. Subgroup 4 showed the same pattern at a lower level: reading close to 1 year and spelling close to 1/2 year above grade level, and arithmetic more than 1 year below. Subgroup 5 was approximately 1/2 year below the standardization norm in all three areas. Subgroup 6, the lowest achieving subgroup, was more than 1/2 year delayed in reading, and more than 11/2 years below grade level in spelling and arithmetic.
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86 TABLE 11 Mean Grade Equivalent Discrepancy Scores for Combined Sex Achievement Subgroups Based on WRAT Clustering Variables. Subgroup WRAT WRAT WRAT Number N Read i ng* Spel 1 ing* Arithmetic* 1 30 4 .23A 3 .92A 0 60B 2 36 2 .90B 1 .42B .49A 3 94 1.78C .91C .37C 4 51 .95C .39D I.IOD 5 60 .35E .39E .51C 6 29 .72E 1 .52F 1 .55E TOTAL 300 1.35 .69 .50 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05 )
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87 Standard score transformation analysis The total sample means for the three variables differed considerably from the standardization means. Therefore the WRAT profiles were plotted as zscores based on the means and standard deviations for the sample as a whole (Figure 6). The results yielded three pairs of patterns, the members of which were distinguished by elevation. Subgroups 1 and 4 had arithmetic scores which were depressed relative to their reading and spelling scores. However, Subgroup I's reading and spelling scores were significantly high, while the same scores for Subgroup 4 fell just short of being significantly low. The pattern of adequate reading and spelling skills, but depressed arithmetic skills, may represent a specific arithmetic disability subgroup. Subgroups 2 and 5 showed a pattern of arithmetic skills which were advanced relative to reading and spelling scores. Subgroup 2 was significantly above average in arithmetic and nearly so in reading. However, although Subgroup 5 had average arithmetic skills, its reading mean was significantly below average. Subgroup 5, with its average arithmetic, below average spelling, and significantly low reading scores constitutes a specific reading disability subgroup. The achievement profiles of Subgroups 3 and 6 were relatively flat. Subgroup 3 obtained average scores, but Subgroup 6's scores were significantly low. Therefore Subgroup 6's profile is consistent with a nonspecific learning disability subgroup.
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88 Reading Spelling Arithmetic Figure 6. Combined sex achievement subgroups based on WRAT clustering variables; mean based on local population.
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89 OLMAT IQ analysis An analysis of variance on OLMAT IQ was significant for subgroup ( 2(55 ~ 40 .35 g <.0001). The mean IQ scores are listed by subgroup in Table 12. Post hoc comparisons of IQ means (Duncan's procedure, g <.05) showed a strong ordering effect for the subgroups corresponding with overall achievement level. In only two instances were means not significantly different from each other. Subgroups 1 and 2 obtained IQ scores which were significantly higher than the remaining subgroups. The IQ mean for Subgroup 6, the nonspecific learning disability subgroup, was significantly lower than the rest, but was nonetheless above 90. The IQ means for the two specific LD subgroups, clusters 4 and 5, did not differ significantly from each other. The sample mean (108.49) falls within the average range, according to OLMAT standardization norms. Demographic variables analysis Individual ANOVA's produced significant effects for subgroup on CA ( 294 4.22, 2 <.0011) and ISP SES (F^ 291 = 2.95, g <.0130). 2 However there were no significant sex differences (X = 9.354, g <.0958). The mean scores for CA and SES are listed by subgroup in Table 12. Chronological age (CA) was found to be strongly ordered with adjacent means not significantly different from each other. SES means were not significantly different, with the exception of Subgroup 2, whose middle class rating was significantly higher than the rest. The mean SES rating for
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90 TABLE 12 Mean OLMAT IQ Scores, CA, and ISP SES Ratings for Combined Sex Achievement Subgroups Based on WRAT Clustering Variables Subgroup OLMAT ISP IN U lU U C IT M* isJ pa* G t? C 1 30 117. 53A 123 83A 43 .767B 2 36 118 .50A 124 .19A 36 .629A 3 94 110. 96B 124 .69AB 44 .0758 4 51 104 .82C 124 .73AB 44 .300B 5 60 103 .46C 126.53BC 45.383B 6 29 93 .75D 127 .76C 51 .034B TOTAL 300 108 .49 125.22 44.15 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05 ) **Because of missing data, IQ scores are based on 271 subjects and SES ratings on 197 subjects. The correct N for Subgroup 1 is 32 (IQ) and 35 (SES), for Subgroup 3 is 84 (IQ) and 93 (SES), for Subgroup 4 is 45 (IQ) and 50 (SES), for Subgroup 5 is 56 (IQ) and for Subgroup 6 is 24 (IQ).
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91 the sample corresponds to the upper end of the lower middle class range of social position. Combined WRAT and GMRT cluster analysis Increasing the number of clustering variables to four by including GMRT Comprehension along with the WRAT subtests resulted in a dramatic increase in the complexity of the underlying data structure. The optimum number of clusters was not clearly indicated by the dendrogram and clustering coefficients. Therefore several solutions were subjected to iterative partitioning, but none resulted in a subject reassignment of less than 15% of the sample. The 13 cluster solution, the largest of those attempted, resulted in the fewest number of relocations (58/300 = 191/3%) and, in the absence of a better fitting solution, was accepted as optimal. The number of children in each cluster ranged from 7 to 42. Therefore the 13 cluster solution classified 100% of the combined sex sample. A multivariate analysis of variance on GMRT and WRAT subtest scores yielded a significant main effect for subgroup ( Hotell ingLawley Trace = 14.74, F approximation 48 1130 ^ 86.73, 2 <.0001). Individual ANOVA's disclosed significant effects for subgroup on GMRT Comprehension (F^2,287 ^ 93.93, 2 <.0001), WRAT Reading (F^2 287 ^ 115.91, 2 <.0001), WRAT Spelling (F^2 287 91.92, 2 <.0001), and WRAT Arithmetic (F^2 287 ^ 78.97, q <.0001). Mean discrepancy scores for the four achievement variables are listed by subgroup in Table 13. Tests of
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92 TABLE 13 Mean Grade Equivalent Discrepancy Scores for Combined Sex Achievement Subgroups Based on WRAT and GMRT Clustering Variables GMRT Subgroup CompreWRAT WRAT WRAT Number N hens ion* Reading* Spell ing* Arithmetic 1 7 4 4 IB 4 OOB 4 .llA 1 24 A 2 15 3 .44C 5 08A 3 .463 25D 3 11 6 22A 3 24C 1 33C 27C 4 21 2 21D 2 23D 1 1 3CD 55B 5 10 46E 2 60D 4 37A 34DE 6 19 52E 3 57BC 1 .OICD 33DE 7 42 2.55D 1 .39E .78D .38DE 8 31 .75G 1 .27E .76D .22D 9 32 .52E .21G .13E .51E 10 36 .99EF 1 .65E .90CD .97F 11 27 .26FG .37F .40E 1 .37G 12 36 1 .65H .49G .59E .75F 13 13 2.19H 1 .42H 2.08F 1.75H TOTAL 300 .75 1.35 .69 .50 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05 )
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93 significance between pairs of means reveals diminished uniqueness of individual subgroups in comparison to the smaller solution based on WRAT variables alone. The number of instances in which pairs of means were not significantly different rose from one to seven in reading, one to seventeen in arithmetic, and none to twenty in spelling. Comprehension means did not differ significantly in ten instances. Subgroups 1 and 2 obtained superior scores in comprehension, reading, and spelling, ranging from 31/2 to 5 years above grade level. However they were differentiated by their arithmetic scores: Subgroup 1 scored over 1 year above grade level, while Subgroup 2 scored close to grade level. Subgroup 3 also had superior scores in comprehension and reading, 6 and 3 years above grade level respectively. Spelling was high at more than 1 year above grade level, and arithmetic fell close to the standardization norm. Subgroups 4 and 7 were not significantly different in terms of their comprehension means, which were over 2 years above grade level. However Subgroup 4 outscored Subgroup 7 in the other three areas. All means were above grade level, with the exception of Subgroup 7's arithmetic score which was 1/2 year delayed. Subgroups 5 and 6 were not significantly different in terms of comprehension skills, 1/2 year above the norm, as well as arithmetic skills, nearly 1/2 year delayed. High to superior scores were obtained in the other two areas, with Subgroup 6 outscoring Subgroup 5 in reading, and the opposite occurring in spelling.
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94 At the lower end of the achievement spectrum. Subgroup 8 was more than 1/2 year delayed in comprehension, but close to 1 year advanced in reading and spelling. Arithmetic tell close to the standardization norm. Similarly high scores in reading and spelling were obtained by Subgroup 10. Comprehension fell close to the norm, and the arithmetic score was nearly 1 year below grade level. The pattern of adequate to moderately advanced skills in reading (word recognition and comprehension) and spelling, but delayed arithmetic skills, suggests that Subgroup 10 may represent a specific arithmetic disability subgroup. Subgroup 9 fell within 1/2 year of the norm in all areas, as did Subgroup 11 with the exception of arithmetic. Subgroup 11 's 11/2 year delay in arithmetic suggests a second specific disability subgroup. Subgroup 12 was 1/2 to 1 year below grade level on the WRAT subtests and more than 11/2 years below the norm in comprehension, possibly representing a combination of a mild nonspecific LD and a specific comprehension disability subgroup. Subgroup 13 obtained mean scores which were 11/2 to 2 years below grade level in all areas, representing a severe nonspecific learning disability subgroup Standard score transformation analysis The discrepancy scores were once again converted to a normalized scale based on the means and standard deviations for the sample as a whole (Figure 7). The result is a somewhat confusing array of profiles, the shape of which is
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95 Figure 7. Combined sex achievement subgroups based on WRAT and GMRT test clustering variables; based on local popultion.
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96 duplicated in few instances. Several profiles show one area which is advanced relative to flat performance in the remaining three. Subgroup 7 has an above average comprehension mean, but average reading, speling, and arithmetic scores. Subgroup 4 has superior arithmetic skills and above average scores in comprehension, reading, and spelling. Subgroup 12 is advanced in arithmetic relative to its performance in the other three areas; the elevation of the profile reveals significantly delayed comprehension and reading skills, a low spelling score which falls just short of significance, and an arithmetic score which falls within the average range. Two subgroups show the opposite trend, that of a specific skill delay relative to the level of performance in other areas. Subgroup 8 falls below average in comprehension, but obtains average scores in reading, spelling, and arithmetic. Subgroup 11 falls somewhat below average in comprehension, reading, and spelling, but is significantly delayed in arithmetic. A pattern of split performance levels is found in Subgroup 1, whose spelling and arithmetic skills are relatively better developed than comprehension and reading skills. However all scores are significantly above average. Other profiles reveal a more scattered pattern of skill development. Subgroup 3 has advanced comprehension and depressed spelling scores relative to flat performance in reading and arithmetic; all but spelling are significantly high. Subgroup 6 is advanced in reading and delayed in
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97 arithmetic relative to comprehension and spelling scores; the last two skill areas are average, arithmetic falls below average, and reading falls significantly above average. Subgroup 5 spikes in spelling, then shows a pattern of successively decreasing skill competence in reading, arithmetic, and comprehension; all scores except spelling fall within the average range. Subgroup 9 is advanced in both comprehension and arithmetic, and delayed in reading, relative to its spelling skills; the first two skill areas are average, spelling somewhat below average, and reading just short of being significantly low. Subgroups 2 and 10 show the same pattern of advanced reading and spelling, and depressed arithmetic, relative to comprehension skills. However, the profiles are distinguished by elevation. Subgroup 2 is superior in all areas but arithmetic; Subgroup lO's scores all fall within the average range, although arithmetic falls at the lower end. The profile for Subgroup 13 shows a mild downward slope, but all four skill areas are significantly below average. Subgroups 11, 12, and 13 are significantly delayed in one or more academic skill areas, according to sample norms. Subgroup 13 appears to represent a nonspecific learning disability subgroup. Subgroups 11 and 12 show evidence of specific learning disabilities, the former in arithmetic and the latter in reading. However, in neither case is the discrepancy between the significantly delayed and other skills dramatic: all scores tend to fall near the lower end
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98 of the average range or below. In addition, the reading score for Subgroup 9, though not significantly low, does not differ significantly from that of Subgroup 12, which does fall significantly below average. Subgroups 9 and 12 may represent two different types of specific reading disability subgroups by virtue of their vastly discrepant comprehension scores OLMAT IQ analysis An analysis of variance yielded a significant effect for subgroup on OLMAT IQ (F']^2 258 ~ 24.16, g <.0001). Means IQ scores are listed by subgroup in Table 14. IQ again appeared to show a strong ordering effect in which adjacent means were, in most cases, not significantly different. However, the mean IQ for Subgroup 1 was significantly higher, and the mean IQ for Subgroup 13 was significantly lower, than the IQ scores for the remaining subgroups. Subgroups 11, 12, and 13, the three clusters which had significantly skill delays, obtained IQ mean scores which were significantly lower than all of the remaining clusters except Subgroup 9, the nonsignificant specific LD subgroup. No subgroup obtained an IQ mean which fell below the average range. Demographic variables analyses Individual ANOVA's produced significant effects for subgroup on CA (F^2 287 ~ 4.14, g <.0001) and ISP SES (F^2 284 1'87, 2 <.0378). The mean scores for these variables are listed by subgroup in Table 14.
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99 TABLE 14 Mean OLMAT IQ Scores, CA, and ISP SES Ratings for Combined Sex Achievement Subgroups Based on WRAT and GMRT Clustering Variables Subgroup Number N** OLMAT 10* CA* ISP SES* 1 7 126 .71A 123 86A 35 .OOA 2 15 118 .80BC 123 .47A 42 13AB 3 11 120 .78 125.73AB 34 .55A 4 21 118 .74BC 124 .38AB 39.81AB 5 10 110 .30DE 124 .50AB 45 .60AB 6 19 109 .40DEF 125 .OOAB 38.53A 7 42 113 .44CD 123 .86A 45 98AB 8 31 108 .89DEF 124 .35AB 43 .07AB 9 32 104 .27FG 126 .38AB 42.47AB 10 36 107 .28EF 123 25A 45 .OOAB 11 27 101 .33GH 126.11AB 51.59B 12 36 98 .41H 127 .58BC 46 .08AB 13 13 91 .101 130 .38C 51 .15B TOTAL 300 108.49 125.22 44.15 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05) **Because of missing data, IQ scores are based on 271 subjects and SES ratings on 297 subjects. The correct N for Subgroup 3 is 9 (IQ) for Subgroup 4 is 19 (10), for Subgroup 6 is 15 (IQ), for Subgroup 7 is 41 (IQ), for Subgroup 8 is 27 (10), and 29 (SES), for Subgroup 9 is 30 (IQ), for Subgroup 10 is 32 (10) and 35 (SES), for Subgroup 11 is 24 (IQ), for Subgroup 12 is 32 (10), and for Subgroup 13 is 10 ( IQ)
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100 Post hoc comparisons of CA and SES means revealed few significant differences, although those which were obtained fell in the expected direction. Thus the children in Subgroup 13 were significantly older than the children in all other clusters except Subgroup 12. In addition Subgroups 11 and 13 obtained significantly lower SES ratings, corresponding to lower middle class social position, than did high achieving Subgroups 1, 3, and 6, whose rating corresponded to a middle class level. A chisquare test revealed a significant relationship 2 between gender and subgroup (X = 24.858, g <.0155). The frequency distribution for sex is listed by subgroup in Table 15. Interestingly, males are disproportionately represented in both the highest and lowest overall achieving subgroups. Subgroup 1, which has significantly high scores in all achievement areas, is 71% male. Subgroup 13, whose scores are significantly low in all areas, is 92% male. Other clusters which have a predominately male membership are Subgroup 3, which is significantly high in all areas except spelling, and Subgroup 12, which is significantly low in comprehension and reading. Females represent a majority in subgroups whose achievement falls closer to the sample norm. Subgroup 8, which has average skills in all areas (although comprehension is relatively low) is 65% female. Subgroup 9, which has average to below average achievement scores, although none are significantly low, is 68% females. Only Subgroup 6, also 68% female, shows an extreme
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101 TABLE 15 Gender Distribution for Combined Sex Achievement Subgroups Based on WRAT and GMRT Clustering Variables. Subgroup Number N Male Fem 1 7 5 2 2 15 8 7 3 11 7 4 4 21 11 10 5 10 5 5 6 19 6 13 7 42 23 19 8 31 11 20 9 32 10 22 10 36 16 20 11 27 13 14 12 36 23 13 13 13 12 1 TOTAL 300 150 150
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102 achievement score and then only in one area: reading is significantly high, while the remaining three areas fall close to average. Interestingly, in terms of the learning disabled subsample, two subgroups, representing the nonspecific LD subgroup and the specific reading (word recognition and comprehension) subgroup, are predominantly male. These two subgroups show the lowest overall achievement. The specific arithmetic disability subgroup, which is nonetheless mildly impaired in the three remaining areas, has an even sex distribution. The specific reading (word recognition) disability subgroup, whose comprehension and arithmetic skills are average, has a female majority. Comparison of achievement cluster analyses Comparison of the learning disabled subsamples based on the cluster analysis of the 3 and 4 achievement variables reveals considerable overlap. However the proportion of the total sample identified as learning disabled differ. In the WRATonly clustering. Subgroups 4, 5, and 6 constitute nearly half the sample. In contrast, the WRATGMRT LD subsample, including Subgroups 9, 11, 12, and 13, represents slightly more than onethird of the sample. Both solutions have a nonspecific learning disability subgroup which is significantly delayed in all areas when compared with sample as well as standardization norms. A specific arithmetic disability subgroup also appears common to the results of both clusterings. Specific reading disability subgroups appear in both solutions as well, although the inclusion of
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103 a comprehension measure distinguishes dysfluent oral readers with adequate comprehension skills from those readers who are significantly impaired in both skill areas. When subject membership in individual subgroups is compared between the two solutions, however, it is apparent that the inclusion of the GMRT with the WRAT clustering variables added little to the identification of an LD subsample. All subjects in WRATGMRT Subgroup 13 were members of WRAT Subgroup 6, both nonspecific LD subgroups. Twentysix out of 36 children in WRATGMRT Subgroup 12, and 27 out of 32 children in WRATGMRT Subgroup 9, were members of WRAT Subgroup 5, all specific reading disability subgroups. Fifteen out of 27 subjects in WRATGMRT Subgroup 11 fell in WRAT Subgroup 4, both specific arithmetic disability subgroups. Of the remaining 10 children in WRATGMRT subgroup 12, 5 when to WRAT Subgroup 4 and 5 went to WRAT Subgroup 6. Eleven additional subjects from WRATGMRT Subgroup 11 fell in WRAT Subgroup 6, while the remaining subject fell in WRAT Subgroup 5. Four out of 5 of the remaining subjects in WRATGMRT Subgroup 9 fell in WRAT Subgroup 4. Therefore all but one subject in the WRATGMRT LD subsample had already been identified as academically impaired, according to either local or standardization norms, by the cluster analysis of WRAT subtest scores alone. The extra subjects in the WRAT LD subsample appear to result predominantly from the inclusion of 25 out of 36 subjects in WRATGMRT Subgroup 10, a primarily average achieving cluster
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104 whose arithmetic mean was relatively depressed at 1 year below grade level, in WRAT Subgroup 4. However, although the LD subsample appears somewhat over inclus i ve as a result, WRATonly solution provides a better fit to the data. Therefore the addition of a reading comprehension measure did not prove beneficial in the identification of a learning disabled subsample in the combined sex sample. Correlation analysis The correlations between achievement, IQ, and demographic variables are presented in Table 16. As was found in the male and female samples, the correlations between the achievement variables are all highly significant in a positive direction, as are the correlations between achievement and IQ. Although not significant for the most part in the female sample, strong negative correlations between demographic variables and achievement/lO variables in the male sample produced significant correlations in the combined sex sample as well. Summary Cluster analysis of WRAT subtests resulted in the identification of 6 achievement subgroups which were significantly differentiated from each other on the basis of IQ, SES, and CA, as well as achievement. Cluster analysis of combined WRAT and GMRT variables produced a 13 cluster solution; significant effects were found for subgroup on the same variables as in the WRAT only analysis. In addition there was a significant sex effect. A nonspecific learning disability subgroup, as well as specific (oral) reading and arithmetic disability subgroups, were represented in both
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105 Ln O Lu 1 + + 1Ã‚â€” 1 o O Ã‚â€¢ Ã‚â€¢ O M 1 1 1 r" 1 U 0) 0 + Ã‚â€¢K + + K + CN '"^ CJ ^ 1 1 1 1 1 + 1 JJ H + + + < Ã‚â€¢rl 4J o in CN Ã‚â€¢ s < E Ã‚â€¢ Ã‚â€¢ Ã‚â€¢ Ã‚â€¢ w 1 1 Ml P tn + + + + Ã‚â€¢pH + 1 1 Ã‚â€¢T rH o ro iTi 'U r M lO CN 1 1 o M4 1 1 Ci C U n qj + + + + + + + 00 o in 00 1 Ã‚â€” 1 CN 4J Ã‚â€¢ Ã‚â€¢ flj 1 1 rH <1> u c u 0 0 Ã‚â€¢H o o CO rH O 0) iH c IT) rH O O 4J 0) o O O O O rH C 0) x: M CO Ã‚â€¢ Ã‚â€¢ Ã‚â€¢ Ã‚â€¢ jQ Ã‚â€¢rl E V V V V (0 iH x: )^ Eh H H a < U < 0 leC il 05 E Qj OS a 0 J < + > s < u o M u Ã‚â€¢tc + +
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106 analyses. The combined WRAT and GMRT analysis also revealed a subgroup which was significantly impaired in both oral reading and reading comprehension. However examination of subject membership found that all but one member of the WRATGMRT learning disability subsample had already been identified by the cluster analysis of the WRAT subtests alone Phase II; Cluster Analysis of Neuropsychological Variables Male Sample Analyses Identification of the learning disabled subsample Because the results of the Phase I cluster analysis revealed little difference between the solutions based on 3 and 4 clustering variables, only the solution based on WRAT subtests alone was subjected to Phase II analysis. Subgroups 5 and 6, representing a specific reading disability subgroup and a nonspecific learning disability subgroup, comprised the LD subsample. Although one subgroup with relatively depressed arithmetic skills did appear in both the WRATonly and WRATGMRT solutions, in neither case was the arithmetic mean significantly below average. In addition the arithmetic mean was significantly higher than that of the nonspecific LD subgroup in both cases. Therefore there is no specific arithmetic disability subgroup represented in the male LD subsample. Neuropsychological test cluster analysis The 19 children in Subgroup 6 were combined with the 33 children in
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107 Subgroup 5 for Phase II analysis. Data was missing for one child, resulting in a total sample of 51 children. Clustering these 51 subjects on the basis of their neuropsychological test (SIM, VF RD, and VMI) scores resulted in a six cluster solution. The optimum number of clusters was clearly indicated by the dendrogram and clustering coefficients, which showed a dramatic shift in the rate of change of withincluster similarity for every successive combination following the six cluster solution. Subjecting the six cluster solution to the relocation procedure resulted the reassignment of only three children (5.88%). Therefore the six cluster solution was judged near optimal. The number of children in each cluster ranged from 5 to 13, so that 100% of the children were classified. A multivariate analysis of variance (MANOVA) on the four neuropsychological test scores yielded a significant main effect for subtype ( Hotell ingLawley Trace = 9.50, F approximation = 19.23, p <.0001). Individual ANOVA' s Zv Lb Z disclosed significant effects for subgroup on WISC Similarities (F = 11.18, p <.0001), VerbalFluency (F^ = 24.92, 2 <.0001), Recognition Discrimination ( F^ = 17.20, g <.0001), and VisualMotor Integration ( F^ = 22.88 2 < .0001 ) Mean neuropsychological test scores are listed by subtype in Table 17. Post hoc comparisons of means (Duncan's Procedure, g <.05) reveals five instances in which means are not significantly different for VF and VMI. RD
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108 TABLE 17 Mean Neuropsychological Test Scores for Male Learning Disability Subtypes. Subgroup Number N SIM* VF* RD* VMI* 1 9 12, .78A 33 IIA 20. ,78 A 83 67D 2 13 11 .9 2AB 18 .39C 20 .46A 81 31D 3 12 11 .OBBC 23 .92B 21 .83A 128 .08A 4 6 10, .83BC 34 .OOA 17, .83B 104 .33B 5 5 10, .OOC 17 .60C 15, .80C 86 60CD 6 6 7 .67 21 8 3BC 20 .67A 98 67BC TOTAL 51 11 .06 24 .45 20 .10 98. 00 *Means followed by the same different within variables. Alpha level = .05 ) letter are not significantly (Duncan's MultiRange Test,
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109 means are not significantly different in six instances and SIM means in seven instances. Means for the total sample were close to the standardization norms in all areas except VMI, which fell just short of being significantly low. Standard score transformation analysis In order to facilitate the interpretability of the results, the scores were converted to a normalized scale which, in the absence of local norms, was based on standardization norms (Figure 8). Male norms were used whenever available, and age was based on the learning disability subsample mean. The results show a variety of patterns with only one duplication. The profile for Subtype 1 has superior Verbal Fluency and WISC Similarities scores, average RecognitionDiscrimination, and a significantly low VisualMotor Integration mean. Subtype 2 is distinguished from Subtype 1 solely on the basis of its moderately low Verbal Fluency score. Subtype 3 performed at or above the standardization mean in all areas, while Subtype 6 performed at or below the norm in all areas, although in both cases all scores fell within the average range. Subtype 4 falls above the norm on Factor II tasks, but below the norm on Factor I tasks; the VF score is significantly high, while the RD score is significantly low. Subtype 5, like Subtype 6, shows scores which fall at or below the standardization mean in all areas; however. Factor I test means are significantly low. Subtype profiles may be categorized in terms of their specific areas of neuropsychological impairment. Subtypes 1
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110 Figure 8. Male learning disability subtypes based on neuropsychological test clustering variables; mean based on standardization norms.
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Ill and 2 appear to represent Specific VisualMotor Impairment Subtypes, distinguished from each other by their level of language development. Subtype 4 represents a Specific VisualPerceptual Impairment Subtype. The Subtype 5 profile is consistent with a Global VisualPerceptualMotor Impairment Subtype. Subtype 6 appears to represent a Mild Mixed Specific Language (Reasoning) and Nonverbal (Visual Motor) Impairment Subtype. Subtype 3 shows no evidence of impairment in either area and may be characterized as an Unexpected Subtype. Interestingly, no subtype is impaired only in language areas, although Subtype 5 shows evidence of a mild impairment in naming and Subtype 6 has a mild impairment in reasoning. WRAT analysis A multivariate analysis of variance on the WRAT subtest scores failed to reach significance ( HotellingLawley Trace = .45, F approximation = 1 .25 2 < .2412) OLMAT IQ analysis An analysis of variance yielded a significant effect for subtype on OLMAT IQ ( = 3.49, g <.01). Mean IQ scores are listed by subtype in Table 18. 10 showed an ordered tendency, in which adjacent means were generally not significantly different. Subtypes 1 and 3 obtained significantly higher IQ means than Subtype 6, the mean for which did not differ significantly from those of the remaining subtypes. Demographic variables analyses Individual univariate analyses of variance yielded a significant effect for
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112 subtype on CA ( = 3.80, g <.0059), but not ISP SES (F^ = .40, g <.8452). Mean age is listed by subtype in Table 18. Interesting, children in Subtype 6, along with Subtype 4, were significantly older than children in the remaining clusters. CPQ, BPC, and LJST analysis There were no significant differences among the subtypes on measures of personality, behavior, or social adjustment. A MANOVA on the 14 factors of the CPQ was insignificant ( HotellingLawley Trace = 2.01, F approximation ico .87, g <.7331 ), as was the MANOVA / U f X 3 ^ on the 4 factor scores of the BPC (HotellingLawley Trace = .75, F approximation 20 gg = '^2, g <.8844). A MANOVA on the most and least preferred weighted scores of the LJST yielded insignificant results as well (HotellingLawley Trace = .70, F approximation g g = 35, g <.8876). Summary Cluster analysis of the 4 neuropsychological variables resulted in the identification of 6 male learning disability subtypes which were significantly differentiated from each other on the basis of neuropsychological test scores, IQ, and age, but not achievement, socioeconomic status, or behavioral, social, or personality variables. Subtypes emerged which could be categorized by specific nonverbal impairments, global nonverbal impairment, or mixed language and nonverbal impairment. In addition one subtype showed no evidence of impairment in any area tested.
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113 TABLE 18 Mean OLMAT IQ Scores and CA for Male Learning Disability Subtypes Subtype OLMAT Number N** IQ CA 1 9 102 .56AB 128 22A 2 13 95 .9 2ABC 125 85A 3 12 105 .73A 127 92A 4 6 94 .OOBC 134 33B 5 5 91 .50BC 127 40A 6 6 90 .67C 134 33B TOTAL 51 98 .38 128 90 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05 ) **Because of missing data, IQ scores are based on 48 subjects. The correct N for Subtype 2 is 12, for Subtype 3 is 11, and for Subtype 5 is 4.
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114 Female Sample Analyses Identification of the learning disabled subsample Because the addition of reading comprehension measure to the WRAT clustering variables resulted in an overident i f icat ion of learning impairment in the female sample. Phase II analysis was restricted to the LD subsample identified by the WRATonly achievement solution. The 3 clusters which comprised the learning disability subsample. Subgroups 8, 9, and 10, represented specific arithmetic disability, specific reading disability, and nonspecific learning disability subgroups Neuropsychological test cluster analysis Although 58 children were identified in the female learning disability subsample, missing data was present in 14 cases. Therefore 44 subjects were clustered on the basis of their neuropsychological test scores. A 5 cluster solution emerged from the data. When subjected to iterative partitioning, only 3 children (6.82%) were relocated. Therefore the 5 cluster solution was accepted as optimal. A multivariate analysis of variance on the 4 neuropsychological test scores yielded a significant main effect for subtype ( Hotel 1 ingLawley Trace = 9.18, F approximation = 19.80, g <.0001). Individual analyses of variance revealed significant effects for subtype on WISC Similarities ( F^ ~ 15.63, g <.0001), Verbal Fluency (F. = 22.29, g <.0001) Recognition
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115 Discrimination ( ^9 ^ 10.68, g <.0001), and VisualMotor Integration (F^ ^ 18.48, p <.0001). Mean neuropsychological test scores are listed by subtype in Table 19. Post hoc comparisons of means (Duncan's Procedure, q <.05) revealed the female subtypes to be more unique in terms of Factor II abilities than was found in the male analysis. Cluster means were significantly different in all but 1 case for VF and 3 cases for SIM. VMI means were not significantly different in 5 instances and RD means were not significantly different in 6 instances. Mean scores for the total sample were close to the standardization norms in all areas except VMI, which again fell just short of being significantly low. Standard score transformation analysis The scores were converted to a normalized scale, based on standardization norms, having a mean of 0 and a standard deviation of 1. Female norms were used when available, and age was based on the learning disability subsample mean. Because Subtype 5 contained only 2 children and evidenced extreme scores in 3 out of 4 areas, it was considered an outlier cluster and is not represented. Even so, the Phase II cluster analysis classified 95% of the children in the female sample, with the number of subjects in the remaining clusters ranging from 8 to 13. Figure 9 shows 4 distinct profiles for female LD subtypes. Subtype 1 has high average to superior Factor II (VF and SIM) abilities, an average level RD score, and a VMI
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116 TABLE 19 Mean Neuropsychological Test Scores for Female Learning Disability Subtypes. Subgroup Number N SIM* VF* RD* VMI* 1 8 14 .25A 31 .758 20 .888 90 .388 2 12 10 .08C 19 .33D 17 .75C 94 .428 3 13 12.15B 26 .08C 21 .62AB 115. 85A 4 9 9.22C 25 .56C 21 .33A8 81 .788 5 2 8 .50C 47 .OOA 23 .50A 87 .008 TOTAL 44 11 .20 26.11 20.45 97.09 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05 )
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117 SIM VF RD VMI Figure 9. Female learning disability subtypes based on neuropsychological test clustering variables; mean based on standardization norms.
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118 mean that falls just short of being significantly low. Subtype 2 has an average SIM score, but significantly low VF and RD means; VMI again falls just short of being significantly low. Subgroup 3's scores all fall within the average range, although SIM and RD means are moderately high. Subtype 4 is distinguished from Subtype 1 on the basis of its average to somewhat below average Factor II scores; the VMI score is significantly low. The neuropsychological profiles of the 4 female LD subtypes are strikingly similar to 4 of the 6 male LD subtypes. Subtypes 1 and 4, like Male Subtypes 1 and 2, appear to represent two Specific VisualMotor Impairment Subtypes, distinguished by their level of language development. Female Subtype 2 shows the same pattern as Male Subtype 5, but its VF score is significantly low; as such it appears to present a Mixed Specific Language (Naming) and Global VisualPerceptualMotor Impairment Subtype. Subtype 3 in both samples is consistent with an Unexpected Subtype by virtue of its lack of impairment. WHAT analysis A multivariate analysis of variance on the WRAT subtest scores yielded no significant overall effect for subtype ( Hotell ingLawley Trace = .39, F approximation ^2 iqj ~ p <.3155). OLMAT IQ analysis A univariate analysis of variance disclosed a significant effect for subtype on OLMATIQ (F^ = 8.64, g <.0001). Mean IQ scores are listed by subtype in Table 20. Only the outlier cluster has an IQ
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119 TABLE 2 0 Mean OLMAT IQ Scores for Female Learning Disabil ity Subtypes Subtype OLMAT Number N 10 1 8 107 13A 0 Cm 9 99 78A 3 13 106 77A 4 8 99 25A 5 1 80 OOB TOTAL 39 103 00 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = 05 )
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120 which is significantly different from the others. With the exception of this discrepant score, all subtypes had 10 means which fell within the average range. Demographic variables analyses Individual ANOVA's failed to produce significant effects for subtype on either CA (F^ 3g = .79, 2 <.5416) or ISP SES ( ^9 112, 2 < .3592 ) CPQ, BPC, and LJST analyses As was found in the male LD subsample, there were no significant differences among female LD subtypes on measures of personality or social functioning. A MANOVA on the 14 CPQ factors was insignificant (HotellingLawley Trace = 1.40, F approximation = .61, p <.9769), as was the MANOVA on the LJST scores (HotellingLawley Trace = 1.69, F approximation g ~ 1*69, g <.2068). Insufficient data prevented comparison of the subtypes on the BPC. Summary Cluster analysis of the 4 neuropsychological variables resulted in the identification of 5 female learning disability subtypes, one of which was dismissed as an outlier. The clusters were significantly differentiated on the basis of IQ and neuropsychological test scores, but not achievement, demographic variables, or measures of behavioral, social, or personality functioning. Subtypes emerged which could be categorized by a specific nonverbal impairment or a mixed language and nonverbal impairment. In addition, as was found in the male subsample analysis, one subtype showed no evidence of impairment in either area.
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121 Combined Sex Sample Analyses Identification of the learning disabled subsample Because the addition of a reading comprehension measure to the original achievement variables did not significantly contribute to the identification of an LD subsample, Phase II analyses were confined to the WRATonly achievement solution. Subgroups 4,5, and 6, representing specific arithmetic disability, specific reading disability, and nonspecific learning disability subgroups, were combined, for a total of 140 subjects in the combined sex LD subsample. Missing data was present in 28 cases, reducing the sample size to 112 subjects. Neuropsychological test cluster analysis A cluster analysis of the 4 neuropsychological tests scores resulted in a 4 cluster solution. Although several solutions were subjected to the relocation procedure the 4 cluster solution resulted in the fewest subject reassignments (17/112 = 15.18%). The number of children in each cluster ranged from 17 to 37. Therefore, in the absence of any outlier clusters, the analysis classified 100% of the children in the sample. A MANOVA on the 4 neuropsychological tests scores yielded a significant main effect for subtype (HotellingLawley Trace = 4.72, F approximation = 40.75, g <.0001). Individual ANOVA's showed significant effects for subtypes on SIM (F 3 ,108 = 9.73, g < .0001 ) VF ( F 3,108 43.45, Q < .0001 ) RD ( F 3,108 = 32.43, e <.0001), and VMI
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122 (fD TOO = 56.18, p <.0001). Mean neuropsychological test 3 1 U o scores are listed by subtype in Table 21. Post hoc comparisons of means (Duncan's Procedure, g <.05) shows the combined sex subtypes to be more unique than either the male or female LD subtypes. Cluster means were significantly different in all but 1 instance for VF 2 instances for SIM and RD, and 3 instances for VMI Again, the mean scores for the total sample were close to standardization norms for all tests except VMI, which fell just short of being significantly low. Standard score transformation analysis The scores were converted to a normalized scale based on standardization norms (Figure 10). Combined sex norms were used whenever available and age was based on the learning disability subsample mean. The profiles suggest 4 distinct subtypes. Subtype 1 falls within the average range in all areas, although RD is moderately high. Subtype 2 has superior Factor II abilities, average RD, and a significantly low VMI mean. Subtype 3 has an average SIM score, but falls significantly below average in other areas. Subtype 4 falls within the average range in all areas except VMI, which was significantly low. Subtypes 2 and 4, like Male Subtypes 1 and 2 and Female Subtypes 1 and 4, appear to represent to Specific VisualMotor Impairment Subtypes, distinguished by their level of language development. Subtype 3 is similar to Male Subtype 5 and Female Subtype 2; it seems to represent a Mixed Specific Language (Naming) and
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123 TABLE 21 Mean Neuropsychological Test Scores for Combined Sex Learning Disability Subtypes. Subgroup Number N SIM* VF* RD* VMI* 1 30 11 .208 23 .97B 21 .70A 127 .53A 2 28 12.57A 33 .43A 20.39B 92 .79B 3 17 10 .88BC 17 .82C 16 .77C 90.538 4 37 9 .97C 21 .62B 20 .84AB 89.41B TOTAL 112 11 .09 24 .63 20 .34 100 .63 *Means followed by the same different within variables. Alpha level = .05) letter are not significantly (Duncan's MultiRange Test,
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124 SIM VF RD VMI Figure 10. Combined sex learning disability subtypes based on neuropsychological test clustering variables; mean based on standardization norms
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125 Global VisualPerceptualMotor Impairment Subtype. The profile for Subtype 1 is consistent with a designation of Unexpected Subtype, like Male and Female Subtypes 3. WRAT analysis A multivariate analysis of variance on the WRAT subtest scores was insignificant ( Hote 1 1 ingLawley Trace = .11, F approximation g = 1.25, p <.2654). OLMAT IQ analysis An ANOVA disclosed significant a effect for subtype on OLMAT IQ (F^ = 6.13, p <.0008). Mean IQ scores are listed by subtype in Table 22. Subgroup 1 has a higher IQ score than the other clusters except Subtype 2. However all subtypes have an IQ mean which falls in the average range. Demographic variables analyses Individual analyses of variance failed to yield a significant effect for either CA (F^ 108 ^ I'O'^' e <.3656) or ISP SES (F^ = .75, g <.5268). A chisquare test revealed no significant sex 2 difference among the subtypes (X = 1.76, p <.624). CPQ, BPC, and LJST analyses Again, there were no significant differences among subtypes on measures of personality, behavior, or social adjustment. A MANOVA on the 14 CPQ factors was insignificant ( HotellingLawley Trace = .58, F approximation 2IQ ~ B <.1287), as was a MANOVA on the 4 BPC factor scores (HotellingLawley Trace = .26, F approximation ~ 86, g <.5898). A MANOVA also yielded insignificant results for subtype on the LJST scores (HotellingLawley Trace = .25, F approximation g 55 = 1.19, e < .3253)
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126 TABLE 22 Mean OLMAT IQ Scores for Combined Sex Learning Disability Subtypes Subtype OLMAT Number N 10* 1 28 106 .61A 2 26 101 .81AB 3 32 96.408 4 15 98 .008 TOTAL 101 101.13 *Means followed by the same letter are not significantly different within variables. (Duncan's MultiRange Test, Alpha level = .05)
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127 Summary Cluster analysis of neuropsychological test scores resulted in the identification of 4 combined sex learning disability subtypes, which were differentiated from each other on the basis of IQ and neuropsychological test scores, but not achievement, demographic information, or behavioral, social, or personality variables. Subtypes could be categorized on the basis of a specific nonverbal impairment or a mixed language and nonverbal impairment. Again an unexpected subtype emerged, which showed no evidence of impairment in any area tested.
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CHAPTER IV DISCUSSION Discussion of Hypotheses Hypothesis I; Naturally Occurring Achievement Subgroups Will Differ According to Pattern and Level for Relatively Unselected Male and Female Samples The results of the data analysis do not fully support Hypothesis I. Although differences did emerge in the profiles of the achievement subgroups for the male and female samples, the results are remarkable for similarities between the supposedly high and low risk groups. Male and female samples did not differ significantly in terms of achievement, intelligence or socioeconomic status. When clustered on the basis of WRAT subtest scores, both samples yielded a nonspecific learning disability subgroup and a specific reading disability subgroup. Pattern and elevation for the two learning impaired subgroups were highly similar in both samples. The nonspecific learning disability subgroups fell significantly below average in all academic skill areas tested, revealing a relatively flat profile. The profile for the specific reading disability subgroups showed an upward slope, with severely impaired reading skills, somewhat below average spelling skills, and adequate arithmetic skills. These same two profiles emerged as well 128
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129 when the two samples were combined and reclustered according to WRAT achievement. The results indicate a stable and reliable group of children who, regardless of sex, show evidence of being either uniformly impaired in all areas of achievement or specifically impaired in reading when compared with their peers. Children in both learning impaired subgroups tended to be less competent intellectually than their classmates. However, in none of the clusterings did either subgroup obtain an IQ mean which fell below the average range. Similarities between the male and female samples also extend to academically unimpaired subgroups. Both cluster analyses revealed one subgroup which showed superior academic skills in all areas tested, as well as one which was significantly high in reading and spelling, but close to average in arithmetic. Another subgroup showed the opposite pattern, that of average skills in reading and spelling and superior skills in arithmetic. Interestingly, the uniformly superior achieving subgroup did not emerge in the combined sex clustering on WRAT achievement variables. The counterparts of the other two subgroups appeared, but their relatively weaker skill areas were not as depressed as in the male and female clusterings. The emergence of a large group of average achievers in the combined sex cluster analysis may explain this difference. A major difference between the results of the male and female cluster analyses was in the emergence of a specific
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130 arithmetic disability subgroup only in the latter sample. This group showed reading and spelling achievement which fell close to average, but arithmetic skills which were significantly low. Although a similar pattern was found in the male sample, its arithmetic mean, while relatively depressed, fell well within the average range. This finding suggests that specific arithmetic disabilities may be a uniquely female phenomenon. Contradictory evidence is provided by the combined sex cluster analysis, which revealed an analogue subgroup that was only 55% female. However, this subgroup was less severely impaired in arithmetic, when compared with sample norms, and obtained a mean arithmetic score that was significantly higher than that in the nonspecific learning disability subgroup. In addition, the combined sex arithmetic disability subgroup represented a larger proportion of the total than its counterpart in the female sample. In any event, there seems to be a naturally occurring subgroup of females who, when compared with their female classmates, show evidence of severe impairment in arithmetic skill development despite adequate reading achievement, a finding which is not duplicated among males. This finding is somewhat unexpected. Although it is a commonly held belief that females have inferior mathematical abilities when compared with males, Meece & Parsons (1982) point out that sex differences on tests of quantitative skills do not appear with any consistency prior to the 10th grade. Indeed, in a
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131 survey of 1500 grade school children, Badian (1983) not only found a higher rate of mathematics (6.2%) than reading (4.9%) retardation, but a predominance of males, 2.32.5/1, in both groups. The results suggest that sex differences may appear earlier than previously thought in a specific subset of the population, although the cause, whether due to innate, maturational or socialization factors is unknown. Differences in incidence rates also distinguish the other two learning impaired subgroups in the male and female samples. The nonspecific learning disabilities subgroup comprised 9% of the female sample, but 13% of the male sample. Similarly, the specific reading disability subgroup represented 17% of the female sample, but 22% of the male sample. Incidence rates in the combined sex clustering fell inbetween, with the nonspecific learning disability subgroup representing 10%, and the specific reading disability subgroup representing 20% of the total sample. The overall rate of learning disabilities, whether global or specific, was similar in the sex segregated samples. The learning disability subsample comprised 35% of the male sample and 39% of the female sample, a surprisingly high incidence. Even so, the combined sex learning disability subsample was even larger, comprising 47% of the sample. One possible reason for the seeming overrepresentat ion of children in the learning disability subsample may be the choice of classification method, which permitted the identification of specific as well as nonspecific learning
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132 disability groups. Previous investigations have focused almost exclusively on reading problems, and have used the terms reading disability and learning disability almost interchangeably. There has been little attention given to arithmetic disabilities until recently, possibly due to the tendency to confine investigations to predominantly or exclusively male populations. Therefore, sampling biases as well as a priori theoretical constraints, may have resulted in incidence estimates which have been misleading. A second factor which may be pertinent in the consideration of incidence rates concerns the use of sample versus population norms. Although cutoffs were purposely avoided in order to allow the identification of naturallyoccurring subgroups of disabled learners, it seems appropriate to consider level of achievement relative to grade placement. The sample as a whole was unusual for its deviance from standardization norms, in that mean reading and spelling scores fell considerably above the standardization mean (1.35 and .69 years, respectively), while the mean arithmetic score fell onehalf year below. In addition, there was no significant difference between the male and female samples, although the latter' s mean scores in reading and spelling exceeded those of the former. As a result of the apparently high level of reading competency in the sample, subgroups which were significantly delayed in reading, according to sample norms, do not appear severely impaired when compared with the standardization norms.
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133 Indeed, the mean grade equivalent score for reading fell less than one year below grade level in both the specific reading disability and nonspecific learning disability subgroups in all three (male, female and combined sex) solutions. Therefore, it is possible that there has been an overidentif ication of learning disabilities in the present study. In fact, one may conclude that there are no naturally occurring learning disability subgroups in any of the three samples, inasmuch as no subgroup meets a standard cutoff criterion of being more than two years below grade level in reading, spelling or arithmetic. Although it is possible that the unusual pattern of achievement in the sample as a whole reflects differences between local educational standards and those of the national standardization sample, it is more likely that outdated test norms (Jastek & Jastek, 1965), which were used in order to permit comparisons with previous research efforts, have provided a distorted picture of achievement relative to grade placement in the current sample. The combination of high incidence rates but relatively low levels of impairment in the learning disability subgroups suggests that the analysis resulted in the identification of more mildly disabled groups of learners. The 30% rate of specific or nonspecific reading disability that was found in the combined sex sample far exceeds previous estimates which have ranged around 10% (Critchley, 1970; Rutter, 1978). Finucci & Childs (1981) reported that 10% of their randomlydrawn school subjects.
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134 selected only with regard for (average) ability, showed evidence of severe reading retardation, defined as an achievement ratio of less than .80. However an additional 17% were considered to have a mild impairment by virtue of quotients which fell between .81 and .90. The total incidence rate of mild or severe reading problems corresponds closely with that found in the present study. That the more severely and more mildly impaired groups failed to remain distinct in the clustering solution suggests more similarities than differences between them. However the tendency of the clustering process to combine these two groups limits the generalization of results to other samples which are specifically selected for severe academic impairment. External validation data, drawn from school records, provides support for the appropriateness of the clustering solution. In the combined sex sample, all children who had been placed in an exceptional education learning disability program were members of the learning disability subsample. Of the schoolidentified learning disability students, 65% fell in the learning disability subgroup, 27% fell in the reading disability subgroup and 9% fell in the arithmetic disability subgroup. In addition, the combined sex learning disability subsample included 83% of the children who were provided with remedial assistance through a federallyfunded program at school. Children who were served by this program fell at least one year below grade level in reading or math.
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135 yet were not sufficiently delayed to be considered eligible for exceptional education placement. Further support of the adequacy of the solution is provided by the reliability of the disability subgroups that were identified in the present study. Reading disabilities, both with and without other areas of academic impairment, have long been the focus of investigation in learning disabilities research. Arithmetic disabilities have more recently been recognized, and have begun to generate considerable research interest as well. In addition, all three profiles are clinically meaningful to professionals who work with children who have learning problems Although sample norms appear more appropriate for purposes of overall interpretation of results, grade equivalent scores derived from standardization norms are useful for comparing relative achievement levels among subgroups, both within and between the samples. In this manner, it becomes apparent that, although the nonspecific learning disability subgroup obtained the lowest mean scores for all three WRAT subtests, it was not significantly more delayed in reading than the specific reading disability subgroup in any of the three samples, nor was it significantly more impaired in arithmetic than the specific arithmetic disability subgroup in the female sample. A comparison of learning impaired subgroups in the male and female samples reveals predominantly lower achievement levels in the former group. The nonspecific learning
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136 disability subgroup obtained mean scores which were onehalf year or more lower in the male than female sample in all areas tested. Similarly, the specific reading disability subgroup was relatively more delayed, although by less than onehalf year, in the male than female clustering in both reading and spelling. Because of this tendency, it is not surprising that males outnumbered females by more than twotoone in the combined sex nonspecific learning disability subgroup. Achievement levels fell inbetween those of the analogue subgroups in the sex segregated samples. The specific reading disability group was 55% male. Achievement levels again fell inbetween for reading and spelling; the arithmetic mean was essentially the same as in the male solution. As previously noted, the combined sex arithmetic disability subgroup was 55% female. Although its reading mean was somewhat lower than in the female solution, spelling and arithmetic levels were essentially unchanged. The sex ratio in each of these subgroups is considerably below that previously reported. Rutter (1978)found a 3.5/1 maletofemale ratio for reading disability, Critchley (1970) a 4/1 proportion, and Benton (1975) a 6/1 ratio. Satz (1982) reported a 4/1 male predominance in his clinic sample of children referred for reading or learning difficulties. However he noted that the female subsample had a higher proportion of neurological problems and borderline intelligence, leading him to theorize that selection bias in referral procedures
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137 invalidated the finding. Finucci & Child's (1981) report lends support to this hypothesis. Although they found a 3/1 to 15/1 male predominance in the enrollment in private schools for dyslexic children, their own findings, based on a survey of a relatively unselected school population, suggested a much lower sex ratio. The maletofemale proportion was 1.9/1 for a group of severely retarded readers and 1.2/1 for mildly retarded readers. Present results also suggest a more even distribution between the sexes for learning difficulties than has been previously accepted External validation data revealed differences in rate of identification for special services by the local school district, which seemed to vary as a function of sex as well as type of disability. Overall, males were more likely to be provided with special help, which in turn was more likely to take the form of multiple interventions. Both males and females with a specific arithmetic disability tended to be unserved despite the existence of a remedial math, as well as remedial reading, program in the district. Despite substantial representation in all three subgroups in the combined sex learning disability subsample, no females were placed in a learning disabilities program at school. Half of the members of the nonspecific learning disability subgroup in the female sample, and a slightly higher proportion of female members of the analogue subgroup in the combined sex sample, received no special help at school. In
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138 contrast, only 20% of males in the same subgroup in the male and combined sex solutions were unserved. Of the four out of nine female members of the combined sex learning disability subgroup that were identified by the school, three were provided with remedial instruction and one received speech therapy. Sixteen out of twenty males in the same subgroup were identified by the school, and twelve out of that number were provided with multiple interventions. Seven male members were enrolled in a learning disabilities program, eight received remedial assistance (two presumably prior to their learning disabilities placement) five received speech therapy, and twelve had been retained. To the district's credit, no child was retained who did not also receive some form of special assistance. However, retention appeared to be an intervention which tended to be reserved for males. Although 44% of the combined sex learning disability subgroup had been retained, none were females; out of 26 children who had experienced grade failure in the entire combined sex learning disability subsample, only 6 were female. The proportion of reading disability subgroup members who received no special services was fairly even in the male and female samples, ranging from 58 to 67% when retention was not considered. The proportion of arithmetic disability subgroup members who were unserved was substantially higher. Eightythree percent of males and 75% of females in the combined sex arithmetic disability
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139 subgroup, and 84% of the female arithmetic disability subgroup, received no special help at school. Lastly, differences between the male and female samples emerged during cluster analysis. The male sample appeared to represent a less complex data set than the female sample. The optimal solution of the cluster analysis of WRAT subtest scores was clearly indicated in the male sample, and statistical data as well as inspection of individual cluster profiles revealed that valuable information would be lost if the clustering process continued after that point. The number of clusters in the optimal solution was smaller than in the female sample, and the solution itself appeared quite stable, judging from the very small number of subject reassignments during the relocation process. The optimal solution for the female sample was not nearly so obvious, and solutions with fewer numbers of clusters were found to be unstable. The solution which was ultimately accepted as optimal was not only larger, in terms of number of clusters, but less stable than in the male sample. This finding undoubtedly reflects the relatively lower intercorrelat ions among achievement variables in the female than male sample, which resulted in the increased incidence of specific learning disability subgroups in the former group when clustered on the basis of three as well as four achievement variables
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140 Hypothesis II; The Inclusion of a Reading Comprehension Measure Along with Previously Used Measures of Reading Word Recognition, Spelling and Arithmetic Computation Will Not Significantly Affect the Composition of the Achievement Subgroups The addition of a reading comprehension measure to the WRAT subtests appears to have substantially increased the complexity of the data structure in the male and combined sex samples. The added dimensions to the data set resulted in optimal solutions with a larger number of clusters in these two groups. In addition, diminished stability of the optimal solution was evidenced in poor initial assignment of subjects to the clusters, which was subsequently corrected by iterative partitioning. Following this relocation procedure, the solutions for the cluster analysis of the 3 and 4 achievement variables were quite similar for both the male and combined sex samples. The inclusion of a reading comprehension measure, along with measures or reading word recognition, spelling and arithmetic computation, did not significantly affect the composition of academically impaired subgroups in either the male or combined sex samples, thus confirming Hypothesis II for these two groups. The number of children in subgroups which were identified as showing evidence of delayed achievement was somewhat smaller in the solutions based on the cluster analysis of WRAT and GMRT variables as opposed to that of WRAT subtests alone. in the male sample, the largest change was in the subgroup which showed a nonsignificant tendency toward an arithmetic disability; the
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141 corresponding subgroup was smaller and uniformly more delayed, although its arithmetic mean again fell short of significance. Nevertheless, onetoone correspondence between analogue subgroups in the two clusterings was high. Only 8% of children in the three identified subgroups in the WRATGMRT solution changed their subgroup membership in the solution based on WRAT alone; in addition, the few reassignments that did occur all remained within those three subgroups. Similarly, although onetoone correspondence between subgroup membership was not as high in the combined sex clusterings, all but one subject in the learning disability subsample of the solution based on four achievement variables was identified by the three variable cluster analysis. In contrast, the learning disability subsample was larger in the WRATGMRT solution than that in the WRATonly solution for the female sample. The increased incidence was due to the emergence of a new specific learning disability subgroup whose significant impairment in reading comprehension had not been detected by the cluster analysis of WRAT subtests alone. However, the solution was rejected as inappropriate, inasmuch as the number of children identified as academically impaired represented almost twothirds of the sample in a group previously considered to be at low risk for developing learning problems. Therefore, the inclusion of a reading comprehension measure with the WRAT subtest scores did not seem to aid in the identification of children with learning
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142 disabilities in male, female or combined sex samples. Nevertheless, it seemed to have descriptive utility in distinguishing those reading disabled students with oral reading dysfluency from those with a more general impairment involving word recognition as well as comprehension in the combined sex sample. The finding that reading disabilities may take different forms in males and females, in that specific reading disability subgroups in the latter sample involved impairments in either oral reading or comprehension while the former sample revealed only one subgroup with delays in both areas, is intriguing and warrants further invest igat ion Hypothesis III: Characteristics of the Neuropsychological Subtypes of Learning Disables Males Will Be Similar to Those Found by Satz and Associates, But Will Differ from the Female Subtypes A comparison of present achievement subgrouping results with the solutions in previous investigations (Darby, 1978; Satz & Morris, 1981; Van der Vlugt & Satz, 1985) reveals similarities as well as important differences. The Florida, Dutch and present studies have all utilized white male samples of comparable age and grade placement. Sample size was somewhat larger in the two previous investigations, ranging from 234 to 236 subjects versus 150 males in the present one. Coverage was high in all 3 studies, in that 98 to 100% of the subjects were classified as a result of cluster analysis of WRAT subtest scores. However, while the two previous studies revealed nine achievement subgroups (after outlier clusters had been discounted), present
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143 results indicated a six cluster optimal solution. Significant differences were found between subgroups on measures of achievement in both the Florida and Pennsylvania solutions; however, as Satz and Morris (1981) have commented, this finding is not unexpected given the use of a classification method which was designed to form homogeneous clusters."'" Post hoc comparisons of subgroup means in the two solutions reveals the same number of instances in which they were not significantly different for each WRAT subtest, suggesting that the uniqueness of the subgroups was not sacrificed in the smaller solution. Subgroups continued to be significantly differentiated on the basis of intelligence and socioeconomic status; this finding is important in that the present study responded to criticisms of the Florida investigation by utilizing more formal, standardized assessments of these two variables. The only area in which the two solutions differed involved chronological age, in that in the present study a significant effect was found for subgroup on this variable, while no such effect was found in the Florida solution. Interestingly, there was no significant effect for either age or SES in the female solution. The presence of an age effect in the male solution most likely reflects the increased incidence of grade retention in the male as compared to female samples. 1. Comparisons with the Dutch study are not possible because similar data was not reported.
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144 However these two factors suggest that male learning disabled students may be relatively more academically impaired, when compared with chronological grade level, than their female counterparts. Consequently, males in academically impaired subgroups, particularly those in the nonspecific learning disability subgroup, tend to be older, to be less competent intellectually and to come from a less advantaged background. Similarly superior achieving males show the opposite characteristics. The majority of cluster profiles found in the Florida study have been replicated by the Dutch and/or present investigations. When compared with local norms, all three solutions yielded a subgroup which scored significantly above average in all achievement areas, as well as at least one subgroup whose achievement was uniformly and significantly low. The Dutch study revealed three such delayed subgroups, representing a combined total of 12% of the sample. Similarly, the nonspecific learning disability subgroup represented 14% of the Florida sample and 12% of the Pennsylvania male sample. The Pennsylvania and Dutch solutions found a subgroup which had above average reading and spelling means, and a superior arithmetic score. Two subgroups in the Florida sample obtained significantly high arithmetic means, but were distinguished by their level of reading and spelling achievement which was average in one subgroup and high average to superior in the other. A subgroup with superior reading and spelling skills but
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145 average level arithmetic skills was found in the Florida and present solutions. The Florida and Dutch studies also revealed a subgroup with high average reading and spelling scores and an average level arithmetic score. These same two solutions included an average achieving subgroup as well. The only specific disability subgroup that emerged in the Florida and Dutch studies involved arithmetic, which fell just short of being significantly low, while reading and spelling were average; this subgroup represented 5% of the former and 11% of the latter samples. The subgroup in the present study which showed a nonsignificant tendency toward an arithmetic disability appears to fall inbetween the average and specific arithmetic disability subgroups in the other two studies and contains 28% of the sample. Lastly, a specific reading disability subgroup emerged from the Pennsylvania sample, a finding which was not duplicated in the other two samples. Instead, both the Florida and Dutch solutions contained a subgroup which obtained nonsignif icantly low scores in all three achievement areas. This mild nonspecific learning disability subgroup represented 24% of the Florida and 17% of the Dutch samples. The specific reading disability subgroup contained 22% of the Pennsylvania male sample. The learning disability subsample comprised 35% of the Pennsylvania sample, 40% of the Dutch sample and 38% of the Florida sample. This subsample contained at least one severe nonspecific learning disability subgroup in all three samples. In addition, both
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146 the Florida and Dutch studies included a mild nonspecific learning disability subgroup. Although the Dutch studyidentified a specific arithmetic disability subgroup for further investigation, it was omitted from subsequent analyses in the original Florida study (its inclusion would have raised the incidence of learning disabilities to 43% in the Florida sample). The male learning disability subsample in the present study included a specific reading disability subgroup along with the severe nonspecific learning disability subgroup; no specific arithmetic disability or mild nonspecific learning disability subgroups were represented Hypothesis III, involving the replication of learning disability subtypes, was partially confirmed by the results of the present study. Cluster analysis of the male learning disability subsample on the basis of its neuropsychological test scores resulted in a six cluster solution in both the Florida and present studies."'' The six cluster solution was clearly indicated in the present analysis, and appeared quite stable by virtue of its small number of subject reassignments representing 6% of the learning disability subsample, during iterative partitioning; Morris, Blashfield and Satz (1981) report that less that 15% of subjects in the 1. A five cluster solution was intitially reported for the Florida learning disability subsample (Darby, 1978). However, Satz, Morris and Darby (1979) reported that subsequent analysis revealed that a six cluster solution provided a better fit to the data.
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147 Florida subsample were placed in different clusters as a result of the relocation procedure. Coverage was high in both cases; all subjects were classified into primary clusters in the present study and only one outlier cluster of three subjects, representing 3% of the subsample, was found in the Florida solution. The Dutch study found a 4 and 7 cluster solution to be highly replicable, but reported only 6 subtypes from the latter case even though the missing cluster of 10 subjects is too large to be considered an outlier. All three studies report a subtype which is characterized by global visualperceptualmotor impairment. This cluster comprises 10% of the Pennsylvania subsample, 16% of the Dutch subsample, and 26% of the Florida subsample. The profiles for this cluster are highly similar in the Pennsylvania and Dutch solutions, in that the mean score for Verbal Fluency falls just short of being significantly low, suggesting that this subtype may show a tendency toward a mixed verbal and perceptual deficit. A second cluster profile in the Dutch solution which bears a strong resemblance to one in the present study involves a mixed deficit as well. This subtype, which represents 12% of the Pennsylvania subsample and 16% of the Dutch, shows a specific impairment on the WISC Similarities subtest and the Beery Test of VisualMotor Integration, although these scores fall short of significance in the present study. A similar mixed deficit subtype was not found in the Florida
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143 solution. However, the "unexpected" subtype of the Florida study, which was not found in the Dutch solution, was nevertheless, replicated in the present one. This cluster contained 13% of the Florida learning disabled subjects and 24% of those in the present study. Several subtypes which were replicated by the Dutch study were not represented in the present solution. The profile for a subtype with a general verbal deficiency was highly similar in the Florida and Dutch solutions, representing 30% and 12%, respectively, of the corresponding learning disabilty subsample, but was not present in the Pennsylvania results. In addition, a general deficiency subtype, containing 11% of both solutions, was not found in the present study. A specific verbal deficiency subtype, showing evidence of significant impairment only on the Verbal Fluency Test, was identified by the Florida study but not represented in either the Dutch or present solutions. Even so, this subtype is the only one from the original study that has not been replicated by either the crosscultural or present investigations. Subtypes which are unique to the present investigation all involve specific impairments of Factor I (visualperceptualmotor) tests. Indeed, 65% of learning disabled males in the Pennsylvania sample showed evidence of significant difficulty in this area. in contrast, only 37% of the Florida subsample and 31% of children in reported clusters in the Dutch subsample fell in subtypes which obtained severely low scores on
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149 either RecognitionDiscrimination or VisualMotor Integration. A sharper contrast is found for Factor II abilities. Fiftyfive percent of the children in the Florida subsample and 82% of those in reported clusters in the Dutch subsample showed evidence of some type of significant language difficulty on the neuropsychological tests. No subtype in the present study obtained a mean score which was significantly low on either WISC Similarities or Verbal Fluency. The finding of apparent overrepresentation of visualperceptualmotor deficiencies and underrepresentat ion of language difficulties in the present study most likely reflects the different comparison groups which were used in the three investigations. Sample norms were available for neuropsychological as well as achievement tests in the Florida Longitudinal Project (Morris, Blashfield & Satz, 1981). Van der Vlugt and Satz (1985) report that neuropsychological test data was collected for a normal control group as well as the learning disability subsample in the Dutch study. In absence of either sample norms or a normal control group, the present study interpreted results of the Phase II cluster analyses according to standardization norms. However, these different groups are not necessarily comparable. For example, although the learning disability subsample mean approximated the standardization mean for three of the neuropsyscholog ical tests in the present study, the mean score for VMI fell just short of
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150 being significantly low. The mean VMI score for the Florida learning disability subsaraple was similarly depressed when compared with the standardization norm, but only slightly below average when compared with the sample mean. Consequently, while three subgroups were found to have significant impairment in this area in the present study, only one was identified by the Florida study. When current results are interpreted according to Florida population norms, several changes occur in subtype categorization. Subtype 1 continues to show evidence of specific visualmotor impairment, but its VMI score no longer reaches significance. Subtype 2, previously considered as another specific visualmotor impairment subtype, now appears to represent a mixed deficit by virtue of its severely depressed Verbal Fluency as well as VMI scores. Subtype 3 continues to be consistent with an "unexpected" subtype, although its VF mean is relatively low; in addition, the profile for this cluster is similar to that of the specific verbal deficiency subtype in the Florida study. Subtype 4 appears to represent an "unexpected" subtype as well, even though it was previously considered to have a specific visualperceptual impairment. Subtype 5, previously classified as a global visualperceptualmotor impairment subtype, now shows evidence of a mixed deficit in a severely depressed VF mean and Factor I scores which fall short of significance. In contrast. Subtype 6 no longer appears to represent a mixed deficit
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151 subtype; instead its profile, which is similar to the general verbal deficiency subtype in the Florida study, suggests an analogue, although nonsignificant, subtype in the present investigation as well. Therefore, when interpreted according to Florida population norms, present data yields increased indications of language difficulties. However, only clusters representing mixed deficits obtain significantly low scores on verbal tests, so that the results do not in fact replicate either the specific or general verbal deficiency subtypes found in the Florida analysis. In addition, no global deficiency subtype is represented. Finally, the percentage of children (35%) who show evidence of significant difficulty in languagerelated areas continues to fall below that identified in the two previous studies. Perceptual deficits are underrepresented as well: no cluster has a RD or VMI mean that falls significantly below the mean for the Florida population. Alternately, both Florida and Pennsylvania subtyping solutions can be compared according to standardization norms. A global visualperceptualmotor deficiency subtype continues to be common to both solutions. A specific visualperceptual impairment subtype emerges as well from both analyses; however the analogue subtypes are differentiated by their Verbal Fluency score which is significantly high in the present study, but somewhat below average in the Florida results. The previously labeled Unexpected Subtype in the Florida solution evidences a
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152 nons igni f icantly low VMI mean when compared with standardization norms. In addition, the profile for this cluster is more similar to the specific visualmotor impairment subtype than the unexpected subtype in the present solution. The last two subtypes, which are not replicated by present results, involve mixed or global deficits. One cluster falls significantly below the standardization norm in all areas except Verbal Fluency, which is nevertheless nearly so. The other has significantly depressed scores on all four neuropsychological tests, but seems relatively more impaired in visualspatial abilities. When interpreted according to standardization norms, neither the Florida nor Pennsylvania solutions yield a specific or general verbal deficiency subtype. Nevertheless, 42 percent of the Florida learning disability subsample shows evidence of significant difficulty in languagerelated areas. What is more striking is the incidence of significant nonverbal impairment, which reaches 83 percent in the Florida solution when the results are interpreted in this manner. Interestingly, all three of the subtypes which were replicated involve specific or global visualperceptualmotor deficits. Therefore, similarities exist between several learning disability subtypes identified by the Florida and present studies. However, the particular subtypes that were replicated depend on which norms were used. Standardization norms appear more appropriate for purposes of interpretation of neuropsychological than achievement test data, in part
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153 because differing educational standards would presumably have a less direct effect on test results in the former than latter areas. In addition, the total sample as well as learning disability subsample was found to have at least average intelligence when compared with national norms in both studies. When the results of both investigations are interpreted according to standardization norms, three subtypes, involving specific visualmotor impairment and global visualperceptualmotor impairment, appear to have been replicated. However, because subtyping results were compared with sample norms in the Florida study, the first two of the above subtypes were identified as specific language impaired and unexpected, respectively. The learning disability subsamples were not comparable in terms of neuropsychological test performance in the two studies. Although the mean scores for the Pennsylvania subsample fell close to the standardization mean for three out of four tests, the Florida subsample approximated the standardization mean only in Verbal Fluency. WISC Similarities fell onehalf, and Recognition Discrimination nearly three, standard deviations below the standardization norm. Beery VisualMotor Integration was nearly one standard deviation low in both studies. Indeed, the present learning disability subsample was more similar to the Florida sample than subsample in mean neuropsychological test scores. In fact, it exceeded the Florida sample for both SIM and RD, while VF and VMI scores fell approximately
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154 halfway between the Florida sample and subsample means. Even so, the sample distribution, as well as that of the subsample, deviated considerably from the standardization norms, and interpretation of present results using Florida norms did not prove useful. Because of this finding, continued use of sample norms does appear warranted for purposes of comparison of corresponding subsample clustering results. Such comparisons have previously yielded clinically recognizable profiles, many of which have been replicated by the crosscultural research, also interpreted according to sample norms. It is interesting that the one subtype in the Florida solution which was not replicated by the Dutch study, nevertheless emerged from the present solution. In addition, this "unexpected" subtype appeared when present results were interpreted according to standardization norms, even though the analogue cluster in the Florida study disappeared when compared with the same norms. However, it is possible that an unexpected subtype would not have emerged from present data if sample norms had been available for purposes of comparison. Inasmuch as the learning disability subsample was uniformly depressed in neuropsychological test performance when compared with the total sample in the Florida investigation, there is a suggestion that both Florida and standardization norms, the latter with the possible exception of VMI, may underestimate sample means for the present study. Although speculation, the depression in cluster profiles that would have resulted
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155 may have yielded subtypes with specific language or global impairments, neither of which appeared in the present study when interpreted according to standardization norms. The second part of Hypothesis III, involving differences between male and female learning disability subtypes, was predominately disconfirmed by the results of the present study. As in the analysis of achievement variables, clustering solutions based on neuropsychological variables are strikingly similar for the two groups. Although a 5 cluster solution emerged from the female data, versus 6 in the male results, both solutions were judged stable; comparable rates of subject reass ignments (6 and 7%, respectively) were obtained during iterative partitioning. Both solutions were significantly differentiated on the basis of neuropsychological test scores and IQ, but not achievement or socioeconomic status. The clusters were more unique in the female solution with regard to verbal abilities; the number of instances in which cluster means did not differ significantly dropped from 5 to 1 in WISC Similarities, and 7 to 3 in Verbal Fluency between the male and female results. One cluster in the female solution contained only two members and was classified as an outlier, thus reducing coverage to 95% as compared with 100% in the male analysis. However, all four primary clusters in the female solution found counterparts in the male results. Both solutions yielded two specific visualmotor impaired subtypes which were differentiated by their level of
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156 language development. In the female analysis, significant differences were found between the two clusters on both WISC Similarities and Verbal Fluency; male differences reached significance only on the latter test. The profiles for Male Subtype 5 and Female Subtype 2 were similar, with three out of four mean scores being significantly low or falling just short of it. This cluster was considered to represent a visualperceptualmotor impairment subtype with a tendency toward mixed deficiency in the male solution, while primary identification for the analogue female subtype was in terms of the mixed impairment. The last cluster which was common to both solutions was an unexpected subtype, showing a similar profile in terms of pattern and elevation in both studies. The two subtypes which were unique to the male solution involved a mild mixed deficit and a specific visualperceptual impairment subtype. Interestingly, these two clusters, which contained children who were significantly older than the others, were not represented in the combined sex solution either, inasmuch as the four clusters that emerged were analogous to the subtypes which were common to the individual male and female subtyping solutions. Combined sex subtypes were not significantly differentiated on the basis of gender, chronological age, socioeconomic status or achievement. Only IQ and neuropsychological measures were found to yield a significant effect for subtype.
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157 Hypothesis IV; Subtype Characteristics Will Differ for Overall and Specific Learning Impaired Subgroups Although separate cluster analyses of specific and nonspecific learning disability subgroups were prevented by the relatively small size of these achievement clusters, examination of subgroup distribution among the learning disability subtypes tended to support Hypothesis IV. Subtype characteristics appeared to be differentially represented among the three identified subgroups in all three solutions; however this finding can only be considered a tendency inasmuch as the results support the heterogeneity of all 3 learning disability subgroups. The nonspecific learning disability subgroup was consistently most highly represented in the verbally depressed specific visualmotor impairment subtype. This cluster contained 39% of the male nonspecific learning disability subgroup, 38% of the same subgroup in the female solution and 48% of its counterpart in the combined sex solution; in addition, the same tendency held true for both male and female members of the combined sex subgroup. Interestingly, the verbally advanced specific visualmotor impairment subtype contained few subjects from the nonspecific learning disability subgroup. In fact, not one subject from the male nonspecific learning disability subgroup was a member of this subtype, even though they were fairly evenly distributed among the remaining subtypes. In the other two solutions the mixed specific language and global visualperceptualmotor impairment subtype accounted for the next highest share of the subgroup, representing 31%
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158 of the female and 22% of the combined sex nonspecific learning disability subgroup. Inasmuch as these two subtypes also obtained the lowest mean scores on the two language measures, it appears that children with a nonspecific learning disability may show an increased tendency toward a mixed or generalized rather than selective cognitive deficiency in information processing. This hypothesis is supported by the male subtyping solution as well. When the distribution of scores is compared with subtype instead of subgroup, it becomes apparent that the male learning disability subgroup is disproportionately represented among the mild mixed and global visualperceptualmotor impairment subtypes, the latter which is the counterpart of the (severe) mixed impairment subtype in the two other solutions, as well as the specific visualmotor impairment subtype. Although the nonspecific learning disability subgroup comprised 35% of the male learning disability subsample it represented 50%, 60% and 54%, respectively, of these three subtypes. Children in the specific reading disability subgroup evidenced consistently high representation in the unexpected subtype. This cluster contained 27% of male reading disabled subjects, 42% of female reading disabled subjects and 34% of the analogue subgroup from the combined sex clustering. In addition, the unexpected subtype contained the highest proportion of males as well as females in the combined sex reading disability subgroup. However, in the
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159 male sample, an equal number of subjects were placed in the languageadvanced specific visualmotor impairment subtype. When compared with subtype rather than subgroup, the male reading disability subgroup, while comprising 65% of the male learning disability subsample, represented 75% of the unexpected and 100% of the languageadvanced specific visualmotor impairment subtypes. In the female sample, the mixed impairment subtype accounted for the next highest share, representing 33% of the reading disability subgroup. Compared with subtype, the specific reading disability subgroup accounted for 67% of the mixed impairment and 77% of the unexpected subtypes, although it comprised only 55% of the female learning disability subsample. The combined sex reading disability subgroup showed secondary representations in both specific visualmotor impairment subtypes. Examination of cluster membership by sex revealed that although 33% of male disabled readers in the combined sex solutions were placed in the unexpected subtype, 30% were members of the verballyadvanced specific visualmotor impairment subtype. In contrast, although 35% of the females in the same subgroup were placed in the former subtype, 31% fell in the verballydepressed specific visualmotor impairment subtype. Therefore, while disabled readers of both sexes appear most likely to have no apparent cognitive deficiencies, an almost equal proportion of males show evidence of superior language development, adequate visual perception and significantly delayed development in
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160 visualmotor integration. Female disabled readers, in contrast to their male counterparts, appear to be more likely to show evidence of relatively delayed language development, with or without a significant visualperceptual deficit, in addition to visualmotor impairment. The specific arithmetic disability subgroup was not represented in the male learning disability subsample. Although this subgroup seemed to have a fairly even distribution across all clusters in the female subtyping solution, interpretation is hindered by small sample size. However, the outlier cluster was comprised of subjects only from this subgroup. The combined sex analysis revealed that a majority of arithmetic disabled subjects fell in one of the two specific visualmotor impairment subtypes, 35% in the languageadvanced cluster and 31% in the languagedelayed cluster. A majority (53%) of female members of the combined sex arithmetic disability subgroup fell in the former subtype, while the next highest representation (33%) was in the latter. However, males from the same subgroup were most highly represented in the unexpected subtype (45%), followed by the languagedelayed visualmotor impairment subtype, which contained 27% of arithmetic disabled males. These results are comparable to those obtained when the arithmetic disability subgroup was added to the learning disability subsample in the Florida study. Morris, Blashfield and Satz (1981) reported that 50% of the subjects were placed in visualperceptualmotor impairment
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161 subtype, while an additional 33% went into the unexpected subtype. Present results suggest that arithmetic disabled females are more likely than their male counterparts to have difficulties in visualmotor areas. The finding of somewhat deficient visualperceptualorganizational skills in arithmetic disabled children was previously reported by Rourke and Finlayson (1978). However, the pattern of cognitive deficits was not differentiated by sex. Present results which suggest that subtype characteristics may vary as a function of the specific area of academic impairment are considered preliminary and require further study. Particular caution is urged in the interpretation of arithmetic disability subtyping results because of small sample size. In addition, the bulk of the missing data in Phase II of the analysis was derived from this subgroup; hence, the subtyping results may very well not be representative of the entire naturallyoccurring group of children with an arithmetic disability. Only 37% of subjects in the specific arithmetic disability subgroup were represented in the female subtyping analysis; a slightly higher proportion (51%) of the analogue subgroup was represented in the combined sex subtyping analysis. In contrast, 95% of the male, and 93% of the female and combined sex nonspecific learning disability subgroups were contained in their respective cluster analyses. Reading disability subgroups had an even higher representation: 100% for the male, 96% for the female and 98% for the
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162 combined sex samples. The different patterns of cognitive abilities found to characterize the two wellrepresented subgroups suggest that children with a nonspecific learning disability are more likely to have difficulties in language and perceptualmotor areas than those with a specific reading disability, who are more likely to have no apparent cognitive deficiencies. Hypothesis V; Learning Disability Subtypes Will Differ on Personality, Social and Behavioral Measures Hypothesis V was clearly not supported by the results of the present investigation, thus confirming previous findings in the Florida study (Darby, 1978). No significant effect was found for subtype on the Children's Personality Questionnaire in any of the three solutions, despite a change in the method of administration which would theoretically increase the validity of the measure with academically handicapped children. In addition, insignificant results were obtained for the Behavior Problem Checklist and the LJST, even though the BPC and sociometric techniques have been shown to be effective in differentiating learning disabled from regular education (Grieger & Richards, 1976; Bryan, 1974) and emotionally disturbed (McCarthy & Paraskevopoulos 1969) elementary school children. These results suggest that the learning disability subtypes cannot be differentiated on the basis of personality characteristics, teacherrated behavior problems, or social acceptance among peers. In addition it
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163 appears that the academic difficulties experienced by the unexpected subtype cannot readily be explained by social, motivational, or pedagogical factors, as suggested by Lyon (1983). Moreover, the lack of significant effect for WRAT performance indicates that this subtype is not merely higher achieving than the others. Although the unexpected subtype had a significantly higher IQ mean than the other subtypes in the combined sex solution, that very fact makes its presence in the learning disabled subsample even more unexpected. Further external validation of this subtype is needed, possibly through use of more sensitive behavioral or personality measures. That learning disabled children have been successfully classified into behavioral subtypes by means of the cluster analysis of their ratings on measures of adaptive classroom behavior and task orientation (Speece, McKinney, Applebaum, 1985) suggests possible areas for future investigation. Lastly, there is no evidence that any of the subtypes other than the unexpected group are specifically associated with socialemotional disturbance or behavior disorder. Conclusions and Directions for Future Research In conclusion, the present study demonstrated the heterogeneity of learning disabilities as a diagnostic entity and lends support to the need for the delineation of a descriptive typology. It is clear from present results that schoolaged children with learning disabilities vary as to their patterns of academic handicap as well as cognitive
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164 deficiencies (if any) in information processing. Although differences between the sexes did appear, most notably in the lower intercorrelations among achievement variables and the emergence of a specific arithemetic disability subgroup in the female but not male sample, the results of the cluster analyses of achievement and neuropsychological variables were remarkable for their similarities, supporting the conclusions drawn from a recent review of sex differences (Satz, 1982). Both male and female achievement clustering solutions revealed a naturallyoccurring nonspecific learning disability and specific reading disability subgroup, although males tended to be relatively more impaired academically than did their female counterparts in these two subgroups. All neuropsychological subtypes of learning disabilities in the female sample were found in the male sample as well, even though the latter solution revealed two additional clusters (neither of which held up in the combined sex analysis). Those subtypes common to all three solutions involved specific visualmotor impairment, global visualperceptual motor or mixed specific language and global visualperceptualmotor impairment, and a normal diagnostic ("unexpected") profile. The incidence of visualperceptualmotor impairment was surprisingly high, given the relatively low rates reported for visual processing deficiencies in previous subtyping studies. This high incident rate was consistently found in the clustering solutions for all three samples, despite the absence of a
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165 specific arithmetic disability subgroup in the male learning disabled subsample. However this finding is not unique to the present investigation. Lyon and Watson (1981) reported similarly high representation of a visualperceptual motor deficiency subtype. Furthermore, the use of sample rather than standardization norms appears to have obscured this finding in the Florida studies (Satz & Morris, 1981, 1983). The appearance of a normal diagnostic profile replicates the unexpected subtype found in the Florida studies, although this profile shows evidence of specific (but nonsignificant) impairment when interpreted according to standardization norms. However Lyon (1983) reports a consistent finding of a normal subtype in his studies. Lastly, the results provide preliminary evidence of a tendency for subtype characteristics to vary as a function of specific area of academic impairment. Given the differences in the most highly represented subtype profiles found in the specific reading and nonspecific learning disabiltity subgroups, it appears that studies which fail to distinguish between the specific and general nature of academic impairment in reading retardation may be faced with an additional source of heterogeneity in their subject population. Although the present investigation encompassed the first 5 steps described by Morris, Blashfield, & Satz (1981) as necessary in the application of cluster analysis, including choice of population, selection of variables, choice of similarity measure, determination of clustering
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166 method, and decision regarding the optimal number of clusters in a solution, the sixth, validation, is incomplete. Yet this last step was emphasized as "particularly important." Therefore the proposed direction for future work involves strengthening the validity of the subtyping solution. A start has nevertheless been made. The internal validity of the solution has been assessed according to many of the considerations listed by Fletcher (1985). All three achievement and neuropsychological cluster analyses produced homogeneous clusters which provided excellent coverage. The present study at least partially replicated the results of a previous investigation, in which classification variables were found to be quite reliable. Only replicability across techniques remains. The data needs to be reanalyzed using several different clustering methods, as was accomplished in the Florida study (Morris, Blashfield, & Satz, 1981). In addition the relatively high subject to variable ratio makes split sample analysis possible for all 3 subgrouping solutions as well as the combined sex subtyping solution, thus assessing subtype reliability. Classification reliability was touched upon in the addition of a reading comprehension measure to the clustering variables for the analysis of achievement, and found not to significantly affect the composition of the subgroups in the male and combined sex sample, but was not addressed with the subtyping solution. Similarly the construct validity of the
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167 subtypes, assessed by including additional groups of subjects in the analysis, was not accomplished but may be possible in future work. External validation was limited in the present study and will need to be expanded to permit more systematic study of the meaningf ulness and usefulness of the subtyping solution. Differential response to teaching methods, patterns of neuropsychological correlates, and levels of adaptive functioning all appear worthwhile areas to explore. Lastly the following concerns are raised regarding the present investigation. The generalizability of the results are limited by the homogeneity of the sample, which was restricted by age and race. In addition it appears likely that the learning disability subsample represented a milder level of academic handicap than is found among most studies which utilize a sample selected from a clinic population. The clustering variables were limited in number and may not represent the most useful diagnostic measures for describing subgroup and subtype characteristics. More formal measures of memory, attention, and psycholinguistic abilities may be warranted. Finally, the absence of a control group and subject attrition in specific arithmetic disability subgroups hindered the interpretation of results from the subtyping solution. Future studies will need to weigh the advantages of further investigation of academically impaired versus normally achieving subsamples, and may wish to collect data for a normal control group in lieu of one of
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168 the specific learning disability subgroups if resources and arrangements are similarly limited. Nevertheless the present study provided the opportunity for replication of a preliminary typology of learning disabilities in males, and represents the first attempt to describe naturally occurring achievement subgroups, as well as neuropsychological subtypes, of learning disabilities in a large, relatively unselected sample of females, who have traditionally been underrepresented in the research. In addition the investigation permitted the comparison clustering of results according to both pattern and level between males and females, who have traditionally been considered to represent opposite extremes of risk for the development of learning disabilities. The continuation of research efforts toward the delineation of a valid and reliable descriptive typology of learning disabilites offers considerable promise for advancement in the understanding as well as prevention and treatment of this significant educational and social problem.
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BIBLIOGRAPHY Applebee, A. Research in reading retardation: Two critical problems. Journal of Child Psychology and Psychiatry and Allied Disciplines 1971, 1_2, 91113. Badian, N.A. Dyscalculia and nonverbal disorders of learning. In H.R. Myklebust (Ed.), Progress in Learning Disabilities (Vol 5). New York: Grune & Stratton, 1983. Barr, A., Goodnight, J., Sail, J., & Helwig, J. A user' s guide to statistical analysis system 76 Raleigh, North Carolina: SAS Institute, Incorporated, 1976. Beery, K.E. Revised administration, scoring, and teaching manual for the developmental test of visualmotor integration Cleveland: Modern Curriculum Press, 1982. Beery, K., & Buktenica, N. Developmental test of visualmotor integration Chicago: Follett Educational Corp., 1967. Benton, A.L. Developmental dyslexia: Neuropsychological aspects. In W.J. Friedlander (Ed.), Advances in neurology (Vol 7). New York: Raven Press, 1975. Boder, E. Development dyslexia: A diagnostic approach based on three atypical readingspelling patterns. Developmental Medicine and Child Neurology 1973, 15 663687 Bryan, T.H. Peer popularity of learning disabled children. Journal of Learning Disabilities 1974 1_{1Q) 3135. Canning, P.M., Orr, R.R., & Rourke, B.P. Sex differences in the perceptual, visualmotor, linguistic and conceptformation abilities of retarded readers. Journal of Learning Disabilities 1980 13^(9), 3741. Cole, M., & Kraft, M.B. Specific learning disability. Cortex, 1964, 1, 302313. Critchley, M. The dyslexic child New York: William Heinemann Medical Books, 1970. Darby, R.O. Learning disabilities: A multivariate search for subtypes (Doctoral disseration. University of Florida) Ann Arbor, Michigan: University Microfilms, 1979, No. 7913261. 169
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170 Denckla, M.B. Clinical syndromes in learning disabilities: The case for "splitting" vs. "lumping." Journal of Learning Disabilities 1972 5^, 401406 Doehring, D.G., & Hoshko, I.M., Classification of reading problems by the Qtechnique of factor analysis. Cortex 1977, 13, 281294. Doehring, D.G., Hoshko, I.M., & Bryans, B.N. Statistical classification of children with reading problems. Journal of Clinical Neuropsychology 1979, I, 516. Doehring, D.G., Trites, R.L., Patel, P.G., & Fiedorowicz, C. A.M. Reading disabilities: The interaction of reading, language, and neuropsychological deficits New York: Academic Press, 1981. Eisenberg, L. Definitions of dyslexia: Their consequences for research and policy. In A.L. Benton & D. Pearl (Eds.), Dyslexia; An appraisal of current knowledge New York: Oxford University Press, 1978. Everitt, B. Cluster analysis London, Heinemann Educational Books, 1974. Finucci, J.M., & Childs, B. Are there really more dyslexic boys than girls? In A. Ansara, N. Geschwind, A. Galaburda, M. Albert, & N. Gartrell (Eds.), Sex differences in dyslexia Towson, Maryland: The Orton Dyslexia Society, 1981. Fisk, J.L., & Rourke, B.P. Identification of subtypes of learningdisabled children at three age levels: A neuropsychological multivariate approach. Journal of Clinical Neuropsychology 1979 1^(4), 289310. Fletcher, J. External validation of learning disability typologies. In B.P. Rourke (Ed), Neuropsychology of learning disabilities: Essential of subtype analysis New York: Guilford Press, 1985. Fletcher, J., & Satz, P. Cluster analysis and the search for learning disability subtypes. In B.P. Rourke (Ed), Neuropsychology of learning disabilities; Essential of subtype analysis New York; Guilford Press, 1985. Gaddes, W.H. Prevalence estimates and the need for definition of learning disabilities. In R.M. Knights & D. J. Bakker (Eds), The neuropsychology of learning disorders; Theoretical approaches Baltimore; University Press, 1976.
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171 Gaddes, W.H., & Crockett, D.J. The SpreenBenton aphasia tests: Normative data as a measure of normal language development. Brain and Language 1975, 2, 257280. Grieger, R.M., & Richards, H.C. Prevalence and structure o behavior symptoms among children in special education and regular classroom settings. Journal of School Psychology 1976, 1_4 ( 1 ) 2738 Holl ingshead A.B. Two factor index of social position New Haven: (Privately Published), 1957. Hollingshead A.B. Four factor index of social status New Haven: (Privately Published), 1975. Ingram, T.T.S., Mason, A.W. & Blackburn, I. A retrospective study of 82 children with reading disability. Developmental Medicine and Child Neurology 1970 12^, 271281 Jastak, J., & Jastak, S. The wide range achievement test Wilmington, Delaware: Guidance Associates of Delaware, Inc., 1965. Long, N.J., Cook, A.R., Evans, E.D., Kerr, J., Linke, L.A., Neubauer, B., & Payne, D.C. Groups in perspective: A new sociometric technique for classroom teachers. Bulletin of the School of Education Indiana University, 1962 38.' 1105. Lyon, G.R. Learning disabled readers: Identification of subgroups. In H.R. Myklebust (Ed.), Progress in learning disabilities (Vol 5). New York: Grune & Stratton, 1983. Lyon, G.R. Educational validation studies of learning disability subtypes. In B.P. Rourke (Ed.), Neuropsychology of learning disabilities: Essentials of subtype analysis New York: Guilford Press, 1985. Lyon, G.R., Stewart, N., & Freedman, D. Neuropsychological characteristics of empirically derived subgroups of learning disabled readers. Journal of Clinical Neuropsychology 1982, _4 (4 ), 343365. Lyon, G.R., & Watson, B. Empirically derived subgroups of learning disabled readers: Diagnostic characteristics Journal of Learning Disabilities, 1981, 14(5), 256261 MacGinitie, W.H. GatesMacGinitie reading tests (2nd ed ) Boston: Houghton Mifflin Co., 1978.
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172 Mattis, S. Dyslexia syndromes: A working hypothesis that works. In h.L. Benton & D. Pearl (Eds.), Dyslexia: An appraisal of current knowledge New York: Oxford University Press, 1978. Mattis, S., French, J.H., & Rapin, I. Dyslexia in children and young adults: Three independent neuropsychological syndromes. Developmental Medicine and Child Neurology 1975, 17, 150163. McCarthy, J.M., & Paraskevopoulos J. Behavior patterns of learning disabled, emotionally disturbed, and average children. Exceptional Children 1969 36^, 6974 Meece, J.L., & Parsorns, J.E. Sex differences in math achievement: Toward a model of academic choice. Psychological Bulletin 1982, 9J^(2), 324348 Monroe, M. Children who cannot read Chicago: University of Chicago Press, 1932. Morris, R. Blashfield, R. & Satz, P. Neuropsychology and cluster analysis: Potentials and problems. Journal of Clinical Neuropsychology 1981, 2(1)' 7999. Naidoo, S. Specific dyslexia New York: Pitman Publishing, 1972 Office of Education. Assistance to states for education of handicapped children. Federal Register 1976, 41(230) 5240452407 Otis, A.S., & Lennon, R.T. The OtisLennon mental ability test New York: Psychological Corporation, 1967. Petrauskas, R. & Rourke, B.P. Identification of subgroups of retarded readers: A neuropsychological multivariate approach. Journal of Clinical Neuropsychology 1979, I, 1737. Porter, R.D., & Cattell, R.B. Handbook for the children's personality questionnaire Champaign, Illinois: Institute for Personality and Ability Testing, 1972. Quay, H.C., & Peterson, D.R. Manual for the behavior problem checklist Champaign, Illinois: University of Illinois, Children's Research Center, 1967. Rasbury, W.C., Falgout, J.C., & Perry, N.W., Jr. A Yudintype short form of the WISCR: Two aspects of validation. Journal of Clinical Psychology 1978, 34 120126.
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173 Rourke B.P. Reading, spelling, arithmetic disabilities: A neuropsychological perspective. In H.R. Myklebust (Ed.), Progressing in learning disabilities (Vol 4). New York: Grune & Stratton, 1978. Rourke, B.P., & Finlayson, M.A.J. Neuropsychological significance of variations in patterns of academic performance: Verbal and visualspatial abilities. Journal of Abnormal Child Psychology 1978, 6, 121133. Rourke, B.P., & Strang, J.D. Neuropsychological significance of variations in patterns of academic performance: Motor, psychomotor, and tactileperceptual abilities. Journal of Pediatric Psychology 1978, 2' 6266. Rourke, B.P., & Strang, J.D. Subtypes of reading and arithmetic disabilities: A neuropsychological analysis. In M. Rutter (Ed.), Developmental neuropsychiatry New York: Guilford Press, 1983. Rutter, M. Prevalence and types of dyslexia. In A.L. Benton & D. Pearl (Eds.), Dyslexia: An appraisal of current knowledge New York: Oxford University Press, 1978. Satz, P. Sex differences: Clues or myths on genetic aspects of speech and language disorders. In C. Ludlow (Ed.), Genetic aspects of speech and language disorders. New York: Academic Press, 1982. Satz, P., & Friel, J. Some predictive antecedents of specific learning disability: A preliminary oneyear followup. In P. Satz & J. Ross (Eds.), The disabled learner: Early detection and intervention Rotterdam: Rotterdam University Press, 1973. Satz, P., Friel, J., & Rudegeair, F. Differential changes in the acquisition of developmental skills in children who later become dyslexic: A threeyear followup. In D. Stein & N. Butters (Eds.), Recovery of function New York: Academic Press, 1974. Satz, P., & Morris, R. Learning disability subtypes: A review. In F.J. Pirozzolo & M.C. Wittrock (Eds.), Neuropsychological and cognitive processes in reading New York: Academic Press, 1981. Satz, P., & Morris, R. Classification of learning disabled children. In R. Tarter (Ed.), The child at psychiatric risk New York: Oxford University Press, 1983. Satz, P., Morris, R., & Darby, R. Subtypes of learning disabilities: A multivariate search Paper presented to the lYC Symposium, Vancouver, B.C., Canada, March, 1979
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174 Satz, P., Taylor, H.G., Friel, J., & Fletcher, J.M. Some developmental and predictive precursors oE reading disabilities: A sixyear Eollowup. In A.L. Benton & D. Pearl (Eds.), Dyslexia; An appraisal of current knowledge New York: Oxford University Press, 1978. Small, N. Level of perceptual functioning in children: A developmental study Unpublished master's thesis. University of Florida, 1968. Smith, D.E.P., & Carrigan, P.M. The nature of reading disability New York: Harcourt, Brace, & Company, 1959 Smith, M.M. Patterns of intellectual abilities in educationally handicapped children Unpublished doctoral disseration, Claremont College, California, 1970. Speece, D.L., & McKinney, J.D. The relationship between reading achievement and information processing in subtypes of learning disabled children Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, April, 1984 Speece, D.L., McKinney, J.D., & Applebaum, M.I. Classification and validation of behavioral subtypes of learning disabled children. Journal of Educational Psychology 1985, 77(1), 6777. Spreen, 0., & Benton, A.L. S preenBenton language examination profile Iowa City, Iowa: University of Iowa, 1965. Strang, J., & Rourke B.P. Arithmetic disability subtypes: The neuropsychological significance of specific arithmetic impairment in childhood. In B.P. Rourke ( Ed ) Neuropsychology of learning disabilities: Essentials of subtypes analysis New York: Guilford Press, 1985. Taylor, H.G., Satz, P., & Friel, J. Developmental dyslexia in relation to other childhood reading disorders: Significance and clinical utility. Reading Research Quarterly 1979, 15(1), 84101. Van der Vlugt, H., & Satz, P. Subgroups and subtypes of learningdisabled and normal children: A crosscultural replication. In B.P. Rourke (Ed.), Neuropsychology of learning disabilities: Essential of subtype analysis New York: Guilford Press, 1985.
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175 Wechsler, D. Wechsler intelligence scale for children New York: Psychological Corporation, 1949. Winer, B.J. Statistical principles in experimental design (2nd ed.). New York: McGrawHill, 1971. Wishart, D.R. CLUSTAN user manual London: Computer Centre, University of London, 1982.
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BIOGRAPHICAL SKETCH Carol Sue Johnston was born in Ft. Wayne, Indiana, on January 12, 1952. She attended public school there and graduated with honors from North Side High School in 1969. She completed undergraduate study in psychology at Purdue University, graduating with distinction in 1972. During the next two years, she pursued a course of graduate study in clinical psychology at DePaul University in Chicago. She completed her thesis and an internship in school psychology during the subsequent year and received the Master of Arts degree in 1975. Following three years of employment as a school psychologist in Wisconsin and Pennsylvania, she entered the University of Florida Graduate School in Clinical Psychology. She commuted from Pittsburgh to Gainesville in order to complete her course work and was admitted to doctoral candidacy in August, 1981. During the following year she worked on a fulltime basis as a staff psychologist for a county special education agency. Other employment during graduate school included parttime jobs as a psychologist for a mental health/mental retardation clinic and a children's hospital, as well as a senior research associate in neuropsychology at Western Psychiatric 176
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177 Institute in Pittsburgh. She completed her clinical internship in the Department of Psychiatry at Case Western University School of Medicine during the 198384 academic year, and received the Ph.D. degree in clinical psychology from the University of Florida in May, 1986. She is a member of the International Neuropsychological Society and expects to continue to pursue her interests in neuropsychology through workrelated experiences after graduat ion Ms. Johnston has been married to Mark Puda since 1973. They have one child, Rachel Johnston Puda, age 3.
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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Eileen B. Fennell, Chairman Associate Professor of Clinical Psychology I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. W. Keith Berg Associate Professor of Psychology I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Patricia H. Miller Associate Professor of Psychology
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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. This dissertation was submitted to the Graduate Faculty of the College of Health Related Professions and to the Graduate School, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy May, 1986. or^Counselor Education Professions Dean for Graduate Studies and Research
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