Citation
Differentiation of cognitive abilities in children and adolescents

Material Information

Title:
Differentiation of cognitive abilities in children and adolescents
Creator:
Kane, Harrison
Publication Date:
Language:
English
Physical Description:
v, 102 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Adolescents ( jstor )
Age groups ( jstor )
Cognitive models ( jstor )
Cognitive psychology ( jstor )
Factor analysis ( jstor )
Intelligence quotient ( jstor )
Memory ( jstor )
Psychometrics ( jstor )
Standard deviation ( jstor )
Statistical discrepancies ( jstor )
Dissertations, Academic -- Foundations of Education -- UF ( lcsh )
Foundations of Education thesis, Ph.D ( lcsh )
City of Vernon ( local )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1999.
Bibliography:
Includes bibliographical references (leaves 94-101).
Additional Physical Form:
Also available online.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Harrison D. Kane.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
The University of Florida George A. Smathers Libraries respect the intellectual property rights of others and do not claim any copyright interest in this item. This item may be protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work have responsibility for determining copyright status prior to reusing, publishing or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. The Smathers Libraries would like to learn more about this item and invite individuals or organizations to contact the RDS coordinator (ufdissertations@uflib.ufl.edu) with any additional information they can provide.
Resource Identifier:
030360976 ( ALEPH )
41928734 ( OCLC )

Downloads

This item has the following downloads:


Full Text












DIFFERENTIATION OF COGNITIVE ABILITIES IN CHILDREN AND
ADOLESCENTS










By

HARRISON D. KANE


















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

1999















ACKNOWLEDGMENTS

This project could not have been completed without the support and

expertise of John H. Kranzler, Thomas D. Oakland, M. David Miller, and

Walter Cunningham Special appreciation is also extended to Stephen Smith

for his enthusiasm.































ii















TABLE OF CONTENTS

page
ACKNOWLEDGMENTS.................................................... i

A B STRA CT ................................................................... iv

CHAPTERS

1. INTRODUCTION.......................................................... 1

Statement of the Problem...................................................... 1
Purpose of the Study.......................................................... 2
Fundamental Concepts in the Study of Intelligence ..................... 3
Spearman's g................................................ ........ 3
Exploratory Factor Analysis and g........................................ 5
Confirmatory Factor Analysis and g ...................................... 7
Carroll's Three-Stratum Theory......................................... 9

2. REVIEW OF LITERATURE ................................................12

The (In)Variant Nature of General Intelligence................................12
Stability of g Loadings Across Different Test Batteries.............. 12
Stability of g Loadings Across Different Ages....................... 14
Stability ofg Loadings Across Different Ability Levels .............23
Competing Explanations for the Differentiation
of Cognitive Abilities................................................... 29
Summary........................................... ..................... 31

3. M ETHOD ................................. ......... ....... ...... ....... .. ... 33

Participants and Data Collection ............................ ..... 33
Description of the WJ-R........................................... 33
The Model............. .................................................. 42
Statistical Procedures for Subgroup Selection....................... 42
Statistical Analysis............ ......................... .................. 45


iii











4. R E SU L T S .........................................................................49

5. DISCUSSION................................................................. 82

Differentiation of Cognitive Abilities Across
Groups of Different Ability ............................................... 82
Differentiation of Cognitive Abilities Across
Ability Groups of Different Age........................................ 86
Possible Mechanisms of Cognitive Differentiation....................... 89
Implications For Cognitive Assessment.............................. 91
Recommendations For Future Study...................................... 91
Sum m ary...................................................................... .. ... 93

LIST OF REFERENCES..........................................................94

BIOGRAPHICAL SKETCH....................................................102




























iv















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

DIFFERENTIATION OF COGNITIVE ABILITIES IN CHILDREN AND
ADOLESCENTS

By

Harrison D. Kane

May, 1998

Chairman: John H. Kranzler, Ph.D.
Major Department: Foundations of Education

Most psychologists and educators operate on the implicit assumption

that intelligence is a linear construct. Stated differently, the assumption is that

smart people simply have more intelligence than their less gifted peers.

Similarly, retarded individuals are thought to have less intelligence. In contrast

to this widely accepted belief, this study poses the alternative hypothesis that

intelligence is qualitatively different in various populations. Applying

confirmatory factor analysis to the standardization sample of the Woodcock-

Johnson Test of Cognitive Ability, this study examined the structure of intellect

across ability and age. While the structure of intelligence was identical across

age and ability levels, significant differences were noted in factor loadings,

error, and unique variances.

v















CHAPTER 1
INTRODUCTION

It is generally and rightly considered a virtue in a teacher to observe
accurately the difference in ability among his pupils, and to discover the
direction in which the nature of each particularly inclines him. There is an
incredible amount of variability in talent, and the forms of minds are no less
varied than the forms of bodies.
Quintillion (70 AD)

Statement of the Problem

The study of intelligence has a long past, yet a very short history. For

centuries people have philosophized about intelligence, but only in the past 100

years has informal rhetoric yielded to scientific inquiry. Certainly, one of the

most important events in the scientific study of intelligence was the invention

of factor analysis. Factor analysis is a mathematical procedure which

summarizes the interrelationships among variables as an aid in conceptualizing

the underlying structure. Beginning with Spearman's (1904) seminal work,

"General Intelligence: Objectively Determined and Measured," literally

hundreds of investigations have used factor analysis to better understand the

complex nature of intelligence. Most studies (e.g., Kranzler & Jensen, 1991)

have found that intelligence is not a single or unitary construct, but rather a

number of abilities working in concert. Furthermore, many of these studies

have conceptualized a hierarchical structure of cognitive abilities (e.g.,

Kranzler & Weng, 1995). Carroll (1993) surveyed over 450 such studies, and
I





2

based on his findings, proposed a three-stratum theory of intelligence

comprised of narrow, broad, and one general abilities. While Carroll's three-

stratum theory is the most comprehensive psychometric model of intelligence

to date, an intriguing question remains unanswered: Is the three-stratum model

a viable representation of cognitive ability for groups of different intelligence?

Purpose of the Study

The purpose of the present study is to investigate the stability of

Carroll's three-stratum theory of intelligence across the lifespan and ability

levels. A substantial body of research indicates that intelligence changes as

people mature. Mental abilities tend to differentiate and become more

specialized with age (Anastasi, 1970). A much smaller, but equally intriguing

body of research suggests that mental abilities also differentiate according to

IQ level (Spearman, 1927). That is, high-IQ individuals display greater

differentiation among mental abilities than low-IQ individuals. Differentiation is

typically demonstrated in three ways. First, the percentage of variance

attributable to the general factor of intelligence decreases in a systematic

fashion by age or ability. Second, the percentage attributable to group factors,

such as verbal ability, increases with age or ability. Third, correlations between

IQ subtests decrease with age or ability. Inquiry into the differentiation of

mental ability will provide insight into the cognitive structures underlying

intelligence. This study will attempt to answer the question of whether the

structure of "intelligence" is the same construct, more or less, for high- and

low-IQ individuals, or whether qualitative, as well as purely quantitative,






3


differences exist across ability levels. The answer to this question is important

because many common assessment and teaching practices are based on the

assumption that abilities are organized in essentially the same manner for all

people and remain constant throughout the lifespan. By understanding the

nature of intelligence for individuals of different IQ levels, educators and

psychologists can begin to better appreciate and respond to the diversity of the

human condition.

Fundamental Concepts in the Study of Psychometric Intelligence
Spearman's g.

Spearman (1904) discovered g as part of an experiment to "find out

whether, as Galton has indicated, the abilities commonly taken to be

intellectual had any correlation with each other or with sensory discrimination"

(Spearman, 1927, p. 322). Spearman obtained teacher evaluations of 36

students from a nearby village school. Students were rated on traditional

academic subjects (Latin, English, Math) as well as on Music and Pitch

Discrimination. The observed correlation among the variables prompted

Spearman to hypothesize that they shared a common source of variance, which

he termed a "general factor of intelligence" (Spearman, 1904, p. 36). From the

observation that variables had different levels of intercorrelation, he concluded

that the variables had different levels of saturation with the general factor. The

different levels of saturation represented different loadings on the general

factor.






4


Spearman (1927) also noted that the general factor did not account for

all the variance in students' scores. To amount for these findings, he posited a

two-factor theory of intelligence. That is, each variable may be described or

accounted for by two factors, the general factor and a factor specific to each

variable or narrow class of variables. Spearman suggested that "all branches of

intellectual activity have in common one fundamental function, whereas the

remaining or specific elements seem in every case to be wholly different..." (p.

202). Spearman devoted the rest of his academic career to explicating the

general factor, which he later referred to simply as g. Spearman conceived ofg

as "mental energy," and stated that g was the "leading part of intelligence, and

is displayed by the ability to handle not merely abstract ideas, but above all

symbols" (p. 211). The specific factors were portrayed as a large number of

engines activated by this mental energy. Later, working from several data sets

collected over 20 years, Spearman conceptualized g as consisting of three

processes. The first process is "the apprehension of experience." Spearman

assumed, as did Galton (1892), that the greater the sphere of experiences an

individual may draw upon, the more complex the problem solving that he or

she may undertake. The second process is the "eduction of relationships."

Spearman conceived of eduction as the "drawing out of a logical relationship

between two stimuli" (p. 227). The third process is the "eduction of

correlates," in which an individual notes the similarities between two stimuli. A

cognitive task was loaded on g to the extent that it drew on these three

processes.








Spearman regarded g as the "common and essential element in

intelligence" (1927, p. 126). In a comprehensive review of intelligence theory,

Brody (1992) confirmed:

The first systematic theory of intelligence presented by Spearman in
1904 is alive and well. At the center of Spearman's paper of 1904 is a
belief that links exist between abstract reasoning, basic information
processing abilities, and academic performance. Contemporary
knowledge is congruent with this belief. Contemporary psychometric
analysis provides clear support for a theory that assigns....g to a
singular position at the apex of a hierarchy of abilities. (p. 349)

Psychometric g outweighs all other factors derived from a battery of tests. It is

the single most important factor in predicting scholastic and occupational

achievement, as well as a host of desirable and undesirable social outcomes

(Hermstein & Murray, 1994).

Exploratory Factor Analysis and g.

Exploratory factor analysis is a statistical method of minimizing the

number of variables under investigation while concomitantly maximizing the

amount of information in the analysis (Gorsuch, 1983). This aspect of factor

analysis is especially useful when the sheer amount of information in a study

exceeds comprehensibility, or when certain distinctions and relationships

between variables are hypothesized. Consider the following example. The

Wecshler Adult Intelligence Scale, Third Edition (WAIS-IU; 1997) has 14

subtests. Thus, there are 91 simple correlations between the subtests.

Undoubtedly, the WAIS-III is not measuring 14 different constructs (e.g., the

Information subtest certainly shares a common source of variance with the

Similarities and Vocabulary subtests, since each of these subtests are included






6


in the Verbal Scale). With 91 correlations, some means are needed for

determining if there are a smaller number of underlying constructs which might

account for the main sources of variation in such a complex matrix of

correlations. By partitioning the variance among the original variables into a

smaller number of latent variables (i.e., factors), factor analysis obtains the

most concise and parsimonious explanation for the interrelationships existing in

the data.

Spearman's g is a latent variable, manifested in factor analysis. The

ubiquity ofg arises from positive manifold, the phenomenon in which all

mental tests correlate to some degree. Therefore, statistical and

methodological considerations determine, at least in part, how "good" g will be

in a factor analysis (Jensen & Weng, 1993). To find a good g, the

psychological tests must be diverse with respect to content, type of response,

and stimulus. Certainly, psychometric g will vary according to the reliability of

the test, the number of tests, the number of participants in the sample, and the

number of diverse abilities represented by the tests. However, not every

general factor that arises from a factor analysis is Spearman's g. For example,

personality tests do not yield a g. Psychometric g arise only from a battery of

cognitive tests. Although some tests, such as Raven's Progressive Matrices

(RPM; Raven, 1956), are referenced as being saturated with g (Jensen, 1998),

every cognitive test measures g to some extent. Therefore, there is no uniquely

defining characteristic to g that can be expressed in psychological terms. Tests





7


differing in content, stimulus modality, and response modality may ultimately

have identical g-loadings (Jensen, 1998).

Thurstone (1940) was the first to pose the possibility that exploratory

factor analysis can be applied in a hierarchical manner, with the goal of finding

the order of factors. A first-order factor analysis is the application of factor

analysis techniques to the correlation matrix derived from the observed

variables of a study. Such analysis usually results in a smaller number of first-

order factors which account for the maximum amount of variance in the data

set. Frequently, these first-order factors are also inter-correlated. Therefore, a

second-order factor analysis may be conducted, further analyzing the

correlation matrix of the first-order factors. A second-order factor analysis

results in a still smaller set of third-order factors. When hierarchical techniques

are applied to data representing cognitive performance, g is always manifested

at the apex of the hierarchy, usually at the third-order.

Confirmatory Factor Analysis and g.

In exploratory factor analysis, the researcher does not know the

underlying latent variable structure. Therefore, the focus of the analysis is to

reveal the minimum number of unknown factors that will best account for the

variance in a larger set of observed variables. Confirmatory factor analysis, on

the other hand, requires an a priori knowledge of the underlying latent variable

structure. This knowledge may be based on theory or past empirical

investigations using the variables under study. In any case, the researcher

using confirmatory techniques postulates a priori that certain observed






8


variables will be related to certain latent variables in a theoretical model. The

relationship between observed and latent variables is quantified by factor

loadings. Data on all the variables specified in the hypothesized model are then

collected. The researcher then examines the "goodness-of-fit" between the

hypothesized model and the model comprised of observed variables. Because

the researcher must specify an a priori model, confirmatory factor analysis is

inherently driven by theory, whether formal or informal. Thus, confirmatory

factor analysis presents an ideal vehicle for establishing the construct validity of

theories of intelligence.

In recent years, confirmatory techniques have become almost common

place in testing the latent structure of intelligence tests. One reason for the

increased usage of confirmatory techniques is that test manuals and journal

articles frequently publish an obligatory correlation matrix which researchers

can use as a starting point for independent analysis. Most intelligence tests

(e.g., WAIS-II) combine various subtests to arrive at a single score to reflect

overall cognitive ability. Therefore, whether tacitly or openly, these tests

acknowledge the existence ofg in their underlying structure. Confirmatory

studies of intelligence tests (e.g., Carroll, 1993; Kranzler & Weng, 1995)

indicate that without exception, g is at the apex of a hierarchical model of

intelligence and common to all of the factors and subtests below it. In factor

analysis, as in life, any g will probably be a good g, and is certainly better than

no g.





9

Carroll's Three-Stratum Theory.

Carroll (1993) published a massive survey of more than 450 data sets

related to intelligence and cognitive ability. Data were drawn from over 1,500

publications and selected on the basis of their broad sampling of cognitive

abilities. His summary lead him to posit his own theory of intelligence, a

hierarchical model with three strata of abilities. The first stratum consists in

part of narrow abilities that appear reflective of specific experience, learning,

and strategies. Examples from the first strata include length estimation and

meaningful memory. The second stratum is characterized by broad factors that

represent some specialization of abilities and established traits, such as broad

retrieval ability and speed of information processing. The third stratum is

essentially Spearman's g. Second-order factors are related to one another to

the extent that they load on the general factor, with some more related to g

than others. Similarly, first-order factors are subsumed by specific second-

order factors and are related to each other by virtue of their respective loadings

on the given second-order factor. Figure 1 provides a graphical representation

of the proposed three-stratum structure of cognitive abilities.

In formulating his theory, Carroll drew on data from a myriad of

sources, including Spearman (1904), Guilford (1967), Vernon (1960), Cattell

(1987), and Thurstone (1973). Therefore, it is no surprise'that his three-

stratum theory retains some common features of other psychometric theories

of intelligence. For example, Carroll preserves Spearman's and Vernon's

conceptualization of a hierarchical general factor. Carroll also avows








10





Coancrp Fomtlon

Gf
Antalyi Synt *is


V\ul Ckloru

Gv
Picture Recognition


Visual MatchngV
Gs

Cross Out


Memory For N rI


Viul Auditory Lming


-Gc ~~ Vocabuiry


Oranl Voaoul ry


A i--- ncomplte Words


Sound Blending


\- Menory For Sentec


Memory frWords

Gq



Appled ProblWm




Figure 1. Carroll's Three Stratum Theory of Cognitive Ability






11


Thurstone's contribution to his methodology, particularly the practice of

successive factorizations of correlation matrices at higher orders. Like Cattell,

Carroll acknowledges the existence of several second-order factors, including

fluid (gf) and crystallized (gc) abilities. Unlike Cattell's gc-gf model, Carroll

postulates-and provides support for-a third-stratum general factor derived

from the shared variance of the second-stratum factors. Carroll's three-stratum

theory has garnered much acclaim in the psychological community, primarily

for its comprehensive representation of the structure of cognitive abilities

(McGrew, 1997).















CHAPTER 2
REVIEW OF THE LITERATURE

The (In)Variant Nature of General Intelligence

Despite scientific and social controversy, Spearman's g has remained

remarkably resilient as a theoretical construct in the study of individual

differences. It is compatible with most theories of intelligence, even those

which hope to disavow its existence (see Gardner, 1983; Guilford, 1981;

Naglieri, 1997). Therefore, g is a phenomenon not easily dismissed.

Differentiation of cognitive abilities is often inferred from the role ofg in

explaining the total variance in IQ; therefore, the stability ofg across

individuals, time, and tests is fundamental to this investigation.

Stability ofg Loadings Across Different Test Batteries.

In his reproving text of intelligence tests and theory, The Mismeasure

of Man, Harvard anthropologist Stephen J. Gould (1981) stated repeatedly that

scientists considered g a reified single thing. He argued that g was nothing

more than a statistical artifact, and that its existence, size, and pattern of

loadings can vary widely, depending on the selected method of factor analysis.

In effect, Gould regarded g as the arbitrary whim ofpsychometricians.

"Spearman's g is not an ineluctable entity; it represents one mathematical

solution from among many equivalent alternatives" (p. 318).

12






13

Ifg were mathematical chimera, as Gould argues, then the g-loadings

of a specific test could be expected to vary across test batteries. The method to

establish the invariance of a test's g loadings is relatively straightforward. Tests

could be assigned a g loading in a particular investigation and the replicability

of the loading could be determined in any other study in which the test was

included.

The largest study to address this particular issue was conducted by the

late R.L. Thordike (1987). He began with 65 diverse tests of information

processing and problem solving given to Air Force recruits. He then composed

seven batteries, each formed of eight randomly selected tests. The remaining

tests were inserted into each battery and subjected to factor analysis. The g

loadings derived from each battery of each probe test correlated .85. Tests

maintained their approximate g-loadings even when analyzed within different

random batteries, demonstrating the invariance of g. Brody (1992) criticized

Thondike's study, however, noting that four of the included tests had

uniformly low g-loadings, falling between .10 and .25. Brody argued that these

tests, with titles such as "Rudder Control" and "Rotary Pursuit," appeared to

measure manual dexterity. Therefore, their inclusion in Thorndike's analysis

may have spuriously inflated the correlation among g-loadings. However, the

counterpoise is that only a diverse battery of tests will yield stable estimates of

g.






14


Stability of g Loadings Across Different Ages.

In theorizing about intelligence, a major issue is the persuasiveness ofg

across groups of varying age and ability. Traditionally, this issue has been

termed the differentiation hypothesis (e.g., Deary & Pagilieri, 1991; Garrett,

1946). Perhaps the first documented study examining the differentiation of

abilities was conducted by the eminent British psychologist, Sir Cyril Burt. In

1919, Burt carried out a large standardization of scholastic tests in the London

schools. Data from 546 students were collected, with three different age

groups represented in the sample. When he factor analyzed the results, Burt

remarked:

There was a marked tendency for the group factors to become
increasingly predominant with increasing age....The application of such
methods through all the classes in all the departments shows that the
relative influence of the more general capacity (so-called intelligence) is
far greater in earlier years as contrasted with later. (p. 80)

He reported the amount of variance accounted for by g decreased from 52% at

8 years, to 35% at 10 years, and to 27% at 12 years of age. Burt was so

intrigued by his findings that he re-analyzed another set of archival data from

the London schools to confirm his hypothesis. With a sample of 300 boys who

were tested at nine years of age and again at 13, Burt (1944) found that "the

influence of the general factor appreciably declines, while the influence of the

group factors increases to nearly twice its original size" (p. 92).

Spearman also noticed this developmental trend, attributing

differentiation as a result of the increasing role of specific factors. Noting the






15


influence of specific abilities across different age groups, he commented on

their protean nature:

For the s's, the life-history cannot be traced on such simple lines as g,
since these s's themselves are far from simple. ....Over and above such
pure aptitude, the s's contain further constituents upon which age acts
in a highly irregular manner. In some directions, especially that of
information, improvement may occur up to any time of life, however
advanced; in other directions, especially that of more or less
accidentally formed habits of procedure, either improvement or
deterioration may occur... (1927, p. 375)

His comments presaged recent findings indicating that crystallized abilities may

continue to develop with age, while fluid abilities typically decline (Horn &

Noll, 1997).

In America, the first studies of differentiation came from Garrett,

Bryan, and Perl (1935). They administered 10 different tests measuring verbal,

numerical, and perceptual abilities to boys and girls aged 9, 12, and 15 years.

Subsequent factor analysis verified that the first unrotated factor accounted for,

respectively, 31%, 32%, and 12% of the variance for the boys, and 31%, 24%,

and 19% for the girls. Garrett et al. concluded that "as age increases, abstract

or symbolic intelligence changes its organization from a fairly unified and

general ability to a loosely organized group of abilities or factors" (p. 121). In

short order, a number of investigations were started, primarily in Europe (e.g.,

Richards, 1941). Each study reached conclusions similar to those of Garrett

and Burt. That is, "the factors under survey tend to become more independent

with increasing age" (Richards, 1941, p. 144). After reviewing his own work

and other studies (e.g., Anastasi 1932; Schiller, 1934; Schneck, 1929),






16


Garrett (1946) presented a theory of emergent differentiation and coined the

term "differentiation hypothesis." In his retirement address as president of the

American Psychological Association, Garrett (1946) stated:

With increasing age there appears to be a gradual breakdown of an
amorphous general ability into a group of fairly distinct
aptitudes.....The conclusion which I draw....is that the overall ability
which looms large during the elementary school years becomes
progressively less important at the high school and college level...(pp.
375-376).

With a growing number of standardized intelligence tests available to

researchers, the 1940s and 1950s saw a steady stream of investigations

devoted to emergent differentiation, now termed the "Garrett hypothesis."

Clark (1944) administered the Chicago Tests of Primary Mental Abilities to

320 boys, approximately 100 subjects at each of three age levels. The children

were drawn from public schools and matched according to social and

economic levels. As in earlier studies, correlations between the six factor

scores declined with age level. Average correlations were .55, .44, and .43,

respectively, for ages 11, 13, and 15 years of age. Using the standardization

data of the Wechsler-Bellevue Scale, Balinsky (1941) found that a general

factor "is found for the nine year old age group, then is apparently submerged

and appears again, but not as definitely, at age 50 to 59" (p. 230). Stated

differently, the differentiation of cognitive abilities continues from adolescence

to early adulthood, then reverses with later adulthood. Owens and Thompson

(1954) reported a similar trend when they analyzed data from a sample of 127

men who had taken the Army Alpha in 1919 and again in 1950. The first






17

unrotated principal component accounted for 53% of the variance in the Army

Alpha at age 19 and increased to 63% at age 50. That is, Spearman's g

reasserts itself as an increasing source of variance in late adulthood.

In one of the few differentiation studies to address gender, Dye and

Very (1968) administered a battery of 20 tests measuring mathematical

achievement, verbal ability, numerical reasoning, and perceptual speed. The

total sample consisted of 556 ninth grade (n = 165), eleventh grade (n = 193),

and university students (n = 198). Each grade level contained an approximately

equal number of young men and women. Mean ages for the eighth grade,

eleventh grade, and university students were 14, 16, and 20 years, respectively.

Correlations between tests were calculated, and factor analysis was performed

within each grade level and by gender. Results again supported Garrett's

hypothesis, with the greatest differentiation occurring for males at each of the

grade levels.

Certainly, not every study of this period supported Garrett's hypothesis

of emergent differentiation. Peel and Graham (1952) administered a battery of

10 group intelligence tests to 352 students from British public schools. The

children were retested one year later. On the first occasion, g accounted for

65% and 67% of the variance in scores for boys and girls, respectively. On the

occasion ofretesting, the respective contribution ofg rose to 72% and 75% for

boys and girls. Peel and Graham concluded "the evidence appears against

differentiation of ability with increasing age, and rather in favour of

integration" (p. 33). Although Peel and Graham did not explicate what they






18


meant by the term "integration," they were quite clear in their rejection of the

Garrett hypothesis. The eminent psychometrician P.E. Vernon (1950) also

offered no support for emergent differentiation. In his classic text, The

Structure of Mental Abilities, Vernon stated that he "at one time accepted the

view that g tends to differentiate into more specialized abilities during early

adolescence and adulthood" (p. 30). However, Vernon's own investigations

prompted him to reconsider his position. For example, Vernon and Parry

(1949) gave the standard British naval battery of five tests to a sample of 1,171

boys at 14 years of age. These results were compared with 265 naval seaman

aged 18 years. Vernon and Parry reported "the average inter-correlations and

the g-saturations were almost identical between the groups" (p.30). Vernon

also cites a "particularly striking" study by Williams, Hunt, and French (1948)

in which, for a sample of 250 boys at three age levels, first factor variances

rose from 51% to 62%. Regarding the structure of intelligence across age,

Vernon succinctly concluded that "there is no general tendency towards

differentiation" (p. 31).

Guilford (1967) reviewed 27 studies of this period related to the

Garrett hypothesis and noted a number of methodological shortcomings that

may have clouded results. First, several studies utilized tests with recognizably

poor reliabilities. The magnitude of a correlation depends on the tests'

reliability. Therefore, the lower their reliability, the lower their inter-

correlations. Second, studies typically did not include young children in their

samples. The search for undifferentiated abilities needs to begin before






19


adolescence, when cognitive abilities are essentially tantamount to those

identified in adults. Third, few studies had any uniformity in their test battery,

even when using a single standardized test across age levels. For example,

Jones (1949) examined the performance of 800 children in four different age

groups on the Stanford-Binet. His results supported emergent differentiation.

However, the content of Stanford-Binet subtest items varied markedly with

age, with more heterogeneous items appearing as age increases. Therefore, the

differentiation observed across age levels may simply be the result of new,

additional information fed into the factor analysis. Finally, in accordance with

his disputation ofg as a psychological construct, Guilford found the Garrett

hypothesis theoretically untenable: "When there is no insistence of a g factor,

no g factor is found even down to the first year. There is therefore no need for

assuming a general ability from which differentiation can proceed in

development" (p. 416). Of the 27 studied reviewed by Guilford, 11 favored

Garrett's hypothesis, while 16 of the studies provided no support.

Subsequent studies of Garrett's hypothesis attempted to address these

acknowledged imperfections. Atkin, Bray, Davison, Herzberger, Humphreys,

and Seizer (1977) analyzed archival data provided by ETS to identify patterns

in the gradual differentiation occurring between fifth and eleventh grades.

Sixteen achievement tests representing all curricular domains were

administered to the same group of approximately 1,700 students at the

beginning of each academic year. Factors were extracted and rotated into an

oblique solution. These factor correlations were then transformed into an





20


orthogonal hierarchical structure in accordance with Schmid and Leiman

(1957). Atkin et al. Reported:

There is a gradual sharpening of the factor pattern during the six year
period. Large loadings tend to become larger with increased age of the
group factors while the size of the loadings on the general factor
become somewhat smaller" (p. 73).

As with Dye and Very (1968), the greatest differentiation occurred for males.

Most studies of the Garrett hypothesis utilized school-aged samples.

Comparatively few have investigated cognitive differentiation beyond early

adulthood. In one of the first applications of confirmatory factor analysis to the

study of differentiation, Cunningham (1980) analyzed data from three groups,

each exclusively comprised of young adults (age range 15-32 years), younger

old adults (age range 53-68 years), and older adults (age range 69-91 years).

Cunningham reported that, while the structure of abilities remained consistent

across age, the factor covariances displayed a pattern of increase across the

three age levels. Stated differently, there appeared to be an integration, rather

than differentiation, of cognitive abilities as individuals entered old age. In an

extension of this study, Cunningham (1981) administered parallel batteries to a

sample of 234 college students and 388 senior citizens. Each battery was

constructed to measure Verbal Comprehension, Number Facility, Perceptual

Speed, Symbolic Cognition, and Flexibility of Closure. Cunningham again





21

identified the pattern of"integration" noted earlier by Owens and Thompson

(1954) but explicated in greater detail:

Although it is a subtle point, the indication from the current findings is
that it is less an issue of simplification of structure so much as it is an
increasing interdependence of different aspects of intellectual
functioning. Two prominent candidates for a mechanism to explain
such increasing dependencies are intellectual speed and the health-
terminal decline phenomenon. (p. 19)

Although not intended as a direct study of the Garrett hypothesis, Keith and

Witta (1997) examined the implied structure of the Wechsler Intelligence Scale

for Children, Third Edtion (WISC-III; Wechsler, 1991) for children 6 to 16

years of age. Confirmatory analysis of the standardization data provided no

support for differentiation of cognitive abilities:

The WISC-III appears to be remarkably consistent in what it measures
from ages 6 to 16; indeed the matrices at different age levels were
statistically indistinguishable. Furthermore, it appears that the WISC-III
does indeed measure four factors as defined in the manual, and that it
does so extremely consistently across the test's age range. (p. 104)

As a test of the structure of cognitive abilities across the lifespan, Bickley,

Keith and Wolfe (1995) used 16 cognitive and achievement subtests of the

Woodcock-Johnson Psychoeducational Battery-Revised standardization

sample to represent eight broad factors at Carroll's second stratum. Bickley et

al. found the correlation matrices and factor structure equivalent across all age

groups represented in the standardization. The general factor had consistently

high loadings on the eight represented primary abilities across each age level,

providing no support for differentiation. In addition, the g loadings obtained

with principal components analysis were extremely congruent with those





22


obtained from confirmatory factor analysis, correlating .9994. Thus, Carroll's

three stratum model, as depicted by the Woodcock-Johnson Psychoeducational

Battery, Revised, is remarkably stable across the lifespan.

At present, the most comprehensive word regarding the emergent

differentiation of cognitive factors comes from Carroll's (1993) Human

Cognitive Abilities: A Survey of Factor-Analytic Studies. In addition to the

several of the selected studies offered in this review, Carroll examined 48 other

data sets that, because they included samples of different ages and highly

similar test variables, could show differentiation by age or grade. Carroll

agreed that common sense suggests that differentiation should occur with age,

insofar as abilities are formed, maintained, and developed through experience.

However, he found no supportive evidence:

I am struck by the fact that nearly all the major types of abilities can be
detected and isolated over a wide range of ages-often at a quite early
age-and as a rule they appear to be the same factors regardless of age
level...My general conclusion on age-differentiation of cognitive ability
factors is that it is a phenomenon who's existence is hard to
demonstrate. (p. 680-681)

Thus, even some of Garrett's original data, upon reanalysis, did not support

differentiation.

In summary, these studies provide equivocal support for the

differentiation of cognitive abilities with age. A number of past studies seem to

support Garrett's hypothesis, while more recent investigations do not. Because

this developmental issue is extremely important to intelligence theory and the

practice of psychology, research will certainly continue. With the increased use






23


of advanced statistical methods, such as confirmatory factor analysis,

researchers are inching toward a resolution.

Stability of g Loadings Across Different Ability Levels.

In his investigations ofg and positive manifold, Spearman (1927) noted

that correlations between test scores vary according to intellectual ability. Test

correlations are higher in low-IQ individuals and lower in high-IQ individuals.

Although he did not investigate the phenomenon systematically, he did offer

post hoc comments on the "curious matter that has arisen" (1927, p. 5). In

1927, Spearman, using his own data and results from other studies, remarked:

Now, all the changes we have been considering follow a general rule.
The correlations always become smaller-showing the influence ofg
on any ability to grow less-in just the classes of person which, on the
whole, possess this g more abundantly. The rule is, then, that the more
"energy" a person has available already, the less advantage accrues to
his ability from further increments of it.
(p. 219)

Drawn to industrial metaphor, Spearman compared g to the an engine, noting

that an engineer does not achieve a doubling of a ship's speed by doubling the

coal in the boiler (p. 127). Spearman did not write extensively on this

phenomenon, only mentioning it in light of the "diminishing returns ofg" (p.

127). Many researchers (e.g., Brand, 1996; Brody, 1992) have considered

Spearman's hypothesis of "diminishing returns" evidence that the relationship

between g and test performance is stronger for lower-IQ testees. The variant

nature of g, and the accompanying law of diminishing returns, may explain the

differentiation in ability often observed in high-IQ groups (Garrett, 1938).






24

In his text, The Structure of Human Abilities, Vernon (1950) posed the

question that the structure of intellect may be different for high-ability groups

due to the homogeneity of the sample. However, Vernon's brief statements

only concerned the upper range of ability, and offered no insights as to the

comparative structure of intelligence for low-ability groups. Lienert and Faber

(1963) conducted one of the first studies expressly designed to investigate

ability differentiation across groups of different overall intelligence. An analysis

of the Hamburg-Wechsler Intelligence Test for Children (HAWIK), the

German version of the WISC, found a smaller first centroid factor for children

with IQs above 109 than for children with IQs below 109. Lienert and Crott

(1964) extended this research by administering a battery of 14 tests to three

different age groups. Tests included measures of vocabulary, comprehension,

digit memory, and spatial reasoning. Lienert and Crott found the number of

common factors increased from five (for children aged 10-12 years) to six (for

adolescents aged 18-20 years), and subsequently dropped to four (for adults

aged 45-60 years). When the sample of children was divided into high- and

low-ability groups, Lienert and Crott identified four factors for the low-ability

group, and five factors for the high-ability group. Their results agreed with

previous studies of differentiation with age, and prompted their use of the term

"differentiation" to refer to mental abilities differentiating as children increase

in chronological age, and the term "divergence" to reference lower correlations

between mental abilities found among testees with higher levels of overall

intelligence.






25

Lienert and Crott proposed an integration of differentiation and

divergence of mental abilities:

In the same way as the improvement of performance from childhood to
adolescence is accompanied by a differentiation of the underlying ability
structure, and as the decline of performance from adolescence to
adulthood is accompanied by an integration of structure, a divergence
and convergence of the ability structure takes place from low to high
performance level and vice versa respectively. Therefore, it may be
assumed that performance level and degree of differentiation are
interdependent and that-regardless of the subject's age-differences
in intelligence level presuppose variations in the structure of
intelligence in accordance with the divergence hypothesis. (p. 158)

Linert and Crott (1964) also found evidence for convergence when testees

were impaired with LSD and alcohol.

Spearman's observation that test correlations vary among groups of

different ability received little attention from contemporary psychologists until

Detterman and Daniel (1989) divided the standardization samples of the

Wechsler Intelligence Scale for Children, Revised (WISC-R) and Wechsler

Adult Intelligence Scale (WAIS) into five groups based on their performance

on either the Vocabulary or Information subtests. These subtests were selected

for their high correlations with Full Scale IQ, and because Wechsler (1981)

found these subtests relatively stable across age. IQ equivalents for the five

groups, from lowest to highest, were below 78, 78 to 92, 93 to 107, 108 to

122, and above 122. Correlation matrices were computed for each group.

Detterman and Daniel found that subtest intercorrelations for the lowest IQ

group (below 78) were twice as large as the intercorrelations for the highest IQ

group (above 122). For the low-IQ group, intercorrelations averaged .56,






26


uncorrected for range restriction; for the high-IQ group, intercorrelations

averaged .22. Confirmatory analyses with the LInear Structural RELlations

computer program (LISREL; Joreskog & Sorbom, 1989) verified that none of

the correlation matrices could be considered equal for any of the tests or

methods of group selection. Thus, subtest correlations change across ability

levels. Deary and Pagliari (1991) credited Detterman and Daniels for

rediscovering Spearman's law of diminishing returns.

Replicating Detterman and Daniels' procedures for subsample grouping

and analysis, Lynn (1990) obtained similar results with the WISC-R

standardization samples from Scotland. Subtest correlations, from low- to

high-ability groups, were .44, .38, .17, .14, and .20. Lynn and Cooper (1994)

also used the law of diminishing returns to investigate a secular decline in g.

Because IQs have increased substantially in the last few decades, Lynn and

Cooper hypothesized that subtest intercorrelations should be lower for the

WISC-R than for the WISC. Using the standardization samples of the French

WISC and WISC-R, Lynn and Cooper reported average correlations of.38

and .29 for the WISC and WISC-R, respectively.

One important question regarding the divergence of mental abilities was

whether Spearman's law of diminishing returns applied only to individually

administered intelligence tests, such as the Wechsler scales. Legree, Pifer, and

Grafton (1996) extended these results to group ability tests, analyzing the 1980

norming sample of the Armed Services Vocational Aptitude Battery (ASVAB).

Using a sample of 9,173 participants, Legree et al. formed five ability groups






27

based on performance on each of the 10 ASVAB subtests. Thus, there were 10

sets of five correlation matrices. Correlations were corrected for restriction of

range and submitted to confrimatory factor analysis. Seven of the 10 scales of

the ASVAB conformed to Spearman's law of diminishing returns, with

intercorrelations being higher for the low ability group than the high ability

group. A review of the three scales excepted from this pattern indicated

substantial measurement error and skewness. The authors concluded, "These

data support the conclusion that cognitive abilities are less correlated within

more intelligent groups" (p. 53). Thus, for cognitive tests with adequate

psychometric properties, the law of diminishing returns seems to hold.

This pattern of test correlations has also been substantiated using

elementary cognitive tasks (ECTs). For example, the correlation between IQ

and inspection time (IT) for individuals with IQs of 60 is around .80. The IQ-

IT correlation shrinks to .50 for individuals with IQs above 110, however

(Brand, 1996). Interestingly, the law of diminishing returns may not extend to

all speeded perceptual tasks. Fogarty and Stankov (1995) administered RPM

and four perceptual speed tasks (Number Comparison, Symbol Search, Digit

Symbol, and Stroop paradigm) to a sample consisting of 179 university

students. High- and low-ability groups were identified, based on total raw

scores which were either one standard deviation above or below the mean on

RPM. Thus, two groups were formed, consisting of 29 low-ability and 28

high-ability individuals. IQ equivalents for low-ability group were between 92

and 103. Participants in the high-ability group all had IQ equivalents above





28


125. Correlations between the perceptual tasks were calculated for each group

and subjected to confirmatory analysis. The resulting test of equality indicated

that the matrices were essentially the same in both groups. Fogarty and

Stankov argued that "employing tests with a more or less uniform difficulty

level for different ability groups (as measured by some external criterion),

showed that under these conditions, the correlations are the same for the

various groups" (p. 172). Unfortunately, the extremely small sample sizes

employed in Fogarty and Stankov's investigation preclude it from being a

serious challenge to the law of diminishing returns.

The most recent investigation of cognitive divergence comes from

Edinburgh University. Deary, Egan, Gibson, Brand, and Kellaghan (1996)

analyzed the standardization data from the British-Irish version of the

Differential Aptitude Test (DAT; 1986). The DAT consists of eight subtests

measuring verbal ability, abstract reasoning, numerical reasoning, clerical

speed, mechanical reasoning, spatial ability, spelling, and language usage. Total

sample consisted of 10,535 participants in eighth, ninth, tenth, and eleventh

grades. Deary et al. divided the sample into four smaller subsamples based on

grade and ability (e.g., high grade-high IQ; high grade-low IQ; low grade-low

IQ; low grade-low IQ). Average IQs of the low- and high-ability groups were

90 and 110, respectively. Average ages of the young and old groups were 14.2

and 16.7 years, respectively. Within each of the four groups, correlation

matrices were subjected to principal components analysis. As an indicant of the

pervasiveness of g, Deary et al. used the percentage of variance accounted for





29

by the first unrotated principal component. The percentage of total variance

explained by g in each of the groups was between 47.8 and 49.8 %. Thus, their

analysis offered no strong support for differentiation by age or ability:

The difference in variance between groups that differ by the equivalent
of 20 IQ points is just over 2%. Moreover, across the age range
investigated...this study finds little evidence to suggest that human
mental ability is more differentiated in older groups. (p. 120)

Deary et al. reasoned that the lack of differentiation in their study, when

compared to the impressive results obtained by Detterman and Daniel, may be

caused by restriction of range. In their study, low- and high-ability participants

differed by 20 IQ points. Conversely, Detterman and Daniel's lowest and

highest groups differed by 44 IQ points. In addition, any differentiation across

age would be difficult to identify, given the narrow age range of this

investigation (2.5 years). In sum, these studies confirm the importance ofg in

explaining cognitive performance, but also suggests that g is variant for

different ability groups.

Competing Explanations for the Differentiation of Cognitive Abilities.

In his text The g Factor, Chris Brand (1996) offered two competing

hypotheses to explain the variant nature ofg and the differentiation of

cognitive abilities in high-IQ individuals. The first hypothesis, initially advanced

by Burt in 1919 and later by Garrett (1938), contends that high-IQ individuals

have intellectual "investment opportunities" that develop with age. Stated

differently, experience affords high-IQ individuals the opportunity to acquire

varied cognitive skills and strategies in a fashion that is superior to their low-





30


IQ peers. Primary abilities are thus seen to develop to a greater extent in high-

ability individuals than they do in low-ability individuals.

The second hypothesis, suggested by Detterman (1989) and Anderson

(1992), focuses on the detectability of cognitive ability. Detterman (1994)

posits that intelligence is made up of a number of inter-related processes. Thus,

deficits in one process may critically affect all other processes:

The differences in correlations across IQ level are consistent with the
systems theory of intelligence...In this theory, lower IQs result from
deficits in important cognitive processes. Because these processes are
part of a system, they affect the functioning of other parts of the
system. If these important processes are deficient, parts dependent on
them will also be impaired. Essentially, a deficit in an important process
will put an upper ceiling or limit on the efficiency of the operation of
other parts of the system. That means that all parts of the system will
be more similar if there is a deficiency in an important process. This
forced similarity in abilities is what causes a higher correlation among
IQ subtests for low IQ subjects. (p. 28)

Stated differently, low-IQ people possess the same skills as high-IQ

individuals; however, their relatively poor performance on cognitive tests

obscures the differentiation of cognitive abilities. A useful analogy is to

consider two stereo systems playing the same song. One stereo system plays

beautifully. The second stereo system is riddled with static. Even though both

stereo systems play the same tune, the better sounding system permits the

listener to hear every note of the song and to distinguish the woodwind section

from the string section. Conversely, the same song playing from the second

stereo system is barely discernible.

Although Spearman did not directly address the source of cognitive

differentiation, passages from The Abilities of Man suggest that he favored the






31

detectability hypothesis. In discussing individual differences in cognitive

abilities, Spearman stated:

The whole frequency distribution (of distinct cognitive abilities in any
individual) will, in fact, have a bell-like shape ....At the extreme ends of
the distribution will lie a very small number for which the person is, on
one side a genius, and on the other an idiot. Every normal man, woman,
and child is, then, a genius at something, as well as an idiot at
something. The question is what-at any rate in respect of the genius.
This must be a most difficult matter, owing to the fact that it occurs in
only a minute proportion out of all possible abilities. It certainly cannot
be detected by any of the testing procedures at present in current usage;
but these procedures seem to be susceptible to vast improvement. (p.
221)

To date, the question of whether the differentiation of cognitive abilities for

subjects of different IQ level is due to detectability or development remains

unanswered.

Summary

Past research indicates that a test's g loading may vary across groups

of different intellectual ability. As a result, low-IQ individuals do not display

the differentiation in abilities often observed in the test performance ofhigh-IQ

individuals (Brand, 1996; Detterman & Daniels, 1989; Spearman, 1927). A

reasonable conclusion drawn from these findings is that the structure of

intellect varies for individuals of differing ability. Researchers have yet to

investigate this particular phenomenon in the context of Carroll's three stratum

theory of intelligence. In addition, the cause of intellectual differentiation has

yet to be identified. Studies to this point have been somewhat equivocal (e.g.,

Anderson, 1992; Carroll, 1993; Deary et al., 1996; Guilford, 1981; Lynn,

1990). Thus, the purpose of this study is twofold. The first purpose is to






32

compare the structures of intellect for low- and high-ability children within the

framework of Carroll's three stratum theory of intelligence. Carroll (1993)

relied exclusively on exploratory factor analysis to formulate his theory. The

confirmatory techniques used in this study would further verify the three-

stratum theory across ability levels. The second purpose is to determine

whether differentiation of cognitive abilities is emergent with experience and

development, or simply detected by IQ tests.















CHAPTER 3
METHOD

Participants and Data Collection

Archival data from the Woodcock-Johnson Psychoeducational Battery,

Revised (WJ-R; Woodcock & Johnson, 1989) has been provided by the test's

co-author, Dr. Richard Woodcock. Normative data for the WJ-R were

collected from 6,359 participants in over 100 geographically diverse

communities in the United States (Mather, 1992). Subjects were sampled

randomly from a stratified sampling design that controlled for ten community

and socio-economic variables. The age of participants ranged from 24 months

to 95 years. All data were gathered from September, 1986 to August, 1988.

The sample was weighted and corresponds closely to the 1980 census on such

relevant characteristics as race, gender, region, community size, and so forth.

Description of the WJ-R

The WJ-R is designed as an operational representation of the Horn-

Cattell gfgc theory of intelligence, with the eight cognitive clusters of the WJ-

R corresponding to an array of broad cognitive factors in the Horn-Cattell

model. With the addition of a general factor and minor revisions of factors at

the second order, the WJ-R also provides an excellent representation of

Carroll's three stratum model (Carroll, 1993; McGrew, 1997).

33






34


The WJ-R is divided into two main parts: the Tests of Cognitive Ability

(WJ-R COG) and the Tests of Achievement (WJ-R ACH). Each of these parts

is divided further into a Standard and Supplemental Battery.

The WJ-R COG Standard Battery is comprised of tests 1 to 7, and the

Supplemental Battery consists of tests 8 through 21. The Standard Battery is

designed to provide a full-scale cognitive score. The tests may be administered

in any order and measures each of seven cognitive factors. Five of the

measures may be used to assess preschool or low-functioning adults. A

description of each test follows, with variable names being those used in

subsequent analysis (Mather, 1992, p 4-18):

Test 1: Memory for Names (memnamw) requires the testee to

remember and identify cartoon drawings of space aliens. The test is designed to

measure the ability to form and retrieve auditory-visual associations.

Test 2: Memory for Sentences (memsenw) measures the ability to

repeat words, phrases, and sentences that are presented by a tape player. This

test primarily measures short-term memory.

Test 3: Visual Matching (vismatw) measures the ability to identify and

circle quickly and two identical numbers in a row of six numbers. The test has

a 3 minute time limit.

Test 4: Incomplete Words (incwrdw) measures auditory closure, or the

ability to identify words with missing sounds. The test assesses auditory

processing.






35


Test 5: Visual Closure (visclow) measures the ability to identify a

picture or drawing that has been altered in one of several ways. This test

primarily measures visual processing.

Test 6: Picture Vocabulary (picvocw) measures the ability to identify

and name pictured objects. This test primarily assesses comprehension-

knowledge.

Test 7: Analysis-Synthesis (ansynw) measures the ability to determine

the missing component of an incomplete logic puzzle. The test primarily

measures fluid reasoning.

The 14 tests comprising the Supplemental Battery provide additional

information about seven cognitive factors. A description of each test follows:

Test 8: Visual-Auditory Learning (valrngw) measures the ability to

retain visual-auditory associations. This test requires the subject to retain and

identify up to 28 rebuses that are read within the context of a meaningful

sentence.

Test 9: Memory for Words (memwrdw) requires the testee to repeat

lists of unrelated words in the correct order. This test measures short term

memory.

Test 10: Cross Out (crsoutwe) measures the ability to scan and

compare visual information rapidly. The student is asked to mark the 5

drawings in a row of 20 geometric drawings that are identical to a target

drawing. A time limit of 3 minutes is imposed. This test measures processing

speed.






36


Test 11: Sound Blending (sndblndw) measures the ability to synthesize

a series of sounds into whole words. From a taped recording, word parts are

presented first as syllables, and then as phonemes. This test measures auditory

processing.

Test 12: Picture Recognition (picrecwe) measures the ability to

recognizable a subset of previously presented pictures within a field of

distracting pictures. This test primarily measures visual processing.

Test 13: Oral Vocabulary (orlvocw) measures knowledge of word

meanings. The student is asked to provide synonyms and antonyms of words

presented orally. This test measures comprehension-knowledge.

Test 14: Concept Formation (confrmw) measures categorical reasoning

ability. Testees are asked to derive and identify rules for concepts when shown

illustrations of concepts and non-concepts. This test primarily measures fluid

reasoning.

Test 15: Delayed Recall-Memory for Names measures the ability to

recall from 1-8 days later the stimuli presented in Test 1: Memory for Names.

This test primarily measures long-term retrieval.

Test 16: Delayed Recall-Visual Auditory Learning measures the

ability to recall from 1-8 days later the stimuli presented in Test 8: Visual-

Auditory Learning. This test primarily measures long-term retrieval.

Test 17: Numbers Reversed measures the ability to repeat a string of

digits in reverse order. This test requires perceptual reorganization and

primarily measures short-term memory and fluid reasoning.






37


Test 18: Sound Patterns measures the ability to indicate whether pairs

of sound patterns are the same or different. Pairs differ in pitch, rhythm, or

duration. This test primarily measures auditory processing.

Test 19: Spatial Relations measures the ability to math shapes visually

with the component parts. The student must select the correct pieces from a

series of shapes to make a given whole shape. This test is a mixed measure of

visual processing and fluid reasoning.

Test 20: Listening Comprehension measures the ability to listen to a

short tape-recorded passage and supply the single word that best completes

each passage. This test measures comprehension-knowledge.

Test 21: Verbal Analogies requires the testee to complete phrases with

words that indicate appropriate relationships. This test measures fluid

reasoning and comprehension-knowledge.

The WJ-R COG provides three broad based measures of intellectual

ability:

Broad Cognitive Ability-Early Development is appropriate for

children at the preschool level or for low-functioning adults. This cluster

consists of five tests. Test 1: Memory for Names, Test2: Memory for

Sentences, Test 4: Incomplete Words, Test 5:Visual Closure, and Test 6:

Picture Vocabulary.

Broad Cognitive Ability-Standard Scale is based on all seven tests in

the Standard Battery and provides a broad-based measure of intellectual

functioning.






38

Broad Cognitive Ability-Extended Scale is based on the first 14

cognitive tests. If all 14 tests have been administered, this score is used as the

broad-based measure of intellectual ability.

The WJ-R ACH Standard Battery is comprised of tests 22 through 30.

The Supplemental Battery includes tests 31 to 35, and measures written

language skills. A brief description of each test follows:

Test 22: Letter-Word Identification measures the ability to identify

letters and words. Successful word identification does not require

comprehension, as a subject may or may not know the meaning of a word.

Test 23: Passage Comprehension measures the testee's ability to use

syntactic and semantic clues.

Test 24: Calculation (calcw) measures an individual's ability to perform

a variety of mathematical calculations, including addition, subtraction,

multiplication, and division. Problems progress from relatively simple addition

to more advanced geometric, trigonometric, and logarithmic operations.

Test 25: Applied Problems (approbw) requires an individual so solve

practical problems.

Test 26: Dictation measures spelling, knowledge ofprewriting skills,

punctuation and capitalization, and usage.

Test 27: Writing Samples measures ability to produce meaningful

sentences to satisfy a variety of task demands. Emphasis is placed on the

quality of writing, rather than basic skills.






39


Test 28: Science measures knowledge of both biological and physical

sciences.

Test 29: Social Studies measures knowledge of history, geography,

economics, and government.

Test 30: Humanities measures knowledge of art, music, and literature.

Test 31: Word Attack measures the ability to apply phonic and

structural analysis skills in pronouncing phonically regular nonsense words.

Test 32: Reading Vocabulary measures knowledge of word meanings

by providing synonyms and antonyms.

Test 33: Quantitative Concepts measures an individual's knowledge of

basic mathematical concepts and vocabulary.

Test 34: Proofing measures an individual's ability to correct errors in

punctuation, spelling, capitalization, and usage in written passages.

Test 35: Writing Fluency measures the ability to produce correct forms

of writing and correct errors in written passages.

Tests of the WJ-R combine to form eight cognitive factors. A brief

description of each factor follows, with notations being those used by

Woodcock and Mather (1990, p. 23):

Long-term retrieval (Glr) measures the effectiveness in storing and

fluently retrieving information over extended periods of time. The time period

may range from several minutes to several days.

Short-term memory (Gsm) measures the ability to apprehend

information and repeat it within a short period of time.





40


Processing speed (Gs) measures the ability to performed relatively

simple tasks quickly.

Auditory processing (Ga) measures the ability to analyze and synthesize

auditory patterns.

Visual processing (Gv) measures capability in perceiving and thinking

with visual patterns.

Comprehension-knowledge (Gc) measures breadth and depth of

knowledge and its applications.

Fluid Reasoning (Gf) measures the capability for abstraction and

reasoning in novel situations.

Quantitative ability (Gq) measures comprehension of quantitative

concepts and skill in using mathematical symbols.

The hypothesized factor structure of the WJ-R is presented in Figure 2.

Since its publication, a number of studies have investigated the

psychometric properties of the WJ-R. Woodcock (1990) summarized nine

conjoint validity studies which included the WJ-R with various combinations of

the Wechsler scales, Stanford Binet, Fourth Edition (SB:FE; Thorndike,

Hagen, & Sattler, 1986) and Kaufman Assessment Battery for Children







41






Concept Foraton


Analysis Synth~


Visul Clos&t
Gv
Pictur Recognton


Visual MctVhin
Ga

Cmr- Out


Mmony For Neme
Glr

Visual Auditry Lmreg


(c Picau Voulreotcy


Oral Vocabulry


Go hicomnplet Wors


Sound Blendmn


Mmory For Seintens


Memory for Words

Gq
CauIon


Appld Problemn

Figure 2. Three-stratum theory represented by the Woodcock-Johnson,
Revised.


(KABC; Kaufman & Kaufman, 1983). A total of 15 different confirmatory


analyses were conducted using 68 subtests. The results of this summary


provided universal support for the eight factors represented in the WJ-R. The


psychometric properties of the WJ-R have been termed "excellent" (McGrew


et aL, 1991; Bickley et aL, 1995).





42


The Model

The three-stratum model is shown in Figure 3. The first level of the

model represents primary abilities. These abilities are indexed by 16 of the 39

subtests of the WJ-R Tests were selected on the basis of their strong,

exclusive loadings on the proposed factors. The second level represents the

eight cognitive factor clusters measured by the WJ-R. While the WJ-R is

primarily based on the gc-gf model of intelligence, Carroll (1993) has noted

that these cognitive factor clusters also provide a satisfactory representation of

his second-stratum abilities. The third stratum represents Spearman's g.

Statistical Procedures for Subgroup Selection

To answer each of the research questions in this study, the first task

was to form subgroups of high- and low-ability participants. Furthermore, the

desired analyses required that each subgroup was to have near identical

bivariate normal distributions of criterion ability. A review of recent studies in

the area of confirmatory factor analysis offers several methods for forming

subgroups from a large sample. In the most widely cited study, Detterman and

Daniel divided their sample according to subtest scores, forming five groups.







43






Concept Formm)ton

Gf
An"lyrs Symnthe


Vtsul Closnre

Gv
Pcunm Recognition


Visual Mtchig


Cro Out


Mmomy For NWme
















\ SundBlding


M\mory For f Snot


Memoy tor Worts

Gk
Calculttkon


Appftd Problem



Figure 3. Hypothesized structure of the Woodcock-Johnson, Revised.





44


Deary et al. (1996) also used subtest scores, but drew their groups only from

individuals scoring one standard deviation above or below the mean. Fogerty

and Stankov (1996) used full-scale scores to form two groups, one scoring in

the upper three stanines and the other scoring in the lower three stanines.

This study took a slightly different approach, which is now described.

First, it was necessary to identify an independent variable to establish

subgroups. Broad Cognitive Ability indices could not be used for this purpose,

because subtests included in the proposed model also contribute to each of

these measures of overall intelligence. Therefore, a composite variable

(SortIQ) was created by averaging scores on the Numbers Reversed, Listening

Comprehension, and Verbal Analagies subtests. These subtests are not

included in the proposed theoretical model of cognitive ability, and thus

provide an independent measure of overall intelligence. The simple correlation

between SortIQ and Broad Cognitive Ability-Extended (BCAE) was .94. Two

subgroups (i.e., HighIQ and LowIQ) then were formed by dividing the data at

the mean of SortIQ. Once HighIQ and LowIQ individuals were identified, the

next challenge was to sample from each group a normal bivariate distribution

with equal variances. To accomplish this end, the desired sample sizes, means,

and standard deviations were identified. Sample sizes for each subgroup (i.e.,

HighIQ and LowIQ) were set at 500. Standard deviations for each group were

set at 7.5, about half of the standard deviation typically observed in the general

population. Means for the HighIQ and LowIQ subgroups were 115 and 85,

respectively. Once these characteristics were established, z-scores were





45


calculated using the Broad Cognitive Ability-Standard as the criterion variable.

Individuals were then randomly sampled by z-score intervals, with the desired

number of subjects sampled at each z-score interval equal to that which would

be observed in a normal distribution. The exact number of participants sampled

at each z-score interval is found in Table 1. Following this procedure, there

were two normal distributions, with respective means of 115 and 85, each with

equal variances and sample sizes.

Statistical Analysis

Once subgroups of high- and low- IQ individuals were formed,

confirmatory factor analysis then was used to compare the constructs measured

by the WJ-R across each ability level. In confirmatory factor analysis, the

factor structure is restricted a priori according to guidelines offered by theory.

The obtained data is then compared with the restricted, theoretical model.

Keith (1997) operationalized a process for testing increasingly lenient models

as a method of determining if a psychometric instrument measures the same

construct across groups. If analyses leads to rejection in the initial, most

stringent model, increasingly lenient alternative models are developed and used

in subsequent steps. For this investigation, the AMOS (Arbuckle, 1996)

computer program was used to simultaneously evaluate the proposed three-

stratum model of intelligence across two ability levels.

When using AMOS, a nonsignificant x2 shows that the theoretical

model fits the empirical data. Note that the x2 need not be significant to select






46




one model over another. In the event of a nonsignificant chi square, the

degrees of freedom can indicate which model is the most parsimonious. A

Table 1. Summary of Subgroup Selection

z-Score Normal Number
Interval Probabilities Sampled Cumulative

less than -2.5 .01 5 5
-2.5 < -2.0 .02 10 15
-2.0 < -1.5 .04 20 35
-1.5 < -1.0 .09 45 80
-1.0 < -0.5 .15 75 155
-0.5 < 0 .19 95 250
0 < .5 .19 95 345
.5 < 1.0 .15 75 420
1.0 < 1.5 .09 45 465
1.5 < 2.0 .04 20 485
2.0 < 2.5 .02 10 495
greater than 2.5 .01 5 500



common criticism of the x' test relates to its sensitivity to sample size. For

example, large sample sizes can result in a statistically significant x2 value and

lead to a false rejection of models. Conversely, small sample sizes may

contribute to a nonsignificant x2 value and lead to false acceptance of the

model. As a result of the influence of sample size on the x2 value, several

researchers (e.g., Keith, 1997) recommend the use of more than one fit statistic

to evaluate models. The Tucker-Lewis Index (TLI, also called the non-normed

fit index) provided an additional measure of fit. The Parsimonious Fit Index

(PCFI), a fit statistic that favors simpler, more parsimonious models over more

complex models, is also reported. The Bentler-Bonnett non-normed fit index






47

(NFI) estimated the relative improvement of each model over the null

hypothesized model. For each of these additional indices of fit, values range

from 0 to 1.0, with 0 indicating a poor fit, and 1.0 indicating a perfect fit.

Generally, values over .90 are considered excellent.

Loadings across models were compared not only in terms of g, but

also in terms of the cognitive clusters. When compared across groups,

differences in the loadings ofsubtests on the cognitive factors indicate the

relative importance of primary abilities. If the expected cognitive differentiation

occurs at higher levels of intelligence, an important theoretical issue was

whether the differentiation resulted from a diminished role ofg or an increased

role in primary abilities.

To answer the second research question, whether development or

detectability underlies the differentiation of cognitive abilities, the same

procedures described above were used with respect to age and ability. The

young groups consisted of individuals between 6 and 12 years. The older

groups consisted of individuals between 13 and 22 years of age. These ages

correspond closely to guidelines offered by Piaget for the emergence of

abstract reasoning and formal operations. Within each age group, high- and

low-ability subgroups were formed. Thus, a total of four groups were formed:

young-high IQ (ChildHighIQ), young-low IQ (ChildLowlQ), old-high IQ

(AdolHighlQ), and old-low IQ (AdolLowIQ). Again, sample sizes and

standard deviations were equal for each group (n = 250, s = 7.5). Within each

age level, confirmatory maximum likelihood analysis compared the three






48

stratum model simultaneously across each ability group. In addition, g loadings

across age cohorts were examined. Ifg loadings decrease as the cohort age

increases, then the differentiation of intellectual ability is due to the

development of primary abilities. Conversely, stable g loadings across age

groups lend support to the detectability hypothesis.



















CHAPTER 4
RESULTS


Descriptive statistics for HighIQ and LowIQ are presented in Tables 2


and 3. Data are reported in W-scores. W-scores are a special transformation of


the Rasch ability scale and have mathematical properties, such as equal


intervals, that make them well-suited for the subsequent confirmatory analyses


required of this study (Andrich, 1988). The histograms of HighIQ and LowIQ


are presented in Figures 4 and 5. As can be seen clearly, both distributions are


normal, with near equal standard deviations.


120

100

80

60

40

20, Std. Dev= 7.68
Mean = 115.0
0 N = 500.00
97.5 102.5 107.5 112.5 117.5 122.5 127.5 132.5
100.0 105.0 110.0 115.0 120.0 125.0 130.0

BCASTDAS
Critertan Variable Broad Cognitive Ability

Figure 4. Histogram of High-IQ Distribution









49






50


Table 2. Descriptive Statistics for High-IQ Group (HighIQ)

Variable Name Mean Std. Deviation N

Concept Formation 5208.09 147.41 500
Analysis Synthesis 5185.24 115.00 500
Visual Closure 5116.65 100.70 500
Picture Recognition 5119.78 92.39 500
Visual Matching 5285.09 165.33 500
Cross Out 5173.51 112.10 500
Memory for Names 5087.14 127.16 500
Visual Auditory Learning 5076.04 106.33 500
Picture Vocabulary 5372.12 163.71 500
Oral Vocabulary 5414.49 175.20 500
Incomplete Words 5082.30 90.84 500
Sound Blending 5136.39 152.21 499
Memory for Sentences 5218.21 126.35 500
Memory for Words 5178.28 198.05 500
Calculation 5431.33 209.26 499
Applied Problems 5420.66 187.65 498



100

80,






20, Std. Dev = 7.46
Mean = 85.1
0N = 500.00
67.5 72.5 77.5 82.5 87.5 92.5 97.5 102.5
70.0 75.0 80.0 85.0 90.0 95.0 100.0

BCASTDAS
Criterian Variable Broad Cogntive Ability


Figure 5. Histogram of Low-IQ Distribution






51


Table 3. Descriptive Statistics for Low-IQ Group (LowIQ)

Variable Name Mean Std. Deviation N

Concept Formation 4862 207 495
Analysis Synthesis 4868 179 493
Visual Closure 4936 146 500
Picture Recognition 4957 117 500
Visual Matching 4915 256 500
Cross Out 4938 173 499
Memory for Names 4921 91 500
Visual Auditory Learning 4900 115 498
Picture Vocabulary 4951 217 500
Oral Vocabulary 4926 260 499
Incomplete Words 4913 133 499
Sound Blending 4865 208 499
Memory for Sentences 4890 168 500
Memory for Words 4891 217 500
Calculation 4906 364 481
Applied Problems 4903 278 481



A series of confirmatory analyses were conducted using the variance-

covariance matrices for each group. The first analysis examined whether the

variance-covariance matrices of the three-stratum model were similar across

both ability groups. The factor structure of the data is subsumed in the

variance-covariance matrices. Therefore, if these matrices are identical across

age levels, a logical conclusion is that all aspects of the factor structure (i.e.,

first and second order factor loadings, factor unique variances, and subtest

unique and error variances) are similarly invariant across groups. The

hypothesis that the three-stratum model was invariant across the two ability

levels was rejected (x2 = 1461, df= 231, p < .01), suggesting that significant

differences exist in one or more aspects of the factor structures.





52


As noted earlier, x2 can be affected by large sample sizes and may lead

to rejection of an adequate model (Keith, 1997). Thus, three additional

statistical measures also were reported to overcome this possible difficulty: the

Tucker-Lewis Index (TLI), the Parsimonious Fit Index (PFI), and Bentler-

Bonnett Normed Fit Index (NFI). Data from these three indices suggest the

constructs measured by the proposed model do not differ significantly across

the two IQ levels. Given these somewhat conflicting initial findings (i.e., the

initial X2 found significant differences in factor structure across age levels,

while three other goodness of fit indices suggested an adequate fit to the data),

further analyses seemed warranted.

The second analysis relaxed the factor model; permitting the values of

the less important aspects of factorial invariance (i.e., the factor unique

variances, subtest unique and error variances) to differ for each age group

(Keith, 1997). That is, this analysis specified identical factor structure and

loadings across ages, but permitted different values in the unique and error

variances of the first order factors and subtests. By requiring the factor

loadings (i.e., regression weights) to be invariant across groups, this analysis

evaluates whether a fixed unit change on an exogenous variable will always

correspond to the same change of the endogenous variable, independent of

whether the respondent is of high- or low-IQ. The fit statistics for the initial

model and this relaxed model are presented in Table 4.

Relaxing the factor model to permit different values for the unique and

error variances of the first order factors and subtests resulted in a significant






53


improvement in model fit as evidenced by the significant decrease in x2. TLI.

NFI, and PFI remained virtually unchanged.


Table 4. Different Hypotheses Tested in Regard to the Structure of Cognitive
Abilities at Different IQ Levels

Hypothesis Tested X2 df TLI NFI PFI X2 Change

Factor Structure Invariant 1461 231 .99 .99 .84 --
(All Parameters Fixed)

Factor Loadings Identical 1253 207 .99 .99 .75 208*
(Error and Unique Variances Vary)

Factor Structure Similar 1192 192 .99 .99 .70 269*
(All Parameters Free to Vary)


*Indicates a statistically significant improvement in model fit based on x2 decrease.



The third and final analysis permitted all parameters of the factor model

(i.e., factor loadings, unique and error variances of the factors and subsets) to

vary across the nine age groups. Allowing all parameters to differ across age

levels resulted in the expected significant decrease in x2 (x = 1192, df= 192, p

<.01).

In summary, a significant decrease in x2 was achieved by permitting the

unique and error variance to vary across high- and low-IQ groups. Further

significant improvements in the model were obtained by permitting the

remaining parameters to vary (i.e., different factor loadings across ability

groups). Figures 6 through 11 summarize the results of these three analyses in

graphical form. The numbers adjacent to the arrows are factor loadings. The

numbers adjacent to the ovals represent the variance accounted for in the first-





54


order group factors by the second-order general factor. The numbers above

each rectangle represent the proportion of variance accounted for in the subtest

by the group factors. Of particular interest are the loadings, which reflect the

degree of generalizability between each factor and variable. Differences in the

factor loadings exist between the High- and Low-IQ groups. Further analysis

indeed confirms that all first- and second-order factor loadings are significantly

different, at the .05 alpha level, regardless of model. These differences follow

the same pattern, with factor loadings (and hence the proportion of variance

accounted for by each factor) significantly larger for the low-IQ group than for

the high-IQ group. As an aid in conceptualizing the pattern of differences

between ability groups, the g loadings to the primary abilities in Figures 10 and

11 also are summarized in Table 5.

Table 5. Summary ofg Loadings of High- and Low-IQ Groups

Primary Ability g Loading

Low IQ / High IQ
Gf .89 .80
Gv .88 .77
Gs .95 .75
Glr .69 .65
Gc .84 .39
Ga .81 .65
Gsm .72 .39
Gq .86 .72







55



.42














(u3f ----- k- /
45connw 3-5 14
.52/ .64. U1
o.65 .42
S5 *ynw -- u2

.37

.47 .61 VWkP U-3-

Gv 60 36
picneDIW- 4-"4
.70
.72 .58 .84 vM mtw us

Gs < .82 .68


u .29
.76/ .16 .53 nuMp w
Gir
.83 .68
.39





.59 .95 .91
maOrw* U10--

.45 \ .35 6 .43


.67 .43
\tdbhd4w u(2

.20 .52


.60


.44
.81








Figure 6. Simultaneous analysis of high and low IQ groups, with all
parameters constrained across both groups. Mean IQ 115, standard
deviation 7.5. Sample size of 500 in each group.








56



.67

.83 u .82 U1nw
68
S.83 MIs
n1ynw u- u2

7 .62

.81 y .79 VdOW 0*-^3)

GV- .78 .81


p .88

.91 .87 .94 vtmtw us

s .93 .87


a39
.93/ .47 .620 ia r

.88 -77
.68


.81 WD.66 U


.85


.73 .72 .63
u S 4.80 ow

.89 .64
sndbkw u1--

.66


.71


.79
.92


.82




Figure 7. Simultaneous analysis of high and low IQ groups, with all
parameters constrained across both groups. Mean IQ 85, standard
deviation 7.5. Sample size of 500 in each group.








57



.42

.60 .65 coo i...WU
of.85 .43

4W ynr u---2u2

.39

.54 .62 vMcw ---u

Gv .57 .33


.73
.77 / -.55 .85 vemw -- u

.85 .72


.24
74 11 .49 memrmmw 0

.34 .95 90









.4 .41 4
Go 1 wCdW U1

.74 5 42


.51


.56
.31











and subtest unique var s free across both groups. Mean IQ 115,
standard deviation 7.5. Samle size of 500 in each rou
C Gq 91 ---- .83








58



.67

.79 .82 3W
81.8


.59

.77 .77 u

o .80 .63


.88
.89 .90 .94 vmOwU

.92 .85



.42
.95/ .52 .65 memr-mw

.72 .82 .68



.83 .69.80


.81 .92





.86 A63


.65
Gme -mu
.74
.75

75 m.5 wr9w

=d- ~ low u 15)

.82
MPmb UI ---("16)



Figure 9. Simultaneous analysis of high and low IQ groups, with factor
and subtest unique variances free across both groups. Mean IQ 85,
standard deviation 7.5. Sample size of 500 in each group.







59



.52

.64 .72C
Gf .59 .


.38

.60 .61uLO

GV .59 .35


.69
.80 .56 J .63 vwrwtw 0-3 -

G .87 .76


.47
.75 .42 ..^42 .68 ~

.75 .57
.65


.39 .15


65 1.03 1.06


.39 Go .42 5 .35U
.59

.72 .51




Figure\d 1l i l u rwth -- al
.1( .42


.80
.36


.82


.63



Figure 10. Simultaneous analysis of high and low IQ groups, with all
parameters free across both groups. Mean IQ 115, standard deviation
7.5. Sample size of 500 in each group.







60





.79P .80o naefm U1


Taniynw 4 u2

.59

.77 /.77 .7CIow 0--- )
GV ~.79 .62


.88
.8/ / .89 .94PWW --us

".92 .85
cnanun u---(s

.95 .47 .61 nnn .90



.84 .7184 .70




81 9.892


.72 .66 .63
\Go .79 U

.86 .62


.5 .67
\Ge h w82w fm o --- |ull






.7 4


.747
.90


.81
'pprobw ---u1l

Figure 11. Simultaneous analysis of high and low IQ groups, with all
parameters free across both groups. Mean IQ 85, standard deviation 7.5.
Sample size of 500 in each group.





61


The remaining analyses address the detectibility and development of

cognitive differentiation. Again, normal distributions were formed using the

procedures previously described. Each group was comprised of 250

individuals. As in the previous analyses, distributions for the high- and low-IQ

groups had respective means of 115 and 85. Standard deviations for each

group were 7.5. The ChildHighlQ group was comprised of children between

the ages of 6 and 12 years (m = 8.7; s = 1.8). The AdolHighlQ group was

comprised of adolescents between the ages of 13 and 22 years (m = 17; s =

2.5). Descriptive statistics of the subtests included in the three-stratum model

for the ChildHighlQ and AdolHighIQ groups are presented in Tables 6 and 7,

respectively. Distributions of Broad Cognitive Ability are offered in Figures 12

and 13 for the respective high-IQ child and adolescent groups. As in the

preceding analysis, the distributions are normal, with nearly identical standard

deviations.

Using the variance-covariance matrices from each distribution,

simultaneous hierarchical confirmatory factor analysis evaluated increasingly

lenient models of the three-stratum theory. Results of these analyses are

summarized in Table 8.

Results of the analyses for the high-IQ children and adolescents follow

the pattern established in the earlier set of analyses. That is, a significant

decrease in x2 was achieved by permitting the unique and error variance to vary

across high- and low-IQ groups. Further significant improvements in the model






62


Table 6. Descriptive Statistics for High-IQ Children (ChildHighIQ)

Variable Name Mean Std. Deviation N

Concept Formation 4974 204 250
Analysis Synthesis 4989 164 250
Visual Closure 4958 118 250
Picture Recognition 4983 107 250
Visual Matching 4875 240 250
Cross Out 4936 153 250
Memory for Names 5011 108 250
Visual Auditory Learning 4988 96 250
Picture Vocabulary 4986 183 250
Oral Vocabulary 4940 214 250
Incomplete Words 4977 88 250
Sound Blending 4986 158 250
Memory for Sentences 5020 162 250
Memory for Words 5011 189 250
Calculation 4759 374 250
Applied Problems 4877 292 250





70,

60,

50,

40

30

20,

10, Std. Dev = 8.06
Mean = 115.0
0 N = 250.00
95.0 100.0 105.0 110.0 115.0 120.0 125.0 130.0 135.0

BCASTDAS
Criteion Variable-Broad Cognitive Ability
Figure 12. Histogram of ChildHighlQ Distribution






63


Table 7. Descriptive Statistics for High-IQ Adolescents (AdolHighIQ)

Variable Name Mean Std. Deviation N

Concept Formation 5248 137 249
Analysis Synthesis 5202 105 250
Visual Closure 5135 93 250
Picture Recognition 5122 90 250
Visual Matching 5319 138 250
Cross Out 5212 83 250
Memory for Names 5122 115 250
Visual Auditory Learning 5107 103 250
Picture Vocabulary 5333 113 250
Oral Vocabulary 5390 137 250
Incomplete Words 5086 70 250
Sound Blending 5149 116 250
Memory for Sentences 5229 125 250
Memory for Words 5190 167 250
Calculation 5482 170 250
Applied Problems 5420 183 250





70-

60,

50

40

30

20

10 Std. Dev= 7.79
Mean = 115.0
0 N = 250.00
95.0 100.0 105.0 110.0 115.0 120.0 125.0 130.0

BCASTDAS
Criterion Variable-Broad Cognitive Ability
Figure 13. Histogram of AdolHighIQ Distribution






64




Table 8. Different Hypotheses Tested in Regard to the Structure of Cognitive
Abilities at Different Ages

Hypothesis Tested X2 df TLI NFI PFI X2 Change

Factor Structure Invariant 594 231 .99 .99 .84 --
(All Parameters Fixed)

Factor Loadings Identical 473 207 .99 .99 .76 121*
(Error and Unique Variances Vary)

Factor Structure Similar 392 192 1.0 .99 .71 202*
(All Parameters Free to Vary)


*Indicates a statistically significant improvement in model fit based on x2 decrease.


were obtained by permitting the remaining parameters to vary (i.e., different

factor loadings across ability groups).

Results for the high-IQ children and adolescents are presented in

graphical form in Figures 14 through 19. Regardless of the model stringency

(i.e., constraints of parameters), there are significant between-group

differences in factor loadings, with the child group having larger loadings on all

first- and second-order factors. When all parameters of the three-stratum

model were free to vary, the average g loading to the first-order primary

abilities was .90 for the child group. In the adolescent group, this value

decreased to .45, a decline of .45. The largest single decrease in factor loadings

occurred in the correlation between g and gs. Values dropped from .95 to .29.







65



.71

.88 .84 .88 U
o a85 .72
n ~ siynw u2

.49

.88 /.70 ta ---

S .68 .47


.90
.9 .85 .95 vwmxtw us

.94 .88


.49
.92/ .5 .70 "mew 0

.75.79 .62
Vl--gw us--

9 .92 .85 / .81


.86 .7.93


.77 .74 .47
\Go .8 kwwrdw U11

.97 79 .63
\*dbldw ^--^u12

.59 .81
SGam .90 n
.70
.50

.95nnw ---u14

Gq .97 c 94
cicw u15

.90
Opprobw U-(u6



Figure 14. Simultaneous analysis of high IQ children and adolescents,
with all parameters constrained across both groups. Mean IQ 115,
standard deviation 7.5. Sample size 250 in each group. (Child group).








66



.34
/ m J onftnw <*-- ( u1
46 .58 ____U
Gf i .60- 3
an synw u2

u .17
.45 .41 VAdw v 3

Gv .40 .16
picr"m e u4

u .68
.68 .38 .83- vimwtw --(us

G .81 .65
7 t /nm 6--(us

uG .33
.62 .12 .57 m ------ 0
Gt-
.35.67 44
.35 u
^ -M( @ vrtnaw Icl U
LT k.50
9 .63 .39 50
G .71 U9

.49 .77
\\ X (Q ortwc <-- \v'

.37 .24 .23
\ Go .\48 wa U- 1

.82 .36
\ \ <(G^ iixfk%*w u-\12)


sm .82
.56
\ /^\ 'A------ ,-.
.32
1 rMrdw 4- (u14
.87
.72
sq ^ .85 c~\
"-----^.^* criw )---(^16)

.57



Figure 15. Simultaneous analysis of high IQ children and adolescents,
with all parameters constrained across both groups. Mean IQ 115,
standard deviation 7.5. Sample size 250 in each group. (Adolescent

group).







67



.70

.87 .84 com U1
Gf .886 .75
--n m u--- 2)

.53

.87 .73 rdow --- 3

GV 71 .50






9 .94 .88


.54
.95[ .72 .74 Jwmem 0

.77 .59
.85


.94 .87 .78
\\ .88 u---- U


e 1. So aoralow of i10

.76 .74 .45
SG 67p h.cww u

.99 7 .60
\ undw --12

.87
\w .93 u1393

.71
.51
U mertWw u--\14
.97
.93
I96 -

.92
apwobw UI---()


Figure 16. Simultaneous analysis of high IQ children and adolescents,
with factor and subtest unique variances free across both groups. Mean
IQ 115, standard deviation 7.5. Sample size 250 in each group. (Child
group).







68



.32










u .65
82 .68 onfw 1

G 1 .57 .35














.20 u2
4.14
.47 .37 ^ h 0tOW
GV .35 .12


6.65
.67 .31 .81 Vw .60--








s.82 .84
7372
.\7 .45
.29







(Adolescentrw rou).
3.56 GC- .75 pj,-- .6 9





.35 \t .20 ._49 ^ .24 U- 1



\\dbindw u12

\wn .^ ~~ .78 "'"" u13





Gq .89-






Figure 17. Simultaneous analysis of high IQ children and adolescents,
with factor and subtest unique variances free across both groups. Mean
IQ 115, standard deviation 7.5. Sample size 250 in each group.
(Adolescent group).







69



S.69

.88 .83 conftm U
of 87 .75
an synw u2

uG.54
.87 .74 VWckw 0C3
GV .71 50
-=. U4--_

.94
.93/ / V P97 vnelt us

.94 .88
ra cnutw -- C 8)

.95 .72 .76 rn .570


.85 .75 .57







.7748 .-7
.93 .87 .78
.89

.86 .98
\-ve\w I --- u10

.76 .74 .45


.99 .60


.88
^num i u13)
.49
\mrtfw -- (u14)
.97
.93


.92
approbw 6--- C"16


Figure 18. Simultaneous analysis of high IQ children and adolescents,
with all parameters free across both groups. Mean IQ 115, standard
deviation 7.5. Sample size 250 in each group. (Child group).







70



U@ .48

.52 .691 _""!"v U1
Gf .49 .24
(a n i -ym u 2'




V .52 .27
pt ennwe u4--- u2


.72 .08 .80 vwUw rn w




.29 .04 .60

.20



.70 .48
.69




.37 .19 .17
S .42


.1 .44

4.94

.41
/*^-----^^" -------






3 0.1 .75







.88
Irbdw u--ul2















Figure 19. Simultaneous analysis of high IQ children and adolescents,
with all parameters free across both groups. Mean IQ 115, standard
deviation 7.5. Sample size 250 in each group. (Adolescent group).
deviation 7.5. Sample size 250 in each group. (Adolescent group).





71




The ChildLowlQ group was comprised of children 6 through 12 years

(m = 8.8; s = 1.9). The AdolLowIQ group was comprised of adolescents 13

through 22 years (m = 17; s = 2.5). Descriptive statistics of the subtests for

the ChildLowlQ and AdolLowIQ groups are presented in Tables 9 and 10,

respectively. Distributions of Broad Cognitive Ability are offered in Figures 20

and 21. As in the preceding analysis, the distributions are normal, with nearly

identical standard deviations.


Table 9. Descriptive Statistics for Low-IQ Children (ChildLowlQ)

Variable Name Mean Std. Deviation N
Concept Formation 5248 137 249
Analysis Synthesis 5202 105 250
Visual Closure 5135 93 250
Picture Recognition 5122 90 250
Visual Matching 5319 138 250
Cross Out 5212 83 250
Memory for Names 5122 115 250
Visual Auditory Learning 5107 103 250
Picture Vocabulary 5333 113 250
Oral Vocabulary 5390 137 250
Incomplete Words 5086 70 250
Sound Blending 5149 116 250
Memory for Sentences 5229 125 250
Memory for Words 5190 167 250
Calculation 5482 170 250
Applied Problems 5420 183 250






72


60

50

40,



20

1, Std. Dev = 7.61
Mean = 852
0 N = 250.00
67.5 72.5 77.5 82.5 87.5 92.5 97.5 102.5
70.0 75.0 80.0 85.0 90.0 95.0 100.0

BCASTDAS
Crlterlan Vartable-Bred Cogntlve Abllty
Figure 20. Histogram of Low-IQ Children Distribution



Table 10. Descriptive Statistics for Low-IQ Adolescents (AdolLowIQ)

Variable Name Mean Std. Deviation N
Concept Formation 5003 162 250
Analysis Synthesis 5008 118 250
Visual Closure 5037 95 250
Picture Recognition 5026 93 250
Visual Matching 5161 133 250
Cross Out 5102 87 250
Memory for Names 4980 87 250
Visual Auditory Learning 4968 90 250
Picture Vocabulary 5088 115 250
Oral Vocabulary 5072 130 250
Incomplete Words 4994 88 250
Sound Blending 4980 136 249
Memory for Sentences 4970 135 250
Memory for Words 4991 175 250
Calculation 5226 154 250
Applied Problems 5086 142 249






73



70-

60

50.

40

30

20

10 StLd Dev = 7.71
Mean 85.0
0 N = 250.00
65.0 70.0 75.0. 0 80 85.0 90.0 95.0 100.0 105.0

BCASTDAS
Critertan Varable-Broad Cognitive Abinty


Figure 21. Histogram of Low-IQ Adolescents Distribution



Results of the confirmatory analyses for the low-IQ children and

adolescents are summarized in Table 11.



Table 11. Different Hypotheses Tested in Regard to the Structure of Cognitive
Abilities at Different Ages

Hypothesis Tested X2 df TLI NFI PFI X2 Change

Factor Structure invariant 546 231 .99 .99 .84 -
(All Parameters Fixed)

Factor Loadings Identical 463 207 .99 .99 .76 83*
(Error and Unique Variances Vary)

Factor Structure Similar 417 192 1.0 .99 .70 129*
(All Parameters Free to Vary)


*Indicates a statistically significant improvement in model fit based on x2 decrease.



Confirmatory analyses of the data from the low-IQ children and

adolescents showed a significant decrease in x2 was achieved by permitting

the unique and error variance to vary across high- and low-IQ groups.






74


Additional significant improvements in the model were obtained by permitting

the remaining parameters to vary (i.e., different factor loadings across ability

groups). All indices of fit suggest that the data fit the model exceptionally well.

The results also are presented in graphical form in Figures 20 through

25. As observed in the high-IQ children and adolescents, factor loadings

decrease with age. This finding is true for g, as well as the primary abilities.

Again, all loadings differ significantly, in the direction supportive of

differentiation of cognitive abilities with age. When all parameters of the three-

stratum model were free to vary, the average g loading for the first-order

primary abilities was .86 for the child group. In the adolescent group, this value

decreased to .48, a decline of.38. The largest single decrease in factor loadings

occurred in the correlation between g and gsm. Values dropped from .67 to

.17, a decline of.50.

For clarity's sake, Table 12 summarizes the results of the analyses for

the age-ability groups when all parameters are free to vary. In brief g loadings

are significantly higher in the low-ability groups, regardless of age.







75













.57

.80 .76 w
Of a77 .60
anilynw -- 2
.46

.82 .68 qmol W--

G y .64 41


.85
.89 .81 .92 vnw s --(w
G8
o .90 .80


.35
.90 .45 59. m O .M w0

IG/ i r JC'^" .50 m
.67.92 .85
..7


9 .87 .78 ..


.82 .95 .91
ovocw -ua10

.683 .687 .46
Go } inawrdw 4-

.98 .52
\ dabldw <----(-u12

\.8
.81 memse
.73
.53
memwrw 4---u

sq .95 .



*ppfw 4--- U16
.83




Figure 22. Simultaneous analysis of low-IQ children and adolescents,
with all parameters constrained across groups. Mean IQ 85, standard
deviation 7.5. Sample size of 250 in each group. (Child group).







76













.30

.37 J5 .55
o .57 .32
am" unynw2

.20

.40 .45 V9W A u---
/ C.42 .17


.63
.1 /.39 .79 SM- vn

o.75 .56


.25
.62 .11 .508 mGmnmw


.33 .78


9 .56 .31 .0


.48
\ vocw U--lu10

.29 .23 .27
Go .52 fw.6
deviation1 7.5 inSwampl f5 h(ulp)
.87 .32
\ndbldw u1---(22

.56
Gem .75 mMemnu13

.43

.76
Gq .79

.48








Figure 23. Simultaneous analysis oflow-IQ children and adolescents,
with all parameters constrained across groups. Mean IQ 85, standard
deviation 7.5. Sample size of 250 in each group. (Adolescent group).







77



.57
cocrmw U1
.84 .75
Of .73 .53
anlsynw u-- 2

.44

.83 .87 viscw ---

G* R A8 .47


90
.92.81 .95 vismw u5

.89 .80


.33
.90/ 52 .5 ------ 0

.87 .76
.72



.9 .78 p- Uw

.85
riocsw U-10

.66 .64 .48
\ t-- 69 inawedw --

.99 .51


.67
Ge J.82 ^ mmunw4



\ @ mmwerdw u--
..8

-crtow U--15
.93
.88






Figure 24. Simultaneous analysis oflow-IQ children and adolescents,
with factor and unique subtest variances free across groups. Mean IQ 85,
standard deviation 7.5. Sample size of 250 in each group. (Child group).






78



.32

.29 .56 C ,11mw
.66 .43
a-nsynw u-
.22

.34 11.146 181 vMkd
G 40 .16


.56
.54 .38J .75 'vMw us-

Go ~.74 .54


.28
.61 .08 .53 mOmnMmw
.93 .87











grroup).
.50
S.46 .21 .71

.96 .91
.49
or\zaw U10-lo


.27 Go .24 .50- .25
.81 .30
.81


..75
Gem .7n5 w <---(e0
.68
.47

.U6









Figure 25. Simultaneous analysis oflow-IQ children and adolescents,
with factor and unique subtest variances free across groups. Mean IQ 85,
standard deviation 7.5. Sample size of 250 in each group. (Adolescent
group).







79



.56

.83 .75I
f .72 .52
anisyrw u2

.47

.84 .69 vMCky 0

/ O .68 .46
icraO- u--("4

.90
.91 .81J .95 viMw m --

G .89 .79


.32

90 .57 .mmm u7
.87 .75
.71
va98--w u\s

.681
-- -.94 .'89 8. I-





.67 .67 .51
.71

.99 .2.52


.88
Gem .82 w
.72
.51
mOwimw u--- 14
.98
Gq .94 .88

.86





Figure 26. Simultaneous analysis of low-IQ children and adolescents,
with all parameters free across groups. Mean IQ 85, standard deviation
7.5. Sample size of 250 in each group. (Child group).







80



40

.58 .M3 c- Vw
.62 .39
anisym u2
.06
vis*loyw ---(u2


O .61 .37


.30





.28

G 9 .9- .92
.42 .28 1.4 .28




25.
7 .06 .07


.2500 .21
with all parameters free across groups. Mean IQ 85, standard deviation10

7.5. Sample size.17 of 250 in each roup. (Adolescent roup).
\Go .2 inc,.mrw 1 u4-
.78 .82






mwnwrbw u-14l*









Figure 27. Simultaneous analysis oflow-IQ children and adolescents,
with all parameters firee across groups. Mean IQ 85, standard deviation
7.5. Sample size of 250 in each group. (Adolescent group).






81

Table 12. g Loadings of High- and Low-IQ Children and Adolescent Groups

Primary Ability g Loading

ChildLowlQ/AdolLowIO ChildHighlQ/AdolHighIO
Gf .91 .76 .93 .72
Gv .92 .44 .94 .40
Gs .90 .42 .95 .29
Glr .71 .53 .85 .20
Gc .94 .49 .93 .70
Ga .82 .25 .86 .44
Gsm .67 .17 .76 .37
Gq .99 .78 .99 .86

















CHAPTER 5
DISCUSSION

Most studies investigating the structure of mental abilities confirm that

a substantial amount of the variance observed in cognitive performance can be

attributed to a general factor, often referred to as Spearman's g. For this

reason, Spearman's g has been termed the sin qua non of intelligence

(Humphreys, 1992). However, some studies have suggested that the

percentage of variance in human abilities explained by g may vary across

different age and ability levels. Although this observation was made nearly a

century ago, only recently have empirical studies of good quality addressed this

important issue (Detterman & Daniel, 1989). The present study is one of the

few to apply confirmatory factor analysis to this phenomenon and perhaps the

first to examine the structure of cognitive abilities, as represented by a three-

stratum theory of intelligence, across different IQ levels.

Differentiation of Cognitive Abilities Across Groups of Different Ability

Results of the present study indicate that the proposed three-stratum

model of cognitive abilities is structurally identical across high- and low-ability

groups. All reported indices of fit confirm that Carroll's three-stratum theory

provides an excellent representation of cognitive abilities for both high- and

82





83


same constructs for different ability groups, significant differences exist in its

factorial parameters. Ability groups differed significantly with respect to all

factor loadings, error, and unique variances.

This study also offers strong support for the belief that abilities

differentiate as IQ increases, in that g accounted for less variability in scores

among high-ability individuals than among low-ability individuals. In the low-

and high-IQ groups, when all parameters were free to vary, g accounted for

52% and 29% of the respective variance in cognitive performance. Stated

differently, g explained nearly twice the amount of variance in the low-ability

group as compared to the high-ability group. This pattern of loadings is

consistent with observations made by Spearman (1927), Burt (1944), and

Detterman and Daniel (1989) and advances empirical evidence in favor of

Spearman's law of diminishing returns.

These findings were further substantiated by the confirmatory analyses.

Regardless of the restrictions placed on the proposed three-stratum model of

cognitive abilities (e.g., permitting different values for the factor loadings,

error, and unique variances), all g loadings were significantly lower in the high-

ability group. The largest decline in general factor loadings occurred on

measures of crystallized intelligence (gc). The loading of gc on g declined from

.71 for the low-IQ group to .15 for the high-IQ group. Researchers (e.g., Horn

& Noll, 1997) consider gc to be indicative of an individual's store of

information. Therefore, more so than their high-IQ counterparts, low-IQ

individuals depend on g for the acquisition of knowledge and information. This





84


finding offers some evidence that g plays a causal role in the formation of an

individual's fund of knowledge and information. The next largest decrease in

general factor loadings occurred on measures of gsm, usually interpreted as a

measure of working memory capacity. Over the past decade or so, researchers

have assigned an increasingly important role to working memory as an

explanative agent in understanding individual differences in human cognitive

performance. Kyllonen and Christal (1990) have gone so far as to equate

working memory capacity with Spearman's g, citing a simple correlation

between them of .91. Most new and revised intelligence tests, such as the

WAIS-III (1997) also incorporate a working memory component into a model

of cognitive abilities. This study's findings support the idea that working

memory capacity is a salient feature distinguishing high- and low-ability groups

and further confirm the important position of working memory in accounting

for cognitive outcomes.

Surprisingly, loadings from the second-order primary abilities also were

significantly lower in the high-IQ group than in the low-IQ group. Permitting

the model parameters to have different loadings across groups indicated that an

increasing amount of the variability in scores could be accounted for by the

unique and error variances of these second-order gc-gf abilities. These findings

pose the possibility that, more so among high-IQ individuals than low-IQ

individuals, additional noncognitive constructs may exist that, while excluded

from the three-stratum model, contribute importantly to successful cognitive

performance. This idea is not new. A number of noted scholars (e.g.,






85


Sternberg, 1985; Gardner, 1983; & Brand, 1995) have suggested that

noncognitive attributes should be held in as equal esteem as abilities

traditionally considered purely cognitive in nature.

In particular reference to the constructs measured by the WJ-R,

Woodcock (1993) has incorporated noncognitive factors into a Cognitive

Performance Model (CPM). The CPM implies that the various gf-gc abilities

are not autonomous, but fall into distinct functional categories. Further, an

individual's cognitive performance is enhanced or modified by facilitators-

inhibitors, such as health, emotional state, and motivation. Woodcock

perceives the source of facilitators-inhibitors as being situational or

environmental (e.g., teaching method, environmental distractions, and the

specific tests used in assessment). Woodcock (1993) and Keith (1997) have

offered confirmatory support for the organization of the cognitive abilities and

facilitators-inhibitors in the CPM. The present study extends these previous

findings and advances that high-IQ individuals may utilize these situational

variables to a greater extent than low-IQ individuals.

Differentiation of Cognitive Abilities Across Ability Groups of Different Age

In addition, this study provides some evidence that the differentiation of

abilities may be attributable to developmental influences. Groups were matched

on ability and compared across age (i.e., ChildHighlQ AdolHighIQ /

ChildLowlQ AdolLowIQ). In each case of the confirmatory analyses,

Carroll's three-stratum model of cognitive abilities was found to be structurally

invariant. That is, for groups of similar overall ability, the constructs measured





86


by the WJ-R are adequately represented by the proposed model, regardless of

age level. However, values of all factorial parameters differed significantly with

respect to age. In brief while the structure is identical for children and

adolescents, different values are found in factor loadings, unique variances, and

error variances. When parameters were freed to vary for high-ability children

and adolescents, g accounted for 62% and 26% of the variance respectively.

The largest single decline in general factor loadings occurred on gs, or

processing speed. The loadings for the children and adolescent groups were

.95 and .29, respectively. This dramatic decline indicates that, among high-

ability children, g and processing speed are strongly related. Conversely, in

high-ability adolescents, g accounts for relatively little of the variability in

processing speed. Most likely, these findings reflect the complimentary roles of

controlled and automatized processing in cognitive performance. Controlled

processes are required when the demands of a task are novel or inconsistent.

Such processes are usually slow, effortful, and dependent upon the use of

limited cognitive resources (Jensen, 1998). In contrast, automatized processes

occur under repeated and consistent conditions, and accrue a fast and effortless

quality. Basically, controlled processes are required for the initial learning of a

task and are gradually supplanted by automatized processes when the task is

learned to a level of fluency. Quickly transitioning from reliance on controlled

processes to automatized processes frees cognitive resources in working

memory which can be applied to other tasks. Because controlled processes





87


extol a greater cost on cognitive resources, they naturally draw upon the

general factor to a greater extent than automatized processes.

Among children, much of their time spent in the early years of

schooling requires controlled processing. Common examples of academic tasks

requiring controlled processing include acquiring simple math facts, writing

cursive, and decoding. Everyone can remember the first strained efforts to

write his/her name or counting with fingers. By adolescence, these basic tasks

are over-learned, and hence draw almost exclusively on automatized processes.

Although processing speed per se remains an important source of individual

differences throughout the lifespan, by adolescence, high-ability individuals

have acquired an extensive repertoire of automatized processes, which places a

lesser demand on g.

Confirmatory analyses yielded the same pattern in low- and high-ability

groups. That is, while the three-stratum model of cognitive abilities is

structurally invariant across age levels, there are significant differences in all

factorial parameters. Significant improvements in model fit were obtained when

factor loadings, unique variances, and error variances were permitted to have

different values for children and adolescents. For low-ability children and

adolescents, g was associated with 53% and 21% of the variability in

performance, respectively. The largest single decline occurred with gy,

interpreted as visual processing. A substantial decline was also observed on

measures of long-term memory retrieval (glm). Therefore, as children move





88


into adolescence, these simple processes become increasingly automatized,

more distinct, and less reliant on g.

In summary, this study suggests that, for both high- and low-ability

groups, cognitive abilities differentiate as individuals develop from childhood

to adolescence.

Possible Mechanisms of Cognitive Differentiation

Different scholars have offered different metaphorical theories to

explain cognitive differentiation. Spearman (1927), who first noted this unusual

phenomenon, equated g to mental energy. Primary abilities were represented as

specific engines. Positive manifold arose because some energy (i.e., g) is

needed to run all engines (i.e., primary abilities or group factors). Thus,

differentiation at higher ability levels occurs because doubling the energy to an

engine does not achieve a doubling of speed. A contemporary view which is

surprisingly similar to Spearman's portrait of cognitive differentiation comes

from Anderson (1992). Instead of an engine, Anderson describes cognitive

differentiation in terms of a computer metaphor. Anderson's Basic Processing

Mechanism bears a strong resemblance to Spearman's g, and his Specific

Processors are indistinguishable from primary abilities. Anderson explained

positive manifold in terms of the processing speed needed to complete all

cognitive tasks. Differentiation occurs at higher levels of intelligence because

greater processing speed increases the output of the various Specific

Processors and allows for differentiation. Conversely, at lower levels of





89


intelligence, the slower speed of the Basic Processing Mechanism serves to

restrict the output of the Specific Processors.

Detterman's (1993) account of cognitive differentiation assumes a

systems approach and incorporates aspects of both Spearman's and

Anderson's theories:

The differences in correlation across IQ level are consistent with the
systems theory of intelligence. In this theory, IQs result from deficits in
important cognitive processes. Because these processes are part of a
system, they affect the functioning of other parts of the system. If these
important processes are deficient, parts dependent upon them will also
be impaired. Essentially, a deficit in an important process will put an
upper ceiling or limit on the efficiency of the operation of other parts of
the system. That means that all parts of the system will be more similar
if there is a deficiency in an important process. This forced similarity in
ability is what causes a higher correlation among IQ subtests for low IQ
subjects. (pp. 27-28)

Regardless of the particular theory, the pattern of correlations

indicating cognitive differentiation is due to processing efficiency. Low-ability

individuals process information inefficiently. The result is a forced similarity

among specific processes, which makes for larger subtest intercorrelations.

High-ability individuals process information more efficiently. The result is that

specific processes and abilities are more distinguishable, providing lower

subtest intercorrelations. Certainly, age and development appear to increase the

efficiency of processing, regardless of overall general ability.

Deary and Paglieri (1991) and Burt (1954) posed the possibility that

the pattern of correlations suggesting cognitive differentiation may be due to

lower reliabilities for high- than for low-ability subjects. Lower reliabilities

would naturally yield lower subtest intercorrelations. Unfortunately, item-level





90


data were not available for this study, so reliabilities for the separate groups

could not be calculated. However, previous studies investigating differential

reliabilities have found that scores tend to be more stable and reliable among

high-IQ testees (Deary et al., 1996). If reliability estimates actually are higher

for high-IQ groups, then, if anything, the results of this study underestimate the

true degree of cognitive differentiation.

Implications For Cognitive Assessment

The structure of cognitive abilities is invariant for high- and low-ability

individuals, regardless of the age of the testee. However, there are significant

differences in the degree to which cognitive abilities are represented for groups

of varying intelligence and development. Cognitive abilities differentiate with

ability and age. However, because the structure of abilities is identical, this

differentiation is not large enough to warrant different tests for groups of

different age and ability. Rather, the primary recommendation for assessment

which can be gleaned from the present study is that additional, not different,

tests should be used if the intent of the assessment is to obtain an informed

portrait of overall cognitive performance. Following the example provided by

Woodcock's Cognitive Processing Model, these additional instruments would

be selected with the purpose of measuring aspects of the facilitator-inhibitors

contributing to overall performance. Of course, the counterpoise is that any

information gleaned from additional instruments may appear trivial relative to

the substantial information already provided by g.





91


Recommendations For Future Study

Contrary to recent investigations regarding differentiation (e.g., Deary

et al., 1996), the present study found that cognitive differentiation occurs not

only according to IQ, but to age as well. Certainly, replication is in order, with

different batteries of tests. In addition, other studies investigating intelligence

may need to incorporate cognitive differentiation into their framework. The

KABC and the CAS are excellent candidates for these future studies, since

they offer several subtests that are qualitatively different from those included in

this study and are based on substantially different theories of intelligence. A

goal of future studies should be to understand why certain primary abilities

seem to differentiate more than others. For example, in the present study, there

were no identifiable patterns that would suggest that crystallized abilities

differentiate more than fluid abilities, or visa versa. Insofar as differentiation

has been shown to occur with development, the incorporation of various

sociometric variables into subgroup selection seems warranted, in order to

characterize certain qualities that may influence intellectual development. For

example, does cognitive differentiation occur at the same rate among

individuals who differ in socioeconomic status? Future studies should strive to

test specific hypotheses about the patterns of differentiation. Such studies may

provide the needed insight into the underlying causes of differentiation.

Another area tangentially related to cognitive differentiation is the

Flynn Effect (Flynn, 1987). The Flynn Effect refers to the finding that in a

number of industrialized nations IQs have risen on a secular level, on the order






92


of 3 to 5 IQ points per decade. It would be informative to see if cognitive

differentiation, as it has been observed in high- and low-ability individuals at

one particular point in time, also has occurred on a secular level with the

passage of time. This study could easily be done using the standardization data

from an original test (e.g., WAIS) and its most recent revision (e.g., WAIS-

III). Confirmatory analysis could yield some enlightening information regarding

the nature and extent of the Flynn Effect.

Another hypothesis that will certainly require future research is the

genetic contribution to intelligence at higher and lower levels. Studies in this

area are few and equivocal, at best. Some scholars (Detterman, Thompson, and

Plomin, 1990) posit that Spearman's law of diminishing returns applies to

genetic variance as well as g, citing larger estimates of heritability (h2) in the

lower spectrum of IQ. Other well-designed studies (Bailey & Revelle, 1991)

found completely opposite results, with higher estimates of heritability for high

ability groups. Therefore, the issue of heritability and its relationship to

cognitive differentiation remains open to debate.

Summary

In conclusion, the present study confirms the differentiation hypothesis

regarding human intelligence and supports the belief that the structure of

cognitive abilities is the same for both low- and high-ability individuals. The

differentiation of cognitive abilities, as evidenced by the amount of variance

accounted for by g, is greater among individuals of higher ability than lower

ability. While the differentiation observed in higher ability individuals may be






93


due to more efficient information processing, this study finds that

differentiation also has a strong developmental component, inasmuch that

abilities were more differentiated in adolescents than in children. This finding

lends substantial support to an "economic investment" metaphor regarding

human abilities. From this perspective, intelligence is equated with money. At

lower levels of income, money is spent on the common necessities, such as

housing, clothing, and food. At higher levels of income, a proportion of money

becomes disposable, and is spent on activities and items reflecting personal

interests, such as vacations, sports, and entertainment. At lower levels of

intelligence, a larger proportion of general and group factors are "spent" on

completion of the immediate cognitive tasks. Conversely, at higher levels of

intelligence, a greater proportion of cognitive resources are available to reflect

personal interests and motivation. Also, like money, returns on investment

accrue over time, regardless of the initial amount invested. Irrespective of

ability level, individuals benefit from experience in that primary cognitive

abilities become more efficient and specialized.















LIST OF REFERENCES

Anastasi, A. (1932). Further studies on the memory factor. Archives of
Psychology. 142, 60.

Anastasi, A. (1970). On the formation of psychological traits. American
Psychologist. 25, 899-910.

Anderson, M. (1992). Intelligence and development : a cognitive
theory. New York, NY: Blackwell Publishers.

Andrich, D. (1988). Rasch models for measurement. Newbury Park,
NJ: Sage Publications.

Arbuckle, J. (1996). AMOS manual. Chicago, IL: SmallWater.

Asch, S. E. (1936). A study of change in mental organization.
Archives of Psychology, 195, 30.

Atkin, L., Bray, J., Davison, A., Herzberger, G, Humphreys, L., &
Seizer, D. (1977). Factors emergent with age and mental ability. Adolescent
Psychology, 11, 65-84.

Bailey, M.J., Revelle, W. (1991). Increased heritability for lower IQ
levels? Behavior Genetics. 21, 397-404.

Balinsky, R. (1941). An analysis of the mental factors of various age
groups from nine to sixty. Genetic Psychology Monographs. 23, 191-234.

Bickley, P.G., Keith, T.Z., & Wolfe, L. (1995). The three-stratum
theory of intelligence: Test of the structure of intelligence across the life span.
Intelligence. 20. 309-328.

Binet, A., & Simon, T. (1905). Methodes nouvelles pour le diagnotic
du niveau intellectuel des anoromauz. L'annee Psycholgique, 11, 191-244.

Brand, C. (1996). The g factor: General intelligence and its
implications. New York: John Wiley & Sons.

94






95


Bray, R., Kerr, N.L., Atkin, R.S. (1978). Effects of group size,
problem difficulty, and sex on group performance and member reactions.
Journal of Personality & Social Psychology. 36, 1224-1240.

Brody, N. (1992). Intelligence. New York, NY: John Wiley & Sons.

Burt, C. (1919). Mental abilities in children and youth. British Journal
of Psychology, 5, 77-89.

Burt, C. (1944). Mental abilities and mental factors. British Journal of
Educational Psychology, 14, 85-94.

Burt, C. (1954). The differentiation of intellectual ability. British
Journal of Educational Psychology, 24, 76-90.

Carroll, J.B. (1993). Human cognitive abilities: A survey of factor
analytic studies. New York: Cambridge University Press.

Cattell, R.B. (1941). Some theoretical issues in adult intelligence
testing. Psychological Bulletin, 38, 592.

Cattell, R.B. (1963). Theory of fluid and crystallized intelligence: A
critical experiment. Journal of Educational Psychology. 54, 1-22.

Catell, R.B. (1987). Intelligence : its structure, growth, and action.
Amsterdam: Belevier Science Pub. Co., 1987.

Clark, M. P. (1944). Changes in primary mental abilities with age.
Archives of Psychology, 291, 30.

Cronbach, L., & Snow, RE. (1977). Aptitudes and instructional
methods: A handbook for research on interactions. New York: Irvington.

Cunningham, W.R. (1980). Age comparative factor analysis of ability
variables in adulthood and old age. Intelligence, 4, 133-149.

Cunningham, W.R. (1981). Age changes in the factor structure of
intellectual abilities in adulthood and old age. Educational & Psychological
Measurement, 40, 3-24.

Deary, I.J., & Pagliari, C. (1991). The strength of g at different
levels of ability: Have Detterman and Daniel rediscovered Spearman's "law of
diminishing returns"? Intelligence. 15. 256-260.




Full Text
xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID EIOE2TALN_FJ06S0 INGEST_TIME 2015-01-06T21:05:35Z PACKAGE AA00026641_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES



PAGE 1

DIFFERENTIATION OF COGNITFVE ABILITIES IN CHILDREN AND ADOLESCENTS By HARRISON D. KANE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARHAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1999

PAGE 2

ACKNOWLEDGMENTS This project could not have been completed without the support and expertise of John H. Kranzler, Thomas D. Oakland, M. David Miller, and Walter Cunningham Special appreciation is also extended to Stephen Smith for his enthusiasm.

PAGE 3

TABLE OF CONTENTS page ACKNOWLEDGMENTS i ABSTRACT iv CHAPTERS L INTRODUCTION 1 Statement of the Problem 1 Pmpose of the Study 2 Fiindamental Concepts in the Study of Intelligence 3 Spearman's g 3 Exploratory Factor Analysis and g 5 Confirmatory Factor Analysis and g 7 Carroll's Three-Stratum Theory 9 2. REVIEW OF LITERATURE 12 The (In)Variant Nature of General Intelligence 12 Stability of g Loadings Across DiflFerent Test Batteries 12 Stability of g Loadings Across Different Ages 14 Stability of g Loadings Across Different Ability Levels 23 Competing Explanations for the Differentiation of Cognitive Abilities 29 Summary 31 3. METHOD 33 Participants and Data Collection 33 Description of the WJ-R 33 The Model 42 Statistical Procedures for Subgroup Selection 42 Statistical Analysis 45 iii

PAGE 4

4. RESULTS 49 5. DISCUSSION 82 DiflFerentiation of Cognitive Abilities Across Groups of Different Ability 82 Differentiation of Cognitive Abilities Across Ability Groups of Different Age 86 Possible Mechanisms of Cognitive Differentiation 89 Implications For Cognitive Assessment 91 Recommendations For Future Study 91 Summary 93 LIST OF REFERENCES 94 BIOGRAPfflCAL SKETCH 102 iv

PAGE 5

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 DIFFERENTIATION OF COGNITFVE ABILITIES IN CHILDREN AND ADOLESCENTS By Harrison D. Kane May, 1998 Chairman: John H. Kranzler, Ph.D. Major Department: Foundations of Education Most psychologists and educators operate on the implicit assumption that intelligence is a linear construct. Stated differently, the assimiption is that smart people simply have more intelligence than their less gifted peers. Similarly, retarded individuals are thought to have less intelligence. In contrast to this widely accepted beUef, this study poses the alternative hypothesis that intelligence is qualitatively different in various populations. Applying confirmatory fector analysis to the standardization sample of the WoodcockJohnson Test of Cognitive AbiHty, this study examined the structure of intellect across abiUty and age. While the structure of inteUigence was identical across age and ability levels, significant differences were noted in factor loadings, error, and lanique variances.

PAGE 6

CHAPTER 1 INTRODUCTION It is generally and rightly considered a virtue in a teacher to observe accurately the difference in ability among his pupils, and to discover the direction in which the nature of each particularly inclines him. There is an incredible amount of variability in talent, and the forms of minds are no less varied than the forms of bodies. Quintillion (70 AD) Statement of the Problem The study of intelligence has a long past, yet a very short history. For centuries people have philosophized about intelligence, but only in the past 100 years has informal rhetoric yielded to scientific inquiry. Certainly, one of the most important events in the scientific study of intelligence was the invention of factor analysis. Factor analysis is a mathematical procedure which summarizes the interrelationships among variables as an aid in conceptualizing the underlying structure. Beginning with Spearman's (1904) seminal work, "General Intelligence: Objectively Determined and Measured," literally himdreds of investigations have used fector analysis to better understand the complex nature of intelligence. Most studies (e.g., Kranzler & Jensen, 1991) have found that intelligence is not a single or xmitary construct, but rather a number of abilities working in concert. Furthermore, many of these studies have conceptualized a hierarchical structure of cognitive abilities (e.g., Kranzler & Weng, 1995). Carroll (1993) surveyed over 450 such studies, and 1

PAGE 7

2 based on his findings, proposed a three-stratum theory of intelligence comprised of narrow, broad, and one general abilities. While Carroll's threestratum theory is the most comprehensive psychometric model of intelligence to date, an intriguing question remains unanswered: Is the three-stratum model a viable representation of cognitive ability for groups of different intelligence? Purpose of the Study The purpose of the present study is to investigate the stability of Carroll's three-stratum theory of intelligence across the lifespan and ability levels. A substantial body of research indicates that intelligence changes as people mature. Mental abilities tend to differentiate and become more specialized v^ age (Anastasi, 1970). A much smaller, but equally intriguing body of research suggests that mental abilities also differentiate according to IQ level (Spearman, 1927). That is, high-IQ individuals display greater differentiation among mental abilities than low-IQ individuals. Differentiation is typically demonstrated in three ways. First, the percentage of variance attributable to the general factor of intelligence decreases in a systematic feshion by age or ability. Second, the percentage attributable to group fectors, such as verbal ability, increases with age or ability. Third, correlations between IQ subtests decrease with age or ability. Inquiry into the differentiation of mental ability will provide insight into the cognitive structures underlying intelligence. This study will attempt to answer the question of whether the structure of "intelligence" is the same construct, more or less, for highand low-IQ individuals, or whether qualitative, as well as purely quantitative,

PAGE 8

3 difiFerences exist across ability levels. The answer to this question is important because many common assessment and teaching practices are based on the assumption that abilities are organized in essentially the same manner for all people and remain constant throughout the lifespan. By understanding the nature of intelligence for individuals of different IQ levels, educators and psychologists can begin to better appreciate and respond to the diversity of the human condition. Fundamental Concepts in the Study of Psychometric Intelligence Spearman's g. Spearman (1904) discovered g as part of an experiment to "find out whether, as Galton has indicated, the abilities commonly taken to be intellectual had any correlation with each other or with sensory discrimination" (Spearman, 1927, p. 322). Spearman obtained teacher evaluations of 36 students fi-om a nearby village school. Students were rated on traditional academic subjects (Latin, English, Math) as well as on Music and Pitch Discrimination. The observed correlation among the variables prompted Spearman to hypothesize that they shared a common source of variance, which he termed a "general fector of intelligence" (Spearman, 1904, p. 36). From the observation that variables had different levels of intercorrelation, he concluded that the variables had different levels of saturation with the general factor. The different levels of saturation represented different loadings on the general factor.

PAGE 9

4 Spearman (1927) also noted that the general factor did not account for all the variance in students' scores. To amount for these findings, he posited a two-factor theory of intelligence. That is, each variable may be described or accounted for by two factors, the general fector and a &ctor specific to each variable or narrow class of variables. Spearman suggested that "all branches of intellectual activity have in common one fimdamental fimction, whereas the remaining or specific elements seem in every case to be wholly different ." (p. 202). Spearman devoted the rest of his academic career to explicating the general &ctor, which he later referred to simply as g. Spearman conceived of g as "mental energy," and stated that g was the "leading part of intelligence, and is displayed by the ability to handle not merely abstract ideas, but above all symbols" (p. 21 1). The specific &ctors were portrayed as a large number of engines activated by this mental energy. Later, working fi-om several data sets collected over 20 years. Spearman conceptualized g as consisting of three processes. The first process is "the apprehension of experience." Spearman assumed, as did Galton (1892), that the greater the sphere of experiences an individual may draw upon, the more con^Iex the problem solving that he or she may imdertake. The second process is the "eduction of relationships." Spearman conceived of eduction as the "drawing out of a logical relationship between two stimuli" (p. 227). The third process is the "eduction of correlates," in which an individual notes the similarities between two stimuli. A cognitive task was loaded on g to the extent that it drew on these three processes.

PAGE 10

5 Spearman regarded g as the "common and essential element in intelligence" (1927, p. 126). In a comprehensive review of intelligence theory, Brody(1992) confirmed: The first systematic theory of intelligence presented by Spearman in 1904 is alive and well. At the center of Spearman's paper of 1904 is a belief that links exist between abstract reasoning, basic information processing abilities, and academic performance. Contemporary knowledge is congruent with this belief Contemporary psychometric analysis provides clear support for a theory that assigns. .g to a singular position at the apex of a hierarchy of abilities, (p. 349) Psychometric g outweighs all other factors derived fi-om a battery of tests. It is the single most inportant fector in predicting scholastic and occupational achievement, as well as a host of desirable and imdesirable social outcomes (Hermstein & Murray, 1994). Exploratory Factor Analysis and g. Exploratory factor analysis is a statistical method of minimizing the number of variables under investigation while concomitantly maximizing the amount of information in the analysis (Gorsuch, 1983). This aspect of factor analysis is especially useful when the sheer amount of information in a study exceeds conqirehensibility, or when certain distinctions and relationships between variables are hypothesized. Consider the following example. The Wecshler Adult Intelligence Scale, Third Edition (WAIS-EI; 1997) has 14 subtests. Thus, there are 91 simple correlations between the subtests. Undoubtedly, the WAIS-III is not measuring 14 different constructs (e.g., the Information subtest certainly shares a common source of variance with the Similarities and Vocabulary subtests, since each of these subtests are included

PAGE 11

6 in the Verbal Scale). With 91 correlations, some means are needed for determining if there are a smaller number of underlying constructs which might account for the main sources of variation in such a complex matrix of correlations. By partitioning the variance among the original variables into a smaller number of latent variables (Le., &ctors), fector analysis obtains the most concise and parsimonious explanation for the interrelationships existing in the data. Spearman's g is a latent variable, manifested in factor analysis. The ubiquity of g arises from positive manifold, the phenomenon in which all mental tests correlate to some degree. Therefore, statistical and methodological considerations determine, at least in part, how "good" g will be in a factor analysis (Jensen & Weng, 1993). To find a good g, the psychological tests must be diverse with respect to content, type of response, and stimulus. Certainly, psychometric g will vary according to the reliability of the test, the number of tests, the number of participants in the sample, and the number of diverse abilities represented by the tests. However, not every general factor that arises from a factor analysis is Spearman's g. For example, personality tests do not yield a g. Psychometric g arise only from a battery of cognitive tests. Although some tests, such as Raven's Progressive Matrices (RPM; Raven, 1956), are referenced as being saturated with g (Jensen, 1998), every cognitive test measures g to some extent. Therefore, there is no uniquely defining characteristic to g that can be expressed in psychological terms. Tests

PAGE 12

7 diflfering in content, stimulus modality, and response modality may ultimately have identical g-loadings (Jensen, 1998). Thurstone (1940) was the first to pose the possibility that exploratory factor analysis can be applied in a hierarchical manner, with the goal of finding the order of factors. A first-order ^tor analysis is the application of factor analysis techniques to the correlation matrix derived fi-om the observed variables of a study. Such analysis usually results in a smaller number of firstorder factors which account for the maximum amount of variance in the data set. Frequently, these first-order Actors are also inter-correlated. Therefore, a second-order factor analysis may be conducted, further analyzing the correlation matrix of the first-order fectors. A second-order fector analysis results in a still smaller set of third-order &ctors. When hierarchical techniques are applied to data representing cognitive performance, g is always manifested at the apex of the hierarchy, usually at the third-order. Confirmatorv Factor Analvsis and g. In exploratory fector analysis, the researcher does not know the underlying latent variable structure. Therefore, the focus of the analysis is to reveal the minimum number of unknown &ctors that will best account for the variance in a larger set of observed variables. Confirmatory factor analysis, on the other hand, requires an a^riorLknowledge of the underlying latent variable structure. This knowledge may be based on theory or past empirical investigations using the variables under study. In any case, the researcher using confirmatory techniques postulates a priori that certain observed

PAGE 13

8 variables will be related to certain latent variables in a theoretical model. The relationship between observed and latent variables is quantified by &ctor loadings. Data on all the variables specified in the hypothesized model are then collected. The researcher then examines the "goodness-of-fit" between the hypothesized model and the model comprised of observed variables. Because the researcher mxist specify an a priori model, confirmatory factor analysis is inherently driven by theory, whether formal or informal. Thus, confirmatory fector analysis presents an ideal vehicle for establishing the construct validity of theories of intelligence. In recent years, confirmatory techniques have become almost common place in testing the latent structure of intelligence tests. One reason for the increased usage of confirmatory techniques is that test manuals and journal articles fi-equently publish an obligatory correlation matrix which researchers can use as a starting point for independent analysis. Most intelligence tests (e.g., WAIS-in) combine various subtests to arrive at a single score to reflect overall cognitive ability. Therefore, whether tacitly or openly, these tests acknowledge the existence of g in their imderlying structure. Confirmatory studies of intelligence tests (e.g., Carroll, 1993; Kranzler & Weng, 1995) indicate that without exception, g is at the apex of a hierarchical model of intelligence and common to all of the factors and subtests below it. In factor analysis, as in life, any g will probably be a good g, and is certainly better than nog.

PAGE 14

9 Carroll's ThreeStratum Theory. Carroll (1993) published a massive survey of more than 450 data sets related to intelligence and cognitive ability. Data were drawn from over 1,500 publications and selected on the basis of their broad sampling of cognitive abilities. His summary lead him to posit his own theory of intelligence, a hierarchical model with three strata of abilities. The first stratum consists in part of narrow abilities that appear reflective of specific experience, learning, and strategies. Exanqjles from the first strata include length estimation and meaningfiil memory. The second stratum is characterized by broad &ctors that represent some specialization of abilities and established traits, such as broad retrieval ability and speed of information processing. The third stratum is essentially Spearman's g. Second-order &ctors are related to one another to the extent that they load on the general fector, with some more related to g than others. Similarly, first-order fectors are subsumed by specific secondorder fectors and are related to each other by virtue of their respective loadings on the given second-order fector. Figure 1 provides a graphical representation of the proposed three-stratum structure of cognitive abilities. In formulating his theory, Carroll drew on data from a myriad of sources, including Spearman (1904), Guilford (1967), Vernon (1960) Cattell (1987), and Thurstone (1973). Therefore, it is no surprise'that his threestratiun theory retains some common features of other psychometric theories of intelligence. For example, Carroll preserves Spearman's and Vernon's conceptualization of a hierarchical general fector. Carroll also avows

PAGE 15

Concept FonrMlon Analysis Synthesis Visual Closurs Picture Recognition Visual Matching Cross Out Memory For Names Visual Auditory Learning ^ Picture Vocabulaiy Oral Vocatxjlary Incomplete Words Sound Blending Memory For Sentences Memory for Words Calculation AppHed ProMama Figure 1. Carroll's Three Stratum Theory of Cognitive Ability

PAGE 16

11 Thurstone's contribution to his methodology, particularly the practice of successive factorizations of correlation matrices at higher orders. Like Cattell, Carroll acknowledges the existence of several second-order factors, including fluid (gf) and crystallized (gc) abilities. Unlike Cattell's gc-gf model, CarroU postulates — and provides support for — a third-stratum general &ctor derived from the shared variance of the second-stratum fectors. Carroll's three-stratum theory has garnered much acclaim in the psychological community, primarily for its comprehensive representation of the structure of cognitive abilities (McGrew, 1997).

PAGE 17

CHAPTER 2 REVIEW OF THE LITERATURE The anWariant Nature of General Intelligence Despite scientific and social controversy, Spearman's g has remained remarkably resilient as a theoretical construct in the study of individual differences. It is compatible with most theories of intelligence, even those which hope to disavow its existence (see Gardner, 1983; Guilford, 1981; Naglieri, 1997). Therefore, g is a phenomenon not easily dismissed. Differentiation of cognitive abilities is often inferred fi-om the role of g in explaining the total variance in IQ; therefore, the stability of g across individuals, time, and tests is fimdamental to this investigation. Stability of g Loadings Across Different Test Batteries. In his reproving text of intelligence tests and theory, The Mismeasure of Man Harvard anthropologist Stephen J. Gould (1981) stated repeatedly that scientists considered g a reified single thing. He argued that g was nothing more than a statistical artifact, and that its existence, size, and pattern of loadings can vary widely, depending on the selected method of factor analysis. In effect, Gould regarded g as the arbitrary whim of psychometricians. "Spearman's g is not an ineluctable entity; it represents one mathematical solution from among many equivalent alternatives" (p. 318). 12

PAGE 18

13 If g were mathematical chimera, as Gould argues, then the g-loadings of a specific test could be expected to vary across test batteries. The method to establish the invariance of a test's g loadings is relatively straightforward. Tests could be assigned a g loading in a particular investigation and the replicability of the loading could be determined in any other study in which the test was included. The largest study to address this particular issue was conducted by the late R.L. Thomdike (1987). He began with 65 diverse tests of information processing and problem solving given to Air Force recruits. He then conqjosed seven batteries, each formed of eight randomly selected tests. The remaining tests were inserted into each battery and subjected to factor analysis. The g loadings derived fi-om each battery of each probe test correlated .85. Tests maintained their approximate g-loadings even when analyzed within different random batteries, demonstrating the invariance of g. Brody (1992) criticized Thondike's study, however, noting that four of the included tests had uniformly low g-loadings, falling between .10 and .25. Brody argued that these tests, with titles such as "Rudder Control" and "Rotary Pursuit," appeared to measure manual dexterity. Therefore, their inclusion in Thomdike's analysis may have spuriously inflated the correlation among g-loadings. However, the counterpoise is that only a diverse battery of tests will yield stable estimates of

PAGE 19

14 Stability of g Loadings Across DiflFerent Ages. In theorizing about intelligence, a major issue is the persuasiveness of g across groups of varying age and ability. Traditionally, this issue has been termed the differentiation hypothesis (e.g., Deary & Pagilieri, 1991; Garrett, 1946). Perhaps the first documented study examining the differentiation of abilities was conducted by the eminent British psychologist. Sir Cyril Burt. In 1919, Burt carried out a large standardization of scholastic tests in the London schools. Data fi-om 546 students were collected, with three different age groups represented in the san^le. When he fector analyzed the results, Burt remarked: There was a marked tendency for the group fectors to become increasingly predominant with increasing age. .The application of such methods through all the classes in all the departments shows that the relative influence of the more general capacity (so-called intelligence) is fer greater in earlier years as contrasted with later, (p. 80) He reported the amount of variance accoimted for by g decreased fi-om 52% at 8 years, to 35% at 10 years, and to 27% at 12 years of age. Burt was so intrigued by his findings that he re-analyzed another set of archival data from the London schools to confirm his hypothesis. With a sample of 300 boys who were tested at nine years of age and again at 13, Burt (1944) found that "the influence of the general fector appreciably declines, while the influence of the group fectors increases to nearly twice its original size" (p. 92). Spearman also noticed this developmental trend, attributing differentiation as a result of the increasing role of specific &ctors. Noting the

PAGE 20

15 influence of specific abilities across different age groups, he commented on their protean nature: For the s's, the life-history cannot be traced on such simple lines as g, since these s's themselves are far fi-om simple Over and above such pure aptitude, the s's contain further constituents upon which age acts in a highly irregular manner. In some directions, especially that of information, inqjrovement may occur up to any time of life, however advanced; in other directions, especially that of more or less accidentally formed habits of procedure, either inprovement or deterioration may occur... (1927, p. 375) His comments presaged recent findings indicating that crystallized abilities may continue to develop with age, while fluid abilities typically decline (Horn & Noll, 1997). In America, the first studies of differentiation came fi-om Garrett, Bryan, and Perl (1935). They administered 10 different tests measuring verbal, numerical, and perceptual abilities to boys and girls aged 9, 12, and 15 years. Subsequent fector analysis verified that the first unrotated fector accounted for, respectively, 31%, 32%, and 12% of the variance for the boys, and 31%, 24%, and 19% for the girls. Garrett et al. concluded that "as age increases, abstract or symbolic intelligence changes its organi2ation fi-om a feirly unified and general ability to a loosely organized group of abilities or fectors" (p. 121). In short order, a number of investigations were started, primarily in Europe (e.g., Richards, 1941). Each study reached conclusions similar to those of Garrett and Burt. That is, "the fectors under survey tend to become more independent with increasing age" (Richards, 1941, p. 144). After reviewing his own work and other studies (e.g., Anastasi, 1932; Schiller, 1934; Schneck, 1929),

PAGE 21

16 Garrett (1946) presented a theory of emergent differentiation and coined the term "differentiation hypothesis." In his retirement address as president of the American Psychological Association, Garrett (1946) stated: With increasing age there appears to be a gradual breakdown of an amorphous general ability into a group of fairly distinct aptitudes The conclusion which I draw. ..is that the overall ability which looms large during the elementary school years becomes progressively less important at the high school and college level... (pp. 375-376). With a growing number of standardized intelligence tests available to researchers, the 1940s and 1950s saw a steady stream of investigations devoted to emergent differentiation, now termed the "Garrett hypothesis." Clark (1944) administered the Chicago Tests of Primary Mental Abilities to 320 boys, approximately 100 subjects at each of three age levels. The children were drawn from public schools and matched according to social and economic levels. As in earlier studies, correlations between the sk factor scores declined with age level. Average correlations were .55, .44, and .43, respectively, for ages 11, 13, and 15 years of age. Using the standardization data of the Wechsler-Bellevue Scale, Balinsky (1941) found that a general fector "is found for the nine year old age group, then is apparently submerged and appears again, but not as definitely, at age 50 to 59" (p. 230). Stated differently, the differentiation of cognitive abilities continues from adolescence to early adulthood, then reverses with later adulthood. Owens and Thompson (1954) reported a similar trend when they analyzed data from a sample of 127 men who had taken the Army Alpha in 1919 and again in 1950. The first

PAGE 22

17 unrotated principal component accounted for 53% of the variance in the Army Alpha at age 19 and increased to 63% at age 50. That is, Spearman's g reasserts itself as an increasing source of variance in late adulthood. In one of the few differentiation studies to address gender. Dye and Very (1968) administered a battery of 20 tests measuring mathematical achievement, verbal ability, nimierical reasoning, and perceptual speed. The total sample consisted of 556 ninth grade (n = 165), eleventh grade (n = 193), and university students (n = 198). Each grade level contained an approximately equal number of yotmg men and women. Mean ages for the eighth grade, eleventh grade, and university students were 14, 16, and 20 years, respectively. Correlations between tests were calculated, and &ctor analysis was performed within each grade level and by gender. Results again supported Garrett's hypothesis, with the greatest differentiation occurring for males at each of the grade levels. Certainly, not every study of this period supported Garrett's hypothesis of emergent differentiation. Peel and Graham (1952) administered a battery of 10 group intelligence tests to 352 students from British public schools. The children were retested one year later. On the first occasion, g accounted for 65% and 67% of the variance in scores for boys and girls, respectively. On the occasion of retesting, the respective contribution of g rose to 72% and 75% for boys and girls. Peel and Graham concluded "the evidence appears against differentiation of ability with increasing age, and rather in favour of integration" (p. 33). Although Peel and Graham did not explicate what they

PAGE 23

18 meant by the term "integration," they were quite clear in their rejection of the Garrett hypothesis. The eminent psychometrician P.E. Vernon (1950) also offered no support for emergent differentiation. In his classic text. The Structure of Mental Abilities Vernon stated that he "at one time accepted the view that g tends to differentiate into more specialized abilities during early adolescence and adulthood" (p. 30). However, Vernon's own investigations prompted him to reconsider his position. For exan^le, Vernon and Parry (1949) gave the standard British naval battery of five tests to a sample of 1,171 boys at 14 years of age. These results were compared with 265 naval seaman aged 18 years. Vernon and Parry reported "the average inter-correlations and the g-saturations were almost identical between the groups" (p.30). Vernon also cites a "particularly striking" study by Williams, Hunt, and French (1948) in which, for a sample of 250 boys at three age levels, first factor variances rose fi-om 51% to 62%. Regarding the structure of intelligence across age, Vernon succinctly concluded that "there is no general tendency towards differentiation" (p. 31). Guilford (1967) reviewed 27 studies of this period related to the Garrett hypothesis and noted a number of methodological shortcomings that may have clouded results. First, several studies utilized tests with recognizably poor reliabilities. The magnitude of a correlation depends on the tests' reliability. Therefore, the lower their reliability, the lower their intercorrelations. Second, studies typically did not include young children in their samples. The search for undifferentiated abilities needs to begin before

PAGE 24

19 adolescence, when cognitive abilities are essentially tantamount to those identified in adults. Third, few studies had any uniformity in their test battery, even when using a single standardized test across age levels. For example, Jones (1949) examined the performance of 800 children in four different age groups on the Stanford-Binet. His results supported emergent differentiation. However, the content of Stanford-Binet subtest items varied markedly with age, with more heterogeneous items appearing as age increases. Therefore, the differentiation observed across age levels may simply be the result of new, additional information fed into the fector analysis. Finally, in accordance with his disputation of g as a psychological construct, Guilford found the Garrett hypothesis theoretically untenable: "When there is no insistence of a g &ctor, no g factor is found even down to the first year. There is therefore no need for assuming a general ability fi-om which differentiation can proceed in development" (p. 416). Of the 27 studied reviewed by Guilford, 1 1 favored Garrett's hypothesis, while 16 of the studies provided no support. Subsequent studies of Garrett's hypothesis attempted to address these acknowledged in:q)erfections. Atkin, Bray, Davison, Herzberger, Humphreys, and Seizer (1977) analyzed archival data provided by ETS to identify patterns in the gradual differentiation occurring between fifth and eleventh grades. Sixteen achievement tests representing all curricular domains were administered to the same group of approximately 1,700 students at the beginning of each academic year. Factors were extracted and rotated into an oblique solution. These fector correlations were then transformed into an

PAGE 25

20 orthogonal hierarchical structure in accordance with Schmid and Leiman (1957). Atkin et al. Reported: There is a gradual sharpening of the factor pattern during the six year period. Large loadings tend to become larger with increased age of the group factors while the size of the loadings on the general factor become somewhat smaller" (p. 73). As with Dye and Very (1968), the greatest differentiation occurred for males. Most studies of the Garrett hypothesis utilized school-aged samples. Comparatively few have investigated cognitive differentiation beyond early adulthood. In one of the first applications of confirmatory factor analysis to the study of differentiation, Cunningham (1980) analyzed data fi'om three groups, each exclusively comprised of young adults (age range 15-32 years), yoimger old adults (age range 53-68 years), and older adults (age range 69-91 years). Cimningham reported that, while the structure of abilities remained consistent across age, the fector co variances displayed a pattern of increase across the three age levels. Stated dififerently, there appeared to be an integration, rather than differentiation, of cognitive abilities as individuals entered old age. In an extension of this study, Cunningham (1981) administered parallel batteries to a sample of 234 college students and 388 senior citizens. Each battery was constructed to measure Verbal Comprehension, Number Facility, Perceptual Speed, Symbolic Cognition, and Flexibility of Closure. Cunningham again

PAGE 26

21 identified the pattern of "integration" noted earlier by Owens and Thompson (1954) but explicated in greater detail: Although it is a subtle point, the indication fi-om the current findings is that it is less an issue of sinplification of structure so much as it is an increasing interdependence of different aspects of intellectual functioning. Two prominent candidates for a mechanism to explain such increasing dependencies are intellectual speed and the healthterminal decline phenomenon, (p. 19) Although not intended as a direct study of the Garrett hypothesis, Keith and Witta (1997) examined the implied structure of the Wechsler Intelligence Scale for Children, Third Edtion (WISC-III; Wechsler, 1991) for children 6 to 16 years of age. Confirmatory analysis of the standardization data provided no support for differentiation of cognitive abilities: The WISC-in appears to be remarkably consistent in what it measures fi-om ages 6 to 16; indeed the matrices at different age levels were statistically indistinguishable. Furthermore, it appears that the WISC-III does iodeed measure four fectors as defined in the manual, and that it does so extremely consistently across the test's age range, (p. 104) As a test of the structure of cognitive abilities across the lifespan, Bickley, Keith and Wolfe (1995) used 16 cognitive and achievement subtests of the WoodcockJohnson Psychoeducational Battery-Revised standardization sample to represent eight broad factors at Carroll's second stratum. Bickley et al. found the correlation matrices and fector structure equivalent across all age groups represented in the standardization. The general fector had consistently high loadings on the eight represented primary abilities across each age level, providing no support for differentiation. In addition, the g loadings obtained with principal components analysis were extremely congruent with those

PAGE 27

22 obtained from confirmatory factor analysis, correlating .9994. Thus, Carroll's three stratum model, as depicted by the WoodcockJohnson Psychoeducational Battery, Revised, is remarkably stable across the lifespaa At present, the most comprehensive word regarding the emergent differentiation of cognitive factors comes from Carroll's (1993) Human Cognitive Abilities: A Survey of FactorAnalytic Studies In addition to the several of the selected studies offered in this review, Carroll examined 48 other data sets that, because they included sanples of different ages and highly similar test variables, could show differentiation by age or grade. Carroll agreed that common sense suggests that differentiation should occur with age, insofar as abilities are formed, maintained, and developed through experience. However, he foimd no supportive evidence: I am struck by the feet that nearly all the major types of abilities can be detected and isolated over a wide range of ages — often at a quite early age — and as a rule they appear to be the same fectors regardless of age level. .My general conclusion on age-differentiation of cognitive ability fectors is that it is a phenomenon who's existence is hard to demonstrate, (p. 680-681) Thus, even some of Garrett's original data, upon reanalysis, did not support differentiation. In summary, these studies provide equivocal support for the differentiation of cognitive abilities with age. A number of past studies seem to support Garrett's hypothesis, while more recent investigations do not. Because this developmental issue is extremely important to intelligence theory and the practice of psychology, research will certainly continue. With the increased use

PAGE 28

23 of advanced statistical methods, such as confirmatory' factor analysis, researchers are inching toward a resolution. Stability of g Loadings Across Different Ability Levels. In his investigations of g and positive manifold. Spearman (1927) noted that correlations between test scores vary according to intellectual ability. Test correlations are higher in low-IQ individuals and lower in high-IQ individuals. Although he did not investigate the phenomenon systematically, he did offer post hoc comments on the "curious matter that has arisen" (1927, p. 5). In 1927, Spearman, using his own data and results fi"om other studies, remarked: Now, all the changes we have been considering follow a general rule. The correlations always become smaller — showing the influence of g on any ability to grow less — in just the classes of person which, on the whole, possess this g more abimdantly. The rule is, then, that the more "energy" a person has available already, the less advantage accrues to his ability fi-om further increments of it. (p. 219) Drawn to industrial metaphor. Spearman compared g to the an engine, noting that an engineer does not achieve a doubling of a ship's speed by doubling the coal in the boiler (p. 127). Spearman did not write extensively on this phenomenon, only mentioning it in light of the "diminishing returns of g" (p. 127). Many researchers (e.g.. Brand, 1996; Brody, 1992) have considered Spearman's hypothesis of "diminishing returns" evidence that the relationship between g and test performance is stronger for lower-IQ testees. The variant nature of g, and the accon^anying law of diminishing returns, may explain the differentiation in ability often observed in high-IQ groups (Garrett, 1938).

PAGE 29

24 In his text, The Structure of Human Abilities Vernon (1950) posed the question that the structure of intellect may be different for high-ability groups due to the homogeneity of the sample. However, Vernon's brief statements only concerned the upper range of ability, and offered no insights as to the comparative structure of intelligence for low-ability groups. Lienert and Faber (1963) conducted one of the first studies expressly designed to investigate ability differentiation across groups of different overall intelligence. An analysis of the HamburgWechsler Intelligence Test for Children (HAWDC), the German version of the WISC, found a smaller first centroid &ctor for children with IQs above 109 than for children with IQs below 109. Lienert and Crott (1964) extended this research by administering a battery of 14 tests to three different age groups. Tests included measures of vocabulary, comprehension, digit memory, and spatial reasoning. Lienert and Crott found the number of common fectors increased fi-om five (for children aged 10-12 years) to six (for adolescents aged 18-20 years), and subsequently dropped to four (for adults aged 45-60 years). When the sample of children was divided into highand low-ability groups, Lienert and Crott identified four factors for the low-ability group, and five factors for the high-ability group. Their results agreed with previous studies of differentiation with age, and prompted their use of the term "differentiation" to refer to mental abilities differentiating as children increase in chronological age, and the term "divergence" to reference lower correlations between mental abilities found among testees with higher levels of overall intelligence.

PAGE 30

25 Lienert and Crott proposed an integration of differentiation and divergence of mental abiKties: In the same way as the in^rovement of performance from childhood to adolescence is accompanied by a differentiation of the imderlying ability structure, and as the decline of performance from adolescence to adulthood is accompanied by an integration of structure, a divergence and convergence of the ability structure takes place from low to high performance level and vice versa respectively. Therefore, it may be assumed that performance level and degree of differentiation are interdependent and that — regardless of the subject's age — differences in intelligence level presuppose variations in the structure of intelligence in accordance with the divergence hypothesis, (p. 158) Linert and Crott (1964) also found evidence for convergence when testees were impaired with LSD and alcohol. Spearman's observation that test correlations vary among groups of different ability received little attention from contemporary psychologists until Detterman and Daniel (1989) divided the standardization samples of the Wechsler Intelligence Scale for Children, Revised (WISC-R) and Wechsler Adult Intelligence Scale (WAIS) into five groups based on their performance on either the Vocabulary or Information subtests. These subtests were selected for their high correlations with Full Scale IQ, and because Wechsler (1981) found these subtests relatively stable across age. IQ equivalents for the five groups, from lowest to highest, were below 78, 78 to 92, 93 to 107, 108 to 122, and above 122. Correlation matrices were computed for each group. Detterman and Daniel found that subtest intercorrelations for the lowest IQ group (below 78) were twice as large as the intercorrelations for the highest IQ group (above 122). For the low-IQ group, intercorrelations averaged .56,

PAGE 31

26 uncorrected for range restriction; for the high-IQ group, intercorrelations averaged .22. Confirmatory analyses with the Linear Structural REL lations computer program (LISREL; Joreskog & Sorbom, 1989) verified that none of the correlation matrices could be considered equal for any of the tests or methods of group selection. Thus, subtest correlations change across ability levels. Deary and Pagliari (1991) credited Detterman and Daniels for rediscovering Spearman's law of diminishing returns. Replicating Detterman and Daniels' procedures for subsample grouping and analysis, Lynn (1990) obtained similar results with the WISC-R standardi2ation sanqjles fi-om Scotland. Subtest correlations, fi-om lowto high-ability groups, were .44, .38, .17, .14, and .20. Lynn and Cooper (1994) also used the law of diminishing returns to investigate a secular decline in g. Because IQs have increased substantially in the last few decades, Lynn and Cooper hypothesized that subtest intercorrelations should be lower for the WISC-R than for the WISC. Using the standardization san^les of the French Wise and WISC-R, Lynn and Cooper reported average correlations of .38 and .29 for the WISC and WISC-R, respectively. One important question regarding the divergence of mental abilities was whether Spearman's law of diminishing returns applied only to individually administered intelligence tests, such as the Wechsler scales. Legree, Pifer, and Graflon (1996) extended these results to group ability tests, analyzing the 1980 norming sample of the Armed Services Vocational Aptitude Battery (ASVAB). Using a sample of 9,173 participants, Legree et al. formed five ability groups

PAGE 32

27 based on performance on each of the 10 ASVAB subtests. Thus, there were 10 sets of five correlation matrices. Correlations were corrected for restriction of range and submitted to confiimatory factor analysis. Seven of the 10 scales of the ASVAB conformed to Spearman's law of diminishing returns, with intercorrelations being higher for the low ability group than the high ability group. A review of the three scales excepted fi'om this pattern indicated substantial measurement error and skewness. The authors concluded, "These data support the conclusion that cognitive abilities are less correlated within more intelligent groups" (p. 53). Thus, for cognitive tests vdth adequate psychometric properties, the law of diminishing returns seems to hold. This pattern of test correlations has also been substantiated using elementary cognitive tasks (ECTs). For example, the correlation between IQ and inspection time (IT) for individuals with IQs of 60 is around .80. The IQIT correlation shrinks to .50 for individuals -with IQs above 110, however (Brand, 1996). Interestingly, the law of diminishing returns may not extend to all speeded perceptual tasks. Fogarty and Stankov (1995) administered RPM and four perceptual speed tasks (Number Conq)arison, Symbol Search, Digit Symbol, and Stroop paradigm) to a sample consisting of 179 university students. Highand low-ability groups were identified, based on total raw scores which were either one standard deviation above or below the mean on RPM. Thus, two groups were formed, consisting of 29 low-ability and 28 high-ability individuals. IQ equivalents for low-ability group were between 92 and 103. Participants in the high-ability group all had IQ equivalents above

PAGE 33

28 125. Correlations between the perceptual tasks were calculated for each group and subjected to confirmatory analysis. The resulting test of equality indicated that the matrices were essentially the same in both groups. Fogarty and Stankov argued that "employing tests with a more or less uniform di£Sculty level for different ability groups (as measured by some external criterion), showed that under these conditions, the correlations are the same for the various groups" (p. 172). Unfortunately, the extremely small sample sizes enq)loyed in Fogarty and Stankov' s investigation preclude it fi-om being a serious challenge to the law of diminishing returns. The most recent investigation of cognitive divergence comes fi-om Edinburgh University. Deary, Egan, Gibson, Brand, and Kellaghan (1996) analyzed the standardization data from the British-Irish version of the Differential Aptitude Test (DAT; 1986). The DAT consists of eight subtests measuring verbal ability, abstract reasoning, numerical reasoning, clerical speed, mechanical reasoning, spatial ability, spelling, and language usage. Total sample consisted of 10,535 participants in eighth, ninth, tenth, and eleventh grades. Deary et al. divided the san:q)le into four smaller subsamples based on grade and ability (e.g., high grade-high IQ; high grade-low IQ; low grade-low IQ; low grade-low IQ). Average IQs of the lowand high-ability groups were 90 and 110, respectively. Average ages of the young and old groups were 14.2 and 16.7 years, respectively. Within each of the four groups, correlation matrices were subjected to principal components analysis. As an indicant of the pervasiveness of g. Deary et al. used the percentage of variance accounted for

PAGE 34

29 by the first unrotated principal component. The percentage of total variance explained by g in each of the groups was between 47.8 and 49.8 %. Thus, their analysis offered no strong support for differentiation by age or ability: The difference in variance between groups that differ by the equivalent of 20 IQ points is just over 2%. Moreover, across the age range investigated. .this study finds little evidence to suggest that human mental ability is more differentiated in older groups, (p. 120) Deary et al. reasoned that the lack of differentiation in their study, when compared to the inpressive results obtained by Detterman and Daniel, may be caused by restriction of range. In their study, lowand high-ability participants differed by 20 IQ points. Conversely, Detterman and Daniel's lowest and highest groups differed by 44 IQ points. In addition, any differentiation across age would be diflBcult to identify, given the narrow age range of this investigation (2.5 years). In sum, these studies confirm the importance of g in explaining cognitive performance, but also suggests that g is variant for different ability groups. Competing Explanations for the Differentiation of Cognitive Abilities. In his text The g Factor. Chris Brand (1996) offered two competing hypotheses to explain the variant nature of g and the differentiation of cognitive abilities in high-IQ individuals. The first hypothesis, initially advanced by Burt in 1919 and later by Garrett (1938), contends that high-IQ individuals have intellectual "investment opportunities" that develop with age. Stated differently, experience affords high-IQ individuals the opportunity to acquire varied cognitive skills and strategies in a feshion that is superior to their low-

PAGE 35

30 IQ peers. Primary abilities are thus seen to develop to a greater extent in highability individuals than they do in low-ability individuals. The second hypothesis, suggested by Detterman (1989) and Anderson (1992), focuses on the detectability of cognitive ability. Detterman (1994) posits that intelligence is made up of a number of inter-related processes. Thus, deficits in one process may critically affect all other processes: The differences in correlations across IQ level are consistent with the systems theory of intelligence. .In this theory, lower IQs result from deficits in important cognitive processes. Because these processes are part of a system, they affect the functioning of other parts of the system If these important processes are deficient, parts dependent on them will also be impaired. Essentially, a deficit in an important process will put an upper ceiling or limit on the efficiency of the operation of other parts of the system That means that all parts of the system will be more similar if there is a deficiency in an important process. This forced similarity in abilities is what causes a higher correlation among IQ subtests for low IQ subjects, (p. 28) Stated differently, low-IQ people possess the same skills as high-IQ individuals; however, their relatively poor performance on cognitive tests obscures the differentiation of cognitive abilities. A useful analogy is to consider two stereo systems playing the same song. One stereo system plays beautifully. The second stereo system is riddled with static. Even though both stereo systems play the same tune, the better sounding system permits the listener to hear every note of the song and to distinguish the woodwind section from the string sectioa Conversely, the same song playing from the second stereo system is barely discernible. Although Spearman did not directly address the source of cognitive differentiation, passages from The Abilities of Man suggest that he favored the

PAGE 36

31 detectability hypothesis. In discussing individual differences in cognitive abilities, Spearman stated: The whole frequency distribution (of distinct cognitive abilities in any individual) will, in fact, have a bell-like shape ....At the extreme ends of the distribution will lie a very small number for which the person is, on one side a genius, and on the other an idiot. Every normal man, woman, and child is, then, a genius at something, as well as an idiot at something. The question is what — at any rate in respect of the genius. This must be a most difficult matter, owing to the &ct that it occurs in only a minute proportion out of all possible abilities. It certainly cannot be detected by any of the testing procedures at present in ciurent usage; but these procedures seem to be susceptible to vast improvement, (p. 221) To date, the question of whether the differentiation of cognitive abilities for subjects of different IQ level is due to detectability or development remains unanswered. Simimary Past research indicates that a test's g loading may vary across groups of different intellectual ability. As a result, low-IQ individuals do not display the differentiation in abilities often observed in the test performance of high-IQ individuals (Brand, 1996; Detterman & Daniels, 1989; Spearman, 1927). A reasonable conclusion drawn from these findings is that the structure of intellect varies for individuals of differing ability. Researchers have yet to investigate this particular phenomenon in the context of Carroll's three stratum theory of intelligence. In addition, the cause of intellectual differentiation has yet to be identified. Studies to this point have been somewhat equivocal (e.g., Anderson, 1992; Carroll, 1993; Deary et al., 1996; Guilford, 1981; Lynn, 1990). Thus, the purpose of this study is twofold. The first purpose is to

PAGE 37

32 compare the structures of intellect for lowand high-ability children within the framework of Carroll's three stratum theory of intelligence. Carroll (1993) relied exclusively on ejqiloratory fector analysis to formulate his theory. The confirmatory techniques used in this study would further verify the threestratum theory across ability levels. The second purpose is to determine whether differentiation of cognitive abilities is emergent with experience and development, or sinqily detected by IQ tests.

PAGE 38

CHAPTERS METHOD Participants and Data Collection Archival data from the WoodcockJohnson Psychoeducational Battery, Revised (WJ-R; Woodcock & Johnson, 1989) has been provided by the test's co-author, Dr. Richard Woodcock. Normative data for the WJ-R were collected from 6,359 participants in over 100 geographically diverse communities in the United States (Mather, 1992). Subjects were sampled randomly from a stratified sampling design that controlled for ten commimity and socio-economic variables. The age of participants ranged from 24 months to 95 years. All data were gathered from September, 1986 to August, 1988. The sample was weighted and corresponds closely to the 1980 census on such relevant characteristics as race, gender, region, community size, and so forth. Description of the WJ-R The WJ-R is designed as an operational representation of the HomCattell gf-_gc theory of intelligence, with the eight cognitive clusters of the WJR corresponding to an array of broad cognitive factors in the Hom-Cattell model. With the addition of a general fector and minor revisions of factors at the second order, the WJ-R also provides an excellent representation of Carroll's three stratum model (Carroll, 1993; McGrew, 1997). 33

PAGE 39

34 The WJ-R is divided into two main parts: the Tests of Cognitive Ability (WJ-R COG) and the Tests of Achievement (WJ-R ACH). Each of these parts is divided further into a Standard and Supplemental Battery. The WJ-R COG Standard Battery is comprised of tests 1 to 7, and the Supplemental Battery consists of tests 8 through 21. The Standard Battery is designed to provide a full-scale cognitive score. The tests may be administered in any order and measures each of seven cognitive fectors. Five of the measures may be used to assess preschool or low-functioning adults. A description of each test follows, vsith variable names being those used in subsequent analysis (Mather, 1992, p 4-18): Test 1 : Memory for Names (memnamw) requires the testee to remember and identify cartoon drawings of space aliens. The test is designed to measure the ability to form and retrieve auditoryvisual associations. Test 2: Memory for Sentences (memsenw) measures the ability to repeat words, phrases, and sentences that are presented by a tape player. This test primarily measures short-term memory. Test 3: Visiial Matching (vismatw) measures the ability to identify and circle quickly and two identical numbers in a row of six numbers. The test has a 3 minute time limit. Test 4: Incon^lete Words (incwrdw) measures auditory closure, or the ability to identify words with missing sounds. The test assesses auditory processing.

PAGE 40

35 Test 5: Visual Closure (visclow) measures the ability to identify a picture or drawing that has been altered in one of several ways. This test primarily measures visual processing. Test 6: Picture Vocabulary (picvocw) measures the ability to identify and name pictured objects. This test primarily assesses comprehensionknowledge. Test 7: AnalysisSynthesis (ansynw) measures the ability to determine the missing component of an incomplete logic puzzle. The test primarily measures fluid reasoning. The 14 tests comprising the Supplemental Battery provide additional information about seven cognitive fectors. A description of each test follows: Test 8: VisualAuditory Learning (valmgw) measures the ability to retain visual-auditory associations. This test requires the subject to retain and identify up to 28 rebuses that are read within the context of a meaningful sentence. Test 9: Memory for Words (memwrdw) requires the testee to repeat lists of unrelated words in the correct order. This test measures short term memory. Test 10: Cross Out (crsoutwe) measures the ability to scan and con^are visual information rapidly. The student is asked to mark the 5 drawings in a row of 20 geometric drawings that are identical to a target drawing. A time limit of 3 minutes is imposed. This test measiires processing speed.

PAGE 41

36 Test 1 1 : Sound Blending (sndblndw) measures the abilit>' to synthesize a series of sounds into whole words. From a taped recording, word parts are presented first as syllables, and then as phonemes. This test measures auditory processing. Test 12: Picture Recognition (picrecwe) measures the ability to recognizable a subset of previously presented pictures within a field of distracting pictures. This test primarily measures visual processing. Test 13: Oral Vocabulary (orlvocw) measures knowledge of word meanings. The student is asked to provide synonyms and antonyms of words presented orally. This test measures comprehension-knowledge. Test 14: Concept Formation (confimw) measures categorical reasoning ability. Testees are asked to derive and identify rules for concepts when shown illustrations of concepts and non-concepts. This test primarily measures fluid reasoning. Test 15: Delayed Recall — Memory for Names measures the ability to recall fi-om 1-8 days later the stimuli presented in Test 1 : Memory for Names. This test primarily measures long-term retrieval. Test 16: Delayed Recall — ^Visual Auditory Learning measures the ability to recall fi-om 1-8 days later the stimuli presented in Test 8: VisualAuditory Learning. This test primarily measures long-term retrieval. Test 17: Numbers Reversed measures the ability to repeat a string of digits in reverse order. This test requires perceptual reorganization and primarily measures short-term memory and fluid reasoning.

PAGE 42

37 Test 18: Sound Patterns measures the ability to indicate whether pairs of sound patterns are the same or different. Pairs differ in pitch, rhythm, or durationThis test primarily measures auditory processing. Test 19: Spatial Relations measures the ability to math shapes visually with the component parts. The student must select the correct pieces from a series of shapes to make a given whole shape. This test is a mixed measure of visual processing and fluid reasoning. Test 20: Listening Con^rehension measures the ability to listen to a short tape-recorded passage and supply the single word that best completes each passage. This test measures comprehension-knowledge. Test 21 : Verbal Analogies requires the testee to conplete phrases with words that indicate appropriate relationships. This test measures fluid reasoning and comprehension-knowledge. The WJ-R COG provides three broad based measures of intellectual ability: Broad Cognitive Ability — Early Development is appropriate for children at the preschool level or for low-functioning adults. This cluster consists of five tests. Test 1 : Memory for Names, Test2: Memory for Sentences, Test 4: Incomplete Words, Test 5: Visual Closure, and Test 6: Picture Vocabulary. Broad Cognitive Ability — Standard Scale is based on all seven tests in the Standard Battery and provides a broad-based measure of intellectual functioning.

PAGE 43

38 Broad Cognitive Ability — ^Extended Scale is based on the first 14 cognitive tests. If all 14 tests have been administered, this score is used as the broad-based measure of intellectual ability. The WJ-R ACH Standard Battery is con^rised of tests 22 through 30. The Supplemental Battery includes tests 3 1 to 35, and measures written language skills. A brief description of each test follows: Test 22: LetterWord Identification measures the ability to identify letters and words. Successfiil word identification does not require conqjrehension, as a subject may or may not know the meaning of a word. Test 23: Passage Comprehension measures the testee's ability to use syntactic and semantic clues. Test 24: Calculation (calcw) measures an individual's ability to perform a variety of mathematical calculations, including addition, subtraction, multiplication, and division. Problems progress fi-om relatively single addition to more advanced geometric, trigonometric, and logarithmic operations. Test 25: Applied Problems (approbw) requires an individual so solve practical problems. Test 26: Dictation measures spelling, knowledge of prewriting skills, punctuation and capitalization, and usage. Test 27: Writing Samples measures ability to produce meaningfiil sentences to satisfy a variety of task demands. Emphasis is placed on the quality of writing, rather than basic skills.

PAGE 44

39 Test 28: Science measures knowledge of both biological and physical sciences. Test 29: Social Studies measures knowledge of history-, geography, economics, and government. Test 30: Humanities measures knowledge of art, music, and literature. Test 3 1 : Word Attack measures the ability to apply phonic and structural analysis skills in pronouncing phonically regxilar nonsense words. Test 32: Reading Vocabulary measures knowledge of word meanings by providing synonyms and antonyms. Test 33: Quantitative Concepts measures an individual's knowledge of basic mathematical concepts and vocabulary. Test 34: Proofing measures an individual's ability to correct errors in punctuation, spelling, capitalization, and usage in written passages. Test 35: Writing Fluency measures the ability to produce correct forms of writing and correct errors in written passages. Tests of the WJ-R combine to form eight cognitive fectors. A brief description of each fector follows, with notations being those used by Woodcock and Mather (1990, p. 23): Long-term retrieval (Glr) measures the effectiveness in storing and fluently retrieving information over extended periods of time. The time period may range from several minutes to several days. Short-term memory (Gsm) measures the ability to apprehend information and repeat it within a short period of time.

PAGE 45

40 Processing speed (Gs) measures the ability to performed relatively simple tasks qtiickly. Auditory processing (Ga) measures the ability to analyze and synthesize auditory patterns. Visual processing (Gv) measures capability in perceiving and thinking with visual patterns. Con:q)rehension-knowledge (Gc) measures breadth and depth of knowledge and its applications. Fluid Reasoning (Gf) measures the capability for abstraction and reasoning in novel situations. Quantitative ability (Gq) measures comprehension of quantitative concepts and skill in using mathematical symbols. The hypothesized fector structure of the WJ-R is presented in Figure 2. Since its publication, a number of studies have investigated the psychometric properties of the WJ-R. Woodcock (1990) summarized nine conjoint validity studies which included the WJ-R with various combinations of the Wechsler scales, Stanford Binet, Fourth Edition (SB:FE; Thomdike, Hagen, & Sattler, 1986) and Kaufinan Assessment Battery for Children

PAGE 46

41 Figure 2. Three-stratum theory represented by the WoodcockJohnson, Revised. (KABC; Kaufinan & Kaufinan, 1983). A total of 15 different confirmatory analyses were conducted using 68 subtests. The results of this simimary provided universal support for the eight fectors represented in the WJ-R, The psychometric properties of the WJ-R have been termed "excellent" (McGrew et aL, 1991; Bickley et aL, 1995).

PAGE 47

42 The Model The three-stratum model is shown in Figure 3. The first level of the model represents primary abilities. These abilities are indexed by 16 of the 39 subtests of the WJ-R. Tests were selected on the basis of their strong, exclusive loadings on the proposed &ctors. The second level represents the eight cognitive factor clusters measured by the WJ-R. While the WJ-R is primarily based on the gc^gf model of intelligence, Carroll (1993) has noted that these cognitive fector clusters also provide a satisfactory representation of his second-stratum abilities. The third stratum represents Spearman's g. Statistical Procedures for Subgroup Selection To answer each of the research questions in this study, the first task was to form subgroups of highand low-ability participants. Furthermore, the desired analyses required that each subgroup was to have near identical bivariate normal distributions of criterion ability. A review of recent studies in the area of confirmatory fector analysis offers several methods for forming subgroups fi-om a large san^)le. In the most widely cited study, Detterman and Daniel divided their sample according to subtest scores, forming five groups.

PAGE 48

43 Concapl Fomtk)n Analytli Synthetlt Vteual Cloture Picture Recognition Vlwal Matching CroH Out Mamory ForNamaa Vlaual Auditory Laammg Picture Vocabulary Oral Vocabulanr liicuiuMa Wofds Sound Standing Mafnory For Santanoaa Mamory ter Worda CalculaUon AppM ProtXana Figure 3. Hypothesized structure of the Woodcock-Johnson, Revised.

PAGE 49

44 Deary et al. (1996) also used subtest scores, but drew their groups only from individuals scoring one standard deviation above or below the mean. Fogerty and Stankov (1996) used full-scale scores to form two groups, one scoring in the upper three stanines and the other scoring in the lower three stanines. This study took a slightly different approach, which is now described. First, it was necessary to identify an independent variable to establish subgroups. Broad Cognitive Ability indices could not be used for this piupose, because subtests included in the proposed model also contribute to each of these measures of overall intelligence. Therefore, a composite variable (SortlQ) was created by averaging scores on the Numbers Reversed, Listening Comprehension, and Verbal Analagies subtests. These subtests are not included in the proposed theoretical model of cognitive ability, and thus provide an independent measure of overall intelligence. The simple correlation between SortlQ and Broad Cognitive Ability-Extended (BCAE) was .94. Two subgroups (i.e., HighlQ and LowIQ) then were formed by dividing the data at the mean of SortlQ. Once HighlQ and LowIQ individuals were identified, the next challenge was to sample from each group a normal bivariate distribution with equal variances. To acconqjlish this end, the desired sample sizes, means, and standard deviations were identified. Sample sizes for each subgroup (i.e., HighlQ and LowIQ) were set at 500. Standard deviations for each group were set at 7.5, about half of the standard deviation typically observed in the general population. Means for the HighlQ and LowIQ subgroups were 115 and 85, respectively. Once these characteristics were established, z-scores were

PAGE 50

45 calculated using the Broad Cognitive AbilityStandard as the criterion variable. Individuals were then randomly san:q)led by z-score intervals, with the desired number of subjects sampled at each z-score interval equal to that which woiild be observed in a normal distribution. The exact number of participants sampled at each z-score interval is found in Table 1 Following this procedure, there were two normal distributions, with respective means of 1 15 and 85, each with equal variances and sample sizes. Statistical Analysis Once subgroups of highand lowIQ individuals were formed, confirmatory factor analysis then was used to conqiare the constructs measured by the WJ-R across each ability level. In confirmatory lactor analysis, the fector structure is restricted a priori according to guidelines offered by theory. The obtained data is then compared with the restricted, theoretical model. Keith (1997) operationalized a process for testing increasingly lenient models as a method of determining if a psychometric instrument measures the same construct across groups. If analyses leads to rejection in the initial, most stringent model, increasingly lenient alternative models are developed and used in subsequent steps. For this investigation, the AMOS (Arbuckle, 1996) computer program was used to simultaneously evaluate the proposed threestratum model of intelligence across two ability levels. When using AMOS, a nonsignificant 2d shows that the theoretical model fits the en^irical data. Note that the 2d need not be significant to select

PAGE 51

46 one model over another. In the event of a nonsignificant chi square, the degrees of fi-eedom can indicate which model is the most parsimonious. A Table 1 Summary of Subgroup Selection z-Score Normal Number Interval Probabilities Sampled Cumulative less than -2.5 .01 5 5 -2.5 < -2.0 .02 10 15 -2.0 < -1.5 .04 20 35 -1.5 < -1.0 .09 45 80 -1.0 < -0.5 .15 75 155 -0.5 < 0 .19 95 250 0 < .5 .19 95 345 .5 < 1.0 .15 75 420 1.0 < 1.5 .09 45 465 1.5 < 2.0 .04 20 485 2.0 < 2.5 .02 10 495 greater than 2.5 .01 5 500 common criticism of the 2d test relates to its sensitivity to sample size. For example, large sample sizes can result in a statistically significant 2d value and lead to a false rejection of models. Conversely, small sample sizes may contribute to a nonsignificant 2d value and lead to false acceptance of the model. As a result of the influence of sample size on the 2d value, several researchers (e.g., Keith, 1997) recommend the use of more than one fit statistic to evaluate models. The Tucker-Lewis Index (TLI, also called the non-normed fit index) provided an additional measure of fit. The Parsimonious Fit Index (PCFI), a fit statistic that fevors simpler, more parsimonious models over more complex models, is also reported. The Bentler-Bonnett non-normed fit index

PAGE 52

47 (NFI) estimated the relative improvement of each model over the null hypothesized model. For each of these additional indices of fit, values range fi-om 0 to 1 .0, with 0 indicating a poor fit, and 1 .0 indicating a perfect fit. Generally, values over .90 are considered excellent. Loadings across models were compared not only in terms of g, but also in terms of the cognitive clixsters. When conqjared across groups, differences in the loadings of subtests on the cognitive &ctors indicate the relative in^ortance of primary abilities. If the expected cognitive diflFerentiation occurs at higher levels of intelligence, an important theoretical issue was whether the differentiation resulted fi-om a diminished role of g or an increased role in primary abilities. To answer the second research question, whether development or detectability underlies the differentiation of cognitive abilities, the same procedures described above were used with respect to age and ability. The young groups consisted of individuals between 6 and 12 years. The older groups consisted of individuals between 13 and 22 years of age. These ages correspond closely to guidelines offered by Piaget for the emergence of abstract reasoning and formal operations. Within each age group, highand low-ability subgroups were formed. Thus, a total of four groups were formed: young-high IQ (ChildHighlQ), young-low IQ (ChildLowIQ), old-high IQ (AdolHighlQ), and old-low IQ (AdoILowIQ). Again, sample sizes and standard deviations were equal for each group (n = 250, s = 7.5). Within each age level, confirmatory maximtim likelihood analysis conqjared the three

PAGE 53

48 Stratum model simultaneously across each ability group. In addition, g loadings across age cohorts were examined. If g loadings decrease as the cohort age increases, then the differentiation of intellectual ability is due to the development of primary abilities. Conversely, stable g loadings across age groups lend support to the detectability hypothesis.

PAGE 54

CHAPTER 4 RESULTS Descriptive statistics for HigWQ and LowIQ are presented in Tables 2 and 3. Data are reported in W-scores. W-scores are a special transformation of the Rasch ability scale and have mathematical properties, such as equal intervals, that make them well-suited for the subsequent confirmatory analyses required of this study (Andrich, 1988). The histograms of HighlQ and LowIQ are presented in Figures 4 and 5. As can be seen clearly, both distributions are normal, with near equal standard deviations. 120 100 80 60 40 20 0 SW. Dev = 7.68 Mean = 115.0 N = 500.00 97.5 5 102.5 107.5 112.5 117.5 122.5 127.5 132.5 100.0 105.0 110.0 115.0 120.0 125.0 130.0 BCASTDAS Criterlan Variable Broad Cognittve Ability Figure 4. Histogram of High-IQ Distribution 49

PAGE 55

50 Table 2. Descriptive Statistics for High-IQ Group (HighlQ) Variable Name Mean Std. Deviation N Concept Formation 5208.09 147.41 500 Analysis Synthesis 5185.24 115.00 500 Visual Closure 5116.65 1 t\(\ 100.70 c c\r\ 500 Picture Recogmtion 5119.78 92.39 500 Visual Matching r ^ c% r f\t\ 5285.09 165.33 r r\r\ 500 Cross Out 5173.51 112.10 500 Memory for Names 5087.14 127.16 500 Visual Auditory Learning 5076.04 106.33 500 Picture Vocabulary 5372.12 163.71 500 Oral Vocabulary 5414.49 175.20 5U0 Incomplete Words 5082.30 90.84 500 Sound Blending 5136.39 152.21 499 Memory for Sentences 5218.21 126.35 500 Memory for Words 5178.28 198.05 500 Calculation 5431.33 209.26 499 Applied Problems 5420.66 187.65 498 std. Dev 7.46 Mean = 85.1 N = 500.00 67.5 72.5 77.5 82.5 87.5 92.5 97.5 102.5 70.0 75.0 80.0 85.0 90.0 95.0 100.0 BCASTDAS Crttailan Variable Broad Cogntlve Ability Figure 5. Histogram of Low-IQ Distribution

PAGE 56

51 Table 3. Descriptive Statistics for Low-IQ Group (LowIQ) Variable Name Mean Std. Deviation N Concept Formation 4862 207 495 Analysis Synthesis AO HO 4868 179 493 Visual Closure 4936 146 ^ AA 500 Picture Recogmtion 495 / 11/ 5U0 Visual Matching 4915 256 500 Cross Out 4938 1 173 A AA 499 Memory for Names 4921 91 500 Visual Auditory Leammg A r\r\r\ 4900 115 498 Picture Vocabulary 4yj 1 TIT zl /
PAGE 57

52 As noted earlier, }i_can be affected by large sample sizes and may lead to rejection of an adequate model (Keith, 1997). Thus, three additional statistical measvires also were reported to overcome this possible drfiSculty: the Tucker-Lewis Index (TLI), the Parsimonious Fit Index (PFI), and BentlerBonnett Normed Fit Index (NFI). Data from these three indices suggest the constructs measured by the proposed model do not differ significantly across the two IQ levels. Given these somewhat conflicting initial findings (i.e., the initial jc! found significant differences in factor structure across age levels, while three other goodness of fit indices suggested an adequate fit to the data), fiirther analyses seemed warranted. The second analysis relaxed the &ctor model; permitting the values of the less inqjortant aspects of factorial invariance (i.e., the factor unique variances, subtest unique and error variances) to differ for each age group (Keith, 1997). That is, this analysis specified identical fector structure and loadings across ages, but permitted different values in the unique and error variances of the first order fectors and subtests. By requiring the factor loadings (i.e., regression weights) to be invariant across groups, this analysis evaluates whether a fixed unit change on an exogenous variable will always correspond to the same change of the endogenous variable, independent of whether the respondent is of highor low-IQ. The fit statistics for the initial model and this relaxed model are presented in Table 4. Relaxing the factor model to permit different values for the unique and error variances of the first order fectors and subtests resulted in a significant

PAGE 58

53 improvement in model fit as evidenced by the significant decrease in 2dTLI, NFI, and PFI remained virtually unchanged. Table 4. Different Hypotheses Tested in Regard to the Structure of Cognitive Abilities at Different IQ Levels Hypothesis Tested df TLI NFI PFI Change Factor Structure Invariant 1461 231 .99 .99 .84 (All Parameters Fixed) Factor Loadings Identical 1253 207 .99 .99 .75 208* (Error and Unique Variances Vary) Factor Structure Similar 1192 192 .99 .99 .70 269* (All Parameters Free to Vary) 'Indicates a statistically significant improvement in model fit based on x~ decrease. The third and final analysis permitted all parameters of the fector model (i.e., factor loadings, imique and error variances of the factors and subsets) to vary across the nine age groups. Allowing all parameters to differ across age levels resulted in the expected significant decrease in 2d (2d = 1 192, df = 192, p <.01). In summary, a significant decrease in 2d was achieved by permitting the imique and error variance to vary across highand low-IQ groups. Further significant inqjrovements in the model were obtained by permitting the remaining parameters to vary (i.e., different fector loadings across ability groups). Figures 6 through 1 1 simimarize the results of these three analyses in graphical form The nimibers adjacent to the arrows are fector loadings. The ntmibers adjacent to the ovals represent the variance accoimted for in the first-

PAGE 59

54 order group fectors by the second-order general factor. The numbers above each rectangle represent the proportion of variance accounted for in the subtest by the group &ctors. Of particular interest are the loadings, which reflect the degree of generalizability between each factor and variable. Differences in the fector loadings exist between the Highand Low-IQ groups. Further analysis indeed confirms that all firstand second-order factor loadings are significantly different, at the .05 alpha level, regardless of model. These differences follow the same pattern, with factor loadings (and hence the proportion of variance accounted for by each factor) significantly larger for the low-IQ group than for the high-IQ group. As an aid in conceptualizing the pattern of differences between ability groups, the g loadings to the primary abilities in Figures 10 and 1 1 also are summarized in Table 5. Table 5. Summary of g Loadings of Highand Low-IQ Groups Primary Ability g Loading Low 10 / High 10 Gf Gv Gs Glr Gc Ga Gsm .89 .88 .95 .69 .84 .81 .72 .86 .80 .77 .75 .65 .39 .65 .39 .72 Gq

PAGE 60

55 2 4 0 7 ^ 4 0 8 9 8 4 (uio) 4 4 ) 4 ) 4 ( 4 ) Figure 6. Simultaneous analysis of high and low IQ groups, with all parameters constrained across both groups. Mean IQ 115, standard deviation 7.5. San^Ie size of 500 in each group.

PAGE 61

56 .67 conftmw — .68 anisynw .62 ^ .61 picncw* .88 4 .87 crsoutvM .39 .77 vatngw .80 .95 ortvoew 4 (uio) .63 kiewrdw MidbMw 4 @ .64 4 0 .66 4 (uia) .50 4 4 (uls) 32 4 (uls) Figure 7. Simuftaneous analysis of high and low IQ groups, with all parameters constrained across both groups. Mean IQ 85, standard deviation 7.5. Sanqjle size of 500 in each group.

PAGE 62

57 Figure 8. Simultaneous analysis of high and low IQ groups, with fector and subtest unique variances free across both groups. Mean IQ 115, standard deviation 7.5. San^jle size of 500 in each group.

PAGE 63

58 Figure 9. Simultaneous analysis of high and low IQ groups, with factor and subtest unique variances free across both groups. Mean IQ 85, standard deviation 7.5. San^le size of 500 in each group.

PAGE 64

59 Figure 10. Simultaneous analysis of high and low IQ groups, with all parameters free across both groups. Mean IQ 1 15, standard deviation 7.5. Sample size of 500 in each group.

PAGE 65

60 Figure 11. Simultaneous analysis of high and low IQ groups with aU parameters free across both groups. Mean IQ 85, standard deviation 7 5 Sanqjle size of 500 in each group.

PAGE 66

61 The remaining analyses address the detectibility and development of cognitive diflferentiation. Again, normal distributions were formed using the procedures previously described. Each group was comprised of 250 individuals. As in the previous analyses, distributions for the highand low-IQ groups had respective means of 115 and 85. Standard deviations for each group were 7.5. The ChildHighlQ group was comprised of children between the ages of 6 and 12 years (m = 8.7; s = 1.8). The AdolHighlQ group was comprised of adolescents between the ages of 13 and 22 years (m = 17; s = 2.5). Descriptive statistics of the subtests included in the three-stratum model for the ChildHighlQ and AdolHighlQ groups are presented in Tables 6 and 7, respectively. Distributions of Broad Cognitive Ability are oiSered in Figures 12 and 13 for the respective high-IQ child and adolescent groups. As in the preceding analysis, the distributions are normal, with nearly identical standard deviations. Using the variance-covariance matrices from each distribution, simiiltaneous hierarchical confirmatory fector analysis evaluated increasingly lenient models of the three-stratum theory. Results of these analyses are summarized in Table 8. Results of the analyses for the high-IQ children and adolescents follow the pattern established in the earlier set of analyses. That is, a significant decrease in was achieved by permitting the imique and error variance to vary across highand low-IQ groups. Further significant improvements in the model

PAGE 67

62 Table 6. Descriptive Statistics for High-IQ Children (ChildHighlQ) Variable Name Mean Std. Deviation N Concept Formation 4974 204 250 Analysis Synthesis 4989 164 250 Visual Closure 4958 118 250 Picture Recognition 4983 107 250 Visual Matching 4875 240 250 Cross Out 4936 153 250 Memory for Names 5011 108 250 Visual Auditory Learning 4988 96 250 Picture Vocabulary 4986 183 250 Oral Vocabulary 4940 214 250 Inconqjlete Words 4977 88 250 Sound Blending 4986 158 250 Memory for Sentences 5020 162 250 Memory for Words 5011 189 250 CalctJation 4759 374 250 Applied Problems 4877 292 250 95.0 100.0 105.0 110.0 115.0 120.0 125.0 130.0 135.0 BCASTDAS Critefion Variable-Broad Cognitive Ability Figure 12. Histogram of ChildHighlQ Distribution

PAGE 68

63 Table 7. Descriptive Statistics for High-IQ Adolescents (AdoIHighlQ) Variable Name Mean Std. Deviation N Concept Formation 5248 137 249 Analysis Synthesis 5202 105 250 Visual Closure 5135 93 250 Picture Recognition 5122 90 250 Visual Matching 5319 138 250 Cross Out 5212 83 250 Memory for Names 5122 115 250 Visual Auditory Learning 5107 103 250 Picture Vocabulary 5333 113 250 Oral Vocabulary 5390 137 250 Incomplete Words 5086 70 250 Sound Blending 5149 116 250 Memory for Sentences 5229 125 250 Memory for Words 5190 167 250 Calculation 5482 170 250 Applied Problems 5420 183 250 std. Dev = 7.79 Mean: 11S.0 N = 250.00 95.0 100.0 105.0 110.0 115.0 120.0 125.0 130.0 BCASTDAS Criterion Variable-Broad Cognitive Ability Figure 13. Histogram of AdoIHighlQ Distribution

PAGE 69

64 Table 8. Different Hypotheses Tested in Regard to the Structure of Cognitive Abilities at Different Ages Hypothesis Tested df TLl NFl PFl Change Factor Structure Invariant (All Parameters Fixed) 594 231 .99 .99 .84 Factor Loadings Identical 473 (Error and Unique Variances Vary) 207 .99 .99 .76 121* Factor Structure Similar (All Parameters Free to Vary) 392 192 1.0 .99 .71 202* Indicates a statistically significant improvement in model fit based on decrease. were obtained by permitting the remaining parameters to vary (i.e., different factor loadings across ability groups). Results for the high-IQ children and adolescents are presented in graphical form in Figures 14 through 19. Regardless of the model stringency (i.e., constraints of parameters), there are significant between-group differences in fector loadings, with the child group having larger loadings on all firstand second-order factors. When all parameters of the three-stratum model were fi"ee to vary, the average g loading to the first-order primary abilities was .90 for the child group. In the adolescent group, this value decreased to .45, a decline of .45. The largest single decrease in factor loadings occiured in the correlation between g and gs. Values dropped fi-om .95 to .29.

PAGE 70

65 .92 .66 .71 COnfTTTMV W5 .85 .72 anttynw .49 4 .66 .47 ptCTBOM M3 .90 4 0 .88 ,49 MS .79 .62 vakngw -0 .81 .90 ptCVOCVM M5) .93 orlvocw 4 (uio) .47 .66 ..79 4 @ .83 tndbmow .59. ^ (ul2) .81 rmmsanw }• .50 4 ( .94 calcw 4 (uls) .90 4 (uie) Figure 14. Simultaneous analysis of high IQ children and adolescents, with all parameters constrained across both groups. Mean IQ 11 5, standard deviation 7.5. Sample size 250 in each group. (Child group).

PAGE 71

66 Figure 15. Sinmftaneous analysis of high IQ children and adolescents, with all parameters constrained across both groups. Mean IQ 1 15, standard deviation 7.5. San^le size 250 in each group. (Adolescent group).

PAGE 72

67 — 0 5 4 3 4 0 6 9 8 •— 6 4 (uio) i 4 0 ^ ( 7 4 (u^3^ 1 J ^— ) 2 4 ) Figure 16. Simultaneous analysis of high IQ children and adolescents with fector and subtest unique variances free across both groups. Me'an IQ 1 15, standard deviation 7.5. Sanqjle size 250 in each group. (Child group). ^ ^ ^

PAGE 73

68 4 4 4 0 4 ( 0 4 (uls) 9 4 (u14) 0 4 ( 4 Figure 17. Simultaneous analysis of high IQ children and adolescents, with fector and subtest unique variances free across both groups. Mean IQ 1 15, standard deviation 7.5. Sanple size 250 in each group. (Adolescent group).

PAGE 74

69 4 (uie) Figure 18. Simultaneous analysis of high IQ chadren and adolescents, with all parameters free across both groups. Mean IQ 1 15, standard deviation 7.5. Sample size 250 in each group. (ChUd group).

PAGE 75

70 confrmw 4 @ 4 4 (uie) Figure 19. Simultaneous analysis of high IQ children and adolescents, with all parameters free across both groups. Mean IQ 115, standard deviation 7.5. Sanqjle size 250 in each group. (Adolescent group).

PAGE 76

71 The ChildLowIQ group was comprised of children 6 through 12 years (m = 8.8; s = 1.9). The AdoILowIQ group was comprised of adolescents 13 through 22 years (m = 17; s = 2.5). Descriptive statistics of the subtests for the ChildLowIQ and AdoILowIQ groups are presented in Tables 9 and 10, respectively. Distributions of Broad Cognitive Ability are offered in Figiu-es 20 and 21 As in the preceding analysis, the distributions are normal, with nearly identical standard deviations. Table 9. Descriptive Statistics for Low-IQ Children (ChildLowIQ) Variable Name Mean Std. Deviation N Concept Formation 5248 137 249 Analysis Synthesis 5202 105 250 Visual Closure 5135 93 250 Picture Recognition 5122 90 250 Visual Matching 5319 138 250 Cross Out 5212 83 250 Memory for Names 5122 115 250 Visual Auditory Learning 5107 103 250 Picture Vocabulary 5333 113 250 Oral Vocabulary 5390 137 250 Inconqjlete Words 5086 70 250 Sound Blending 5149 116 250 Memory for Sentences 5229 125 250 Memory for Words 5190 167 250 Calculation 5482 170 250 Applied Problems 5420 183 250

PAGE 77

72 SW. Dev = 7.61 Mean = 85^ N = 250.x 67.5 T2.5 77.5 82.5 87.5 92.5 97.5 102.5 70.0 75.0 aO.O 85.0 90.0 95.0 100.0 BCASTDAS Ctlterlan Vartable-Broad Cogntlve Ability Figure 20. Histogram of Low-IQ Children Distribution Table 10. Descriptive Statistics for Low-IQ Adolescents (AdolLowIQ) Variable Name Mean Std. Deviation N Concept Formation 5003 162 250 Analysis Synthesis 5008 118 250 Visual Cbsure 5037 95 250 Picture Recognition 5026 93 250 Visual Matching 5161 133 250 Cross Out 5102 87 250 Memory for Names 4980 87 250 Visual Auditory Learning 4968 90 250 Picture Vocabulary 5088 115 250 Oral Vocabulary 5072 130 250 Incomplete Words 4994 88 250 Sound Blending 4980 136 249 Memory for Sentences 4970 135 250 Memory for Words 4991 175 250 Calculation 5226 154 250 Applied Problems 5086 142 249

PAGE 78

73 Std. Dev = 7.71 Mean • 85.0 N = 250.00 65.0 70.0 75.0 80.0 B5.0 90.0 95.0 100.0 105.0 BCASTDAS Cmertan Variable-Broad CognKtve Ability Figure 21. Histogram of Low-IQ Adolescents Distrilnition Results of the confirmatory analyses for the low-IQ children and adolescents are summarized in Table 1 1 Table 11. Dififerent Hypotheses Tested in Regard to the Structure of Cognitive Abilities at Different Ages Hypothesis Tested df TLl NFl PFl Change Factor Structure Invariant 546 231 .99 .99 .84 (All Parameters Fixed) Factor Loadings Identical 463 207 .99 .99 .76 83* (Error and Unique Variances Vary) Factor Structure Similar 417 192 1.0 .99 .70 129* (All Parameters Free to Vary) ^Indicates a statistically significant improvonoit in model fit based cm decease. Confirmatory analyses of the data fi-om the low-IQ children and adolescents showed a significant decrease in 2d was achieved by permitting the imique and error variance to vary across highand low-IQ groups.

PAGE 79

74 Additional significant improvements in the model were obtained by permitting the remaining parameters to vary (i.e., different factor loadings across ability groups). All indices of fit suggest that the data fit the model exceptionally well. The results also are presented in graphical form in Figures 20 through 25. As observed in the high-IQ children and adolescents, factor loadings decrease with age. This finding is true for g, as well as the primary abilities. Again, all loadings differ significantly, in the direction supportive of differentiation of cognitive abilities with age. When all parameters of the threestratiun model were fi-ee to vary, the average g loading for the first-order primary abilities was .86 for the child group. In the adolescent group, this value decreased to .48, a decline of .38. The largest single decrease in factor loadings occurred in the correlation between g and gsm. Values dropped fi"om .67 to .17, a decline of .50. For clarity's sake, Table 12 svmimarizes the results of the analyses for the age-abUity groups when all parameters are fi-ee to vary. In brief^ g loadings are significantly higher in the low-ability groups, regardless of age.

PAGE 80

75 Figure 22. Simukaneous analysis of low-IQ children and adolescents, with all paranwters constrained across groups. Mean IQ 85, standard deviation 7.5. Sanqjle size of 250 in each group. (Child group).

PAGE 81

76 Figure 23. Simultaneous analysis of low-IQ children and adolescents, with all parameters constrained across groups. Mean IQ 85, standard deviation 7.5. Sanple size of 250 in each group. (Adolescent group).

PAGE 82

77 Figure 24. Simultaneous analysis of low-IQ children and adolescents, with fector and unique subtest variances free across groups. Mean IQ 85, standard deviation 7.5. Sanqjle size of 250 in each group. (Child group).

PAGE 83

78 .32 54/ ^61/ .28^ .46 .49 .27 .29/ -56 COnfTTTl' j4 / .46^ .38 / \74 .21 r .71 "^^.96 nitynw 43 .22 picrBcwra .56 .54 .28 .87 PICVQOM orlvocw .24. .50 .55 .07j Own RlimMIW Gq .83 .671 w .16 5 4 0 4 8 17 MS) 0 — II 4 (uio) 5 4 @ 0 4 7 4 ) 17 # ( 9 0 5 4 .50 .25 .30 .57 .45 Figure 25. Simultaneous analysis of low-IQ children and adolescents, with factor and unique subtest variances free across groups. Mean IQ 85, standard deviation 7.5. Sanqjle size of 250 in each group. (Adolescent group).

PAGE 84

79 Figiire 26. Simultaneous analysis of low-IQ children and adolescents, with all parametCTS free across groups. Mean IQ 85, standard deviation 7.5. Sarqjle size of 250 in each group. (CMd group).

PAGE 85

80 Figure 27. Simultaneous analysis of low-IQ children and adolescents, with all parameters free across groups. Mean IQ 85, standard deviation 7.5. San^le size of 250 in each group. (Adolescent group).

PAGE 86

81 Table 12. g Loadings of Highand Low-IQ Children and Adolescent Groups Primary Ability g Loading ChildLowIO/AdolLowIO ChildHighlO/AdolHighIO Gf .91 .76 .93 .72 Gv .92 .44 .94 .40 Gs .90 .42 .95 .29 Glr .71 .53 .85 .20 Gc .94 .49 .93 .70 Ga .82 .25 .86 .44 Gsm .67 .17 .76 .37 Gq .99 .78 .99 .86

PAGE 87

CHAPTERS DISCUSSION Most studies investigating the structure of mental abilities confirm that a substantial amount of the variance observed in cognitive performance can be attributed to a general factor, often referred to as Spearman's g. For this reason. Spearman's g has been termed the sin qua non of intelligence (Humphreys, 1992). However, some studies have suggested that the percentage of variance in human abilities explained by g may vary across different age and ability levels. Although this observation was made nearly a century ago, only recently have empirical studies of good quality addressed this important issue (Detterman & Daniel, 1989). The present study is one of the few to apply confirmatory fector analysis to this phenomenon and perhaps the first to examine the structure of cognitive abilities, as represented by a threestratum theory of intelligence, across different IQ levels. Differentiation of Cognitive Abilities Across Groups of Different Ability Results of the present study indicate that the proposed three-stratum model of cognitive abilities is structurally identical across highand low-ability groups. All reported indices of fit confirm that Carroll's three-stratiun theory provides an excellent representation of cognitive abilities for both highand 82

PAGE 88

83 same constructs for different ability groups, significant differences exist in its fectorial parameters. Ability' groups differed significantly with respect to all fector loadings, error, and unique variances. This study also offers strong support for the belief that abilities differentiate as IQ increases, in that g accounted for less variability in scores among high-ability individuals than among low-ability individuals. In the lowand high-IQ groups, when all parameters were fi-ee to vary, g accounted for 52% and 29% of the respective variance in cognitive performance. Stated differently, g explained nearly twice the amount of variance in the low-ability group as compared to the high-ability group. This pattern of loadings is consistent with observations made by Spearman (1927), Burt (1944), and Detterman and Daniel (1989) and advances empirical evidence in favor of Spearman's law of diminishing retiims. These findings were fiirther substantiated by the confirmatory analyses. Regardless of the restrictions placed on the proposed three-stratum model of cognitive abilities (e.g., permitting different values for the fector loadings, error, and imique variances), all g loadings were significantly lower in the highability group. The largest decline in general factor loadings occurred on measures of crystallized intelligence (gc). The loading of gc on g declined fi-om .71 for the low-IQ group to .15 for the high-IQ group. Researchers (e.g., Horn & Noll, 1997) consider gc to be indicative of an individual's store of information. Therefore, more so than their high-IQ counterparts, low-IQ individuals depend on g for the acquisition of knowledge and information. This

PAGE 89

84 finding oflFers some evidence that g plays a causal role in the formation of an individual's fiind of knowledge and information. The next largest decrease in general factor loadings occurred on measures of gsm, usually interpreted as a measure of working memory capacity. Over the past decade or so, researchers have assigned an increasingly important role to working memory as an explanative agent in vmderstanding individual differences in human cognitive performance. Kyllonen and Christal (1990) have gone so far as to equate working memory capacity with Spearman's g, citing a simple correlation between them of .91 Most new and revised intelligence tests, such as the WAIS-in (1997) also incorporate a working memory component into a model of cognitive abilities. This study's findings support the idea that working memory capacity is a salient feature distinguishing highand low-ability groups and further confirm the inportant position of working memory in accounting for cognitive outcomes. Surprisingly, loadings fi-om the second-order primary abilities also were significantly lower in the high-IQ group than in the low-IQ group. Permitting the model parameters to have different loadings across groups indicated that an increasing amount of the variability in scores could be accounted for by the unique and error variances of these second-order gc-gf abilities. These findings pose the possibility that, more so among high-IQ individuals than low-IQ individuals, additional noncognitive constructs may exist that, while excluded fi-om the three-stratum model, contribute importantly to successful cognitive performance. This idea is not new. A number of noted scholars (e.g..

PAGE 90

8S Sternberg, 1985; Gardner, 1983; & Brand, 1995) have suggested that noncognitive attributes should be held in as equal esteem as abilities traditionally considered purely cognitive in nature. In particular reference to the constructs measured by the WJ-R, Woodcock (1993) has incorporated noncognitive factors into a Cognitive Performance Model (CPM). The CPM in^lies that the various gf-gc abilities are not autonomous, but fall into distinct functional categories. Further, an individual's cognitive performance is enhanced or modified by facUitatorsinhibitors, such as health, emotional state, and motivatioa Woodcock perceives the source of fecilitators-inhibitors as being situational or environmental (e.g., teaching method, environmental distractions, and the specific tests used in assessment). Woodcock (1993) and Keith (1997) have offered confirmatory support for the organization of the cognitive abilities and fecilitators-inhibitors in the CPM. The present study extends these previous findings and advances that high-IQ individuals may utilize these situational variables to a greater extent than low-IQ individuals. Differentiation of Cognitive Abilities Across Ability Groups of Different Age In addition, this study provides some evidence that the differentiation of abilities may be attributable to developmental influences. Groups were matched on ability and compared across age (i.e., ChildHighlQ AdolHighlQ / ChildLowIQ AdolLowIQ). In each case of the confirmatory analyses, Carroll's three-stratum model of cognitive abilities was found to be structurally invariant. That is, for groups of similar overall ability, the constructs measured

PAGE 91

86 by the WJ-R are adequately represented by the proposed model, regardless of age level. However, values of all fectorial parameters differed significantly with respect to age. In brief^ while the structure is identical for children and adolescents, different values are foimd in factor loadings, unique variances, and error variances. When parameters were fi^eed to vary for high-ability children and adolescents, g accomted for 62% and 26% of the variance respectively. The largest single decline in general factor loadings occurred on gs, or processing speed. The loadings for the children and adolescent groups were .95 and .29, respectively. This dramatic decline indicates that, among highability children, g and processing speed are strongly related. Conversely, in high-ability adolescents, g accounts for relatively little of the variability in processing speed. Most likely, these findings reflect the complimentary roles of controlled and automatized processing in cognitive performance. Controlled processes are reqiiired when the demands of a task are novel or inconsistent. Such processes are usually slow, effortful, and dependent upon the use of limited cognitive resources (Jensen, 1998). In contrast, automatized processes occur under repeated and consistent conditions, and accrue a fest and effortless quality. Basically, controlled processes are required for the initial learning of a task and are gradually supplanted by automatized processes when the task is learned to a level of fluency. Quickly transitioning fi'om reliance on controlled processes to automatized processes fi-ees cognitive resources in working memory which can be applied to other tasks. Because controlled processes

PAGE 92

87 extol a greater cost on cognitive resources, they naturally draw upon the general factor to a greater extent than automatized processes. Among children, much of their time spent in the early years of schooling requires controlled processing. Common exartples of academic tasks requiring controlled processing include acquiring simple math fects, writing cursive, and decoding. Everyone can remember the first strained efforts to write his/her name or counting vAth fingers. By adolescence, these basic tasks are over-learned, and hence draw almost exclusively on automatized processes. Although processing speed per se remains an important source of individual differences throughout the lifespan, by adolescence, high-ability individuals have acquired an extensive repertoire of automatized processes, which places a lesser demand on g. Confirmatory analyses yielded the same pattern in lowand high-ability groups. That is, while the three-stratum model of cognitive abilities is structurally invariant across age levels, there are significant differences in all factorial parameters. Significant improvements in model fit were obtained when fector loadings, tmique variances, and error variances were permitted to have different values for children and adolescents. For low-ability children and adolescents, g was associated with 53% and 21% of the variability in performance, respectively. The largest single decline occurred with gv, interpreted as visual processing. A substantial decline was also observed on measures of long-term memory retrieval (glm). Therefore, as children move

PAGE 93

88 into adolescence, these simple processes become increasingly automatized, more distinct, and less reliant on g. In summary, this study suggests that, for both highand low-ability groups, cognitive abilities differentiate as individuals develop from childhood to adolescence. Possible Mechanisms of Cognitive Differentiation Different scholars have offered different metaphorical theories to explain cognitive differentiation. Spearman (1927), who &st noted this unusual phenomenon, equated g to mental energy. Primary abilities were represented as specific engines. Positive manifold arose because some energy (i.e., g) is needed to run all engines (i.e., primary abilities or group &ctors). Thus, differentiation at higher ability levels occurs because doubling the energy to an engine does not achieve a doubling of speed. A contemporary view which is surprisingly similar to Spearman's portrait of cognitive differentiation comes from Anderson (1992). Instead of an engine, Anderson describes cognitive differentiation in terms of a computer metaphor. Anderson's Basic Processing Mechanism bears a strong resemblance to Spearman's g, and his Specific Processors are indistinguishable from primary abilities. Anderson ejqjlained positive manifold in terms of the processing speed needed to complete all cognitive tasks. Differentiation occurs at higher levels of intelligence because greater processing speed increases the output of the various Specific Processors and allows for differentiation. Conversely, at lower levels of

PAGE 94

89 intelligence, the slower speed of the Basic Processing Mechanism serves to restrict the output of the Specific Processors. Detterman's (1993) account of cognitive diflFerentiation assumes a systems approach and incorporates aspects of both Spearman's and Anderson's theories: The differences in correlation across IQ level are consistent with the systems theory of intelligence. In this theory, IQs result fi-om deficits in inqjortant cognitive processes. Because these processes are part of a system, they affect the fimctioning of other parts of the system. If these important processes are deficient, parts dependent upon them will also be impaired. Essentially, a deficit in an important process will put an upper ceiling or limit on the efiBciency of the operation of other parts of the systenx That means that all parts of the system will be more similar if there is a deficiency in an important process. This forced similarity in ability is what causes a higher correlation among IQ subtests for low IQ subjects, (pp. 27-28) Regardless of the particular theory, the pattern of correlations indicating cognitive difierentiation is due to processing efl&ciency. Low-ability individuals process information inefiBciently. The result is a forced similarity among specific processes, which makes for larger subtest intercorrelations. High-ability individuals process information more efficiently. The result is that specific processes and abilities are more distinguishable, providing lower subtest intercorrelations. Certainly, age and development appear to increase the efficiency of processing, regardless of overall general ability. Deary and Paglieri (1991) and Burt (1954) posed the possibility that the pattern of correlations suggesting cognitive differentiation may be due to lower reliabilities for highthan for low-ability subjects. Lower reliabilities would natiirally yield lower subtest intercorrelations. Unfortunately, item-level

PAGE 95

90 data were not available for this study, so reliabilities for the separate groups coiild not be calculated. However, previous studies investigating dififerential reliabilities have found that scores tend to be more stable and reliable among high-IQ testees (Deary et al., 1996). If reliability estimates actually are higher for high-IQ groups, then, if anything, the results of this study underestimate the true degree of cognitive differentiation. Implications For Cognitive Assessment The structure of cognitive abilities is invariant for highand low-ability individuals, regardless of the age of the testee. However, there are significant differences in the degree to which cognitive abilities are represented for groups of varying intelligence and development. Cognitive abilities differentiate with ability and age. However, because the structure of abilities is identical, this differentiation is not large enough to warrant different tests for groups of different age and ability. Rather, the primary recommendation for assessment which can be gleaned from the present study is that additional, not different, tests should be used if the intent of the assessment is to obtain an informed portrait of overall cognitive performance. Following the example provided by Woodcock's Cognitive Processing Model, these additional instruments would be selected with the purpose of measuring aspects of the fecilitator-inhibitors contributing to overall performance. Of course, the counterpoise is that any information gleaned from additional instruments may appear trivial relative to the substantial information already provided by g.

PAGE 96

91 Recommendations For Future Study Contrary to recent investigations regarding differentiation (e.g., Deary et al., 1996), the present study found that cognitive differentiation occurs not only according to IQ, but to age as well. Certainly, replication is in order, with different batteries of tests. In addition, other studies investigating intelligence may need to incorporate cognitive differentiation into their framework. The KABC and the CAS are excellent candidates for these ftiture studies, since they offer several subtests that are qualitatively different from those included in this study and are based on substantially different theories of intelligence. A goal of future studies should be to understand why certain primary abilities seem to differentiate more than others. For example, in the present study, there were no identifiable patterns that would suggest that crystallized abilities differentiate more than fluid abilities, or visa versa. Insofar as differentiation has been shown to occur v^ith development, the incorporation of various sociometric variables into subgroup selection seems warranted, in order to characterize certain qualities that may influence intellectual development. For example, does cognitive differentiation occur at the same rate among individuals who difier in socioeconomic status? Future studies should strive to test specific hypotheses about the patterns of differentiation. Such studies may provide the needed insight into the underlying causes of differentiation. Another area tangentially related to cognitive differentiation is the Flynn Effect (Flynn, 1987). The Flynn Effect refers to the finding that in a number of industrialized nations IQs have risen on a secular level, on the order

PAGE 97

92 of 3 to 5 IQ points per decade. It would be informative to see if cognitive differentiation, as it has been observed in highand low-ability individuals at one particular point in time, also has occurred on a secular level with the passage of time. This study could easily be done using the standardization data from an original test (e.g., WAIS) and its most recent revision (e.g., WAISni). Confirmatory analysis could yield some enlightening information regarding the nature and extent of the Flynn EflFect. Another hypothesis that will certainly require future research is the genetic contribution to intelligence at higher and lower levels. Studies in this area are few and equivocal, at best. Some scholars (Detterman, Thompson, and Plomin, 1990) posit that Spearman's law of diminishing returns applies to genetic variance as well as g, citing larger estimates of heritability (h^) in the lower spectrum of IQ. Other well-designed studies (Bailey & Revelle, 1991) fotmd completely opposite results, with higher estimates of heritability for high ability groups. Therefore, the issue of heritability and its relationship to cognitive differentiation remains open to debate. Summary In conclusion, the present study confirms the diflferentiation hypothesis regarding human intelligence and supports the belief that the structure of cognitive abilities is the same for both lowand high-ability individuals. The differentiation of cognitive abilities, as evidenced by the amount of variance accounted for by g, is greater among individuals of higher ability than lower ability. While the diflferentiation observed in higher ability individuals may be

PAGE 98

93 due to more efficient information processing, this study finds that differentiation also has a strong developmental component, inasmuch that abilities were more differentiated in adolescents than in children. This finding lends substantial support to an "economic investment" metaphor regarding human abilities. From this perspective, intelligence is equated with money. At lower levels of income, money is spent on the common necessities, such as housing, clothing, and food. At higher levels of income, a proportion of money becomes disposable, and is spent on activities and items reflecting personal interests, such as vacations, sports, and entertainment. At lower levels of intelligence, a larger proportion of general and group factors are "spent" on completion of the immediate cognitive tasks. Conversely, at higher levels of intelligence, a greater proportion of cognitive resources are available to reflect personal interests and motivation. Also, like money, returns on investment accrue over time, regardless of the initial amount invested. Irrespective of ability level, individuals benefit fi-om experience in that primary cognitive abilities become more efficient and specialized.

PAGE 99

LIST OF REFERENCES Anastasi, A. (1932). Further studies on the memory fector. Archives of Psychology. 142 60. Anastasi, A. (1970). On the formation of psychological traits. American Psychologist. 25. 899-910. Anderson, M. (1992). Intelligence and development : a cognitive theory. New York, NY: Blackwell Publishers. Andrich, D. (1988). Rasch models for measurement. Newbury Park, NJ: Sage Publications. Arbuckle, J. (1996). AMOS manual Chicago, IL: SmaUWater. Asch, S. E. (1936). A study of change in mental organization. Archives of Psychology. 195 30. Atkin, L., Bray, J., Davison, A., Herzberger, G, Humphreys, L., & Seizer, D. (1977). Factors emergent with age and mental ability. Adolescent Psychology. 11 65-84. Bailey, M.J., Revelle, W. (1991). Increased heritability for lower IQ levels? Behavior Genetics. 21. 397-404. Balinsky, R. (1941). An analysis of the mental factors of various age groups from nine to sixty. Genetic Psychology Monographs. 23. 191-234. Bickley, P.G., Keith, T.Z., & Wolfe, L. (1995). The three-stratum theory of intelligence: Test of the structure of intelligence across the life spaa Intelligence. 20. 309-328. Binet, A., & Simon, T. (1905). Methodes nouvelles pour le diagnotic du niveau intellectuel des anoromauz. L'annee Psycho Igique. 11. 191-244. Brand, C. (1996). The g factor: General intelligence and its implications New York: John Wiley & Sons. 94

PAGE 100

95 Bray, R., Kerr, N.L., Atkin, R.S. (1978). Effects of group size, problem difSculty, and sex on group performance and member reactions. Journal of Personalit>' & Social Psychology. 36 1224-1240. Brody, N. (1992). Intelligence New York, NY: John Wiley & Sons. Biirt, C. (1919). Mental abilities in children and youth. British Journal of Psychology. 5 77-89. Burt, C. (1944). Mental abilities and mental factors. British Journal of Educational Psychology. 14 85-94. Burt, C. (1954). The differentiation of intellecttial ability. British Journal of Educational Psychology. 24 76-90. Carroll, J.B. (1993). Human cognitive abilities: A survey of factor analytic studies. New York: Cambridge University Press. CattelL, R.B. (1941). Some theoretical issues in adult intelligence testing. Psychological Bulletin. 38. 592. Cattell, R.B. (1963). Theory of fluid and crystallized intelligence: A critical experiment. Journal of Educational Psychology. 54 1-22. Catell, R.B. (1987). Intelligence : its structure, growth, and action Amsterdam: Belevier Science Pub. Co., 1987. Clark, M. P. (1944). Changes in primary mental abilities with age. Archives of Psychology. 291 30. Cronbach, L., & Snow, R.E. (1977). Aptitudes and instructional methods: A handbook for research on interactions. New York: Irvington. Cunningham, W.R. (1980). Age comparative factor analysis of ability variables in adulthood and old age. Intelligence. 4. 133-149. Cunningham, W.R. (1981). Age changes in the factor structure of intellectual abilities in adulthood and old age Educational & Psychological Measurement. 40 3-24. Deary, I. J., & Pagliari, C. (1991). The strength of g at different levels of ability: Have Detterman and Daniel rediscovered Spearman's "law of diminishing returns"? Intelligence. 15. 256-260.

PAGE 101

96 Deary, IJ., Egan, V., Gibson, G., Brand, C.R., Kellaghaa T.S. (1996). Intelligence and the differentiation hypothesis. Intelligence. 23 105-132. Detterman, D.K. (1987). Theoretical notions of intelligence and mental retardation. American Journal of Mental DeficieiKv. 92 2-11. Detterman, D.K. (1991). Rq>ly to Deary and Pagliari: Is g intelligence or stupidity? Intelligence. 15 251-255. Detterman, D.K(1994). Toward an intelligent view of intelligence. Psychological Inquiry. 5 201-203. Detterman, D. & Daniel, M.H. (1989). Correlations of mental tests with each other with cognitive variables are highest for low IQ groups. Intelligence. 13 349-359. Detterman, D., Thompson, L., & Plomin, R. (1990). Differences in heritability across groups differing in ability. Behavior Genetics. 20 369-384. Dye, N.W. & Very. P. (1968). Growth changes in factorial structure by age and sex. Genetic Psychology Monographs. 78 55-58. Eckstrom, R.B. (1979). Review of cognitive factors. Multivariate Behavioral Research. 79. 7-56. Eysenck, H.J., & Kamin, L. (1981). The intelligence controversy. New York: Wiley & Sons. Farber, L. (1986). DrEferential aptitude test Chicago: Riverside Publishing. Flynn, J.R. (1987). Massive IQ gains in 14 nations: What IQ tests really measure. Psychological Bulletin. 101 171-191. Fogerty, G.J., & Stankov, L. (1995). ChaUenging the law of diminishing returns. Intelligence. 21. 157-174. Galton, F. (1892). Hereditary genixis: An inquiry into its laws and consequences. London: MacMillan. Gardner, H. (1983). Frames of mind: The theory of multiple intelligences. New York: Basic Books. Garrett, H.E. (1938). Differentiable mental traits. Psychological Record. 2. 259-298.

PAGE 102

97 Garrett, H.E. (1946). A developmental theory of intelligence. American Psychologist. 1 372-377. Garret, H.E., Bryan, L., & Perl, N.S. (1935). Factor structure of mental abilities. Developmental Psychology. 45 1 12-123. Gorsuch, R.L. (1983). Factor analysis Hillsdale, N.J: L. Erlbaum Associates. Gould, S.J. (1981). The mismeasure of man. New York: Norton. Guilford, J.P. (1967). The nature of human intelligence New York: McGraw-Hill. Guilford, J. P. (1968). Intelligence, creativity, and their educational implications San Diego, CA: Knapp. Guilford, J.P. (1981). The structure of intellect model. In B.B. Woman (Eds ). Handbook of intelligence: Theories, measurements, and applications ( pp. 225-2661 New York: Wiley & Sons. Hemnstein, R,J., & Murray, C. (1994). The bell curve : intelligence and class structure in American life New York, NY: Free Press. Horn, J.L., & Cattell R.B. (1966). Refinement and test of the theory of fluid and crystallized ability intelligence. Journal of Education Psychology. 5L 253-270. Horn, J.L,, & Noll, J. (1997). Human cognitive capabilities: gf-gc theory. Found in D.P. Flanagan, J.L. Genshaft, & P.L. Harrison (Eds^ Contemporary intellectual assessment: Theories, tests, and issues (pp. 32-49). New York, NY: The Guilford Press. Humphreys, L.G. (1992). Commentary: What both critics and users of ability tests need to know. Psychological Science. 3. 271-274. Jensen, A.R. (1994). Understanding g in terms of information processing. Educational Psychology Review. 4. 271-308. Jensen, A.R. (1998). The e factor. Westport, CT: Praeger. Jensen, A.R., & Weng, L. (1993). What is a good g ? InteUieence. 18. 231-258.

PAGE 103

98 Jones, T. (1949). Factor structure of the Stanford Binet. Psvchometrics. 12 74-89. Joreskog, K.G., & Sorbom, D. (1989). LISREL7: A guide to the program and applications. Chicago: SPSS. Kaufinan, A. (1994). Intelligent testing with the WISC-III. New York: WUey. Kaufinan, A., Kaufinan, N. (1983). Kaufinan Assessment Battery^ for Children Circle Pines, MN: AGS. Keith, T.Z. (1997). Using confirmatory fector analysis to aid in understanding the constructs measured by intelligence tests. Foimd in D.P. Flanagan, J.L. Genshaft, & P.L. Harrison (Eds .). Contemporary intellectual assessment: Theories, tests, and issues (pp. 373-402). New York, NY: The Guilford Press. Keith, T.Z., & Witta, E.L. (1997). Hierarchical and cross-age confirmatory factor analysis of the WISC-III: What does it measure ? School Psychology Quarterly. 12 89-107. Kranzler, J.H. (1994). Application of the techniques of mental chronometry to the study of learning disabilities. Personality and Individual Differences. 16. 853-859. Kranzler, J.H., & Jensen, A.R. (1991). The nature of psychometric g: Unitary process or a number of independent processes? Intelligence. 15. 397422. Kranzler, J. H., & Weng, L. (1995). Factor structure of the PASS cognitive tasks: A reexamination of Naglieri et al. Journal of School Psychology. 33 143-157. Kyllonen, P.C. & Christal, R.E. (1990). Reasoning ability is little more than working memory capacity?! Intelligence. 14. 389-433. Legree, P.J., Pifer, M.E., & Grafton, F.C. (1996). Correlations among cognitive abilities are lower for high ability groups. Intelligence. 23 45-57. Lienert, G.A. & Faber, L. (1963). Eine varianzanalytische methode zum Nachweis der Gruppenspezifitaet von Testprofilen. Zeitschrift fiier Experimentelle und Angewandte Psychologic. 10. 333-345.

PAGE 104

99 Lienert, G.A. & Crott, H.W. (1964). Studies on the factor structure of intelligence in children, adolescents, and adults. Vita Humana. 7 147-163. Lynn, R. (1990). DiflFerential rates of secular increase of five major primary abilities. Social Biology. 37 137-141. Lynn, R., & Cooper, C. (1994). A secular decline in the strength of Spearman's g in Japan. Current Psychology. 13. 3-9. Luria,A.R. (1973). The working brain: An introduction to neuropsychology. New York: Basic Books. Mather, N. (1991). An instructional guide to the WoodcockJohnson Psycho-Educational Battery. Revised Brandon, VT: CPPC. Mather, N. (1992). WoodcockJohnson psycho-educational batteryrevised: Recommendations and reports. Brandon, Vt. : Clinical Psychology Publishing Co. McGrew, K.S. (1997). Analysis of the major intelligence batteries according to a proposed comprehensive gf-gc fi^amework. Found in D.P. Flanagan, J.L. Genshaft, & P.L. Harrison (Eds.), Contemporary intellectual assessment: Theories, tests, and issues Tpp. 151-174). New York, NY: The Guilford Press. Naglieri, J. A. (1989). A cognitive processing theory for the measurement of intelligence. Educational Psychologist. 24. 185-206. Naglieri, J. A. (1997). Planning, attention, simultaneous, and successive theory and the Cognitive Assessment System: A new theory-based measure of intelligence. Found in D.P. Flanagan, J.L. Genshaft, & P.L. Harrison (Eds.), Contemporary intellectual assessment: Theories, tests, and issues (pp. 247267). New York, NY: The Guilford Press. Owens, W. A., & Thompson, D.E. (1954). DiflFerential effects of age upon intellectual fimctions diflfering in degree of genetic conditionin g. Journal of Gerontology. 34 303-305. Peel, E. A., & Graham, D. (1952). Diflferentiation of ability in primary school children. Research Review. 3. 3 1-34. Raven, J.C. (1956). Guide to using progressive matrices. London: H.K. Lewis.

PAGE 105

100 Richards, T. W. (1941). A curve for mental growth based on overlapping between age levels. Growth, 13 141-147. Schiller, P. (1934). Structure of mental ability in adults. Archives of Psychology. 288 37-45, 217-224. Schhmid, J., Leiman, J.M. (1957). The development of hierarchical fector solutions. Psychometrika. 22. 53-61. Schneck, L. (1929). The nature of intelligence defined in a population of youth. American Journal of Psychology. 32. 147-169. Spearman, C. (1904). General intelligence, objectively determined and measured. American Journal of Psychology. 15. 201-293. Spearman, C. (1927). The abilities of man London: Macmillan. Sternberg (1985). Beyond IQ: A triarchic theory of intelligence. London: Cambridge University Press. Thomdike, R-L. (1987). Stability of factor loadings Personality & Individual Differences. 8 585-586. Thomdike, R. (1997). The early history of intelligence testing. Found in D.P. Flanagan, J.L. Genshaft, & P.L. Harrison (Eds.), Contemporary intellectual assessment: Theories, tests, and issues (pp. 3-17). New York, NY: The Guilford Press. Thomdike, R., Hagen, E., & Sattler, J. (1986). Stanford Binet Intelligence Scale. Fourth Edition Chicago: Riverside Publishing. Thurstone, L.L. (1938). Primary mental abilities. Psychometric Monographs (no. 1). Thurstone, L, L. (1940). Current issues in factor analysis. Psychological Bulletin. 37. 189-236. Thurstone, L. L. (1973). The nature of intelligence Westport, CN: Greenwood Press. Thurstone, L. L. & Thurstone, T. G. (1941). Factorial studies of intelligence. Psychometric Monographs. 2. 94. Vemon, P.E. (1950). The stmcture of human abilities. New York: WUey.

PAGE 106

101 Vernon, P.E. (1960). Intelligence and attainment tests London, University of London Press. Vernon, P.E., & Parry, J. (1949). Personnel selection in the British forces. London: Praegar. Wechsler, D. (1974). Wechsler Intelligence Scale for Children. Revised. San Antonio: Psychological Corporation Wechsler, D. (1981). Wechsler Adult Intelligence Scale. Revised San Antonio: Psychological Corporation Wechsler, D. (1991). Wechsler Intelligence Scale for Children. Third Edition. San Antonio: Psychological Corporation. Wechsler, D. (1997). Wechsler Adult Intelligence Scale. Third Edition. San Antonio: Psychological Corporation. Williams, M., Hunt, W., French, E. (1948). A further standardization and validation of the CVS Abbreviated Individual Intelligence Scale. American Psychologist. 3 365. Woodcock, R.W. (1990). Theoretical foundations of the WJ-R measures of cognitive ability. Journal of Pvschoeducational Assessment. 8 231-258. Woodcock, R.W. (1993). An information processing view of Gf-Gc theory. Found in Bruce Bracken (Ed.) Advances in psychoeducational assessment (pp. 80-102^ Brandon, VT: Clinical Psychology Publishing Co. Woodcock, R.W., & Johnson, M.B. (1989). Woodcock-Johnson Psycho-Educational Battery-Revised Chicago: Riverside.

PAGE 107

BIOHAPICAL SKETCH I was bom in Indiana to Charles and Margaret. After graduation from high school, I worked as a janitor, pizza delivery man, the Easter bunny at a fair, a paratrooper, a short-order cook, a truck driver, an army officer, an elementary school teacher, a college instructor, a landscaper, and a research assistant. Now I live in Florida and work as a psychologist. 102

PAGE 108

I certify that I have read this study and that in ray 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. John ^ H Kranzler', Chair Associate Professor of Foundations of Education 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. Thomas D. Oakland Professor of Foundations of Education 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. M. David Miller Professor of Foundations of Education 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. Walter Cunnmghai 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 qiiaJLity as dissertation for the degree of Doc'^r of, Philosop)' Stephlen W. Smith Associate Professor of Special Education

PAGE 109

This dissertation was submitted to the Graduate Facuhy of the College of Education and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. May 1999 Chairman, Foundations of Education Dean, Collea^ of Education Dean, Graduate School