Title: Personality types and preferred methods of analyzing categorical syllogisms
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Copyright Date: 1984
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PERSONALITY TYPES AND PREFERRED METHODS OF
ANALYZING CATEGORICAL SYLLOGISMS











BY

CHERRY FORD MAY


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


1984


































Copyright 1984

by

Cherry Ford May


































To my husband, Frank, for his love,

encouragement, help, and understanding.
















ACKNOWLEDGMENTS

Many people have been instrumental in assisting the

writer to complete this work. To Dr. Elroy J. Bolduc, Jr.,

chairman of the doctoral committee, I wish to express my

deep gratitude for the invaluable contribution of expert

and perceptive guidance through every phase of this project.

His expertise in the subject area, his ability to speak with

consideration and candor, and his unfailing good humor were

a source of much needed encouragement to a natural "worrier,"

and were very greatly appreciated.

I wish, also, to thank individually the other members of

the doctoral committee:

Dr. Charles W. Nelson, for his careful review of the

manuscript, and for his generous and expert help as a

committee member;

Dr. Arthur J. Lewis, for his perceptive questions and

suggestions especially during the initial and final stages

of this project; and

Dr. Ronald G. Marks, for his expert and patient guidance

through the statistical analysis portion of this study, for

his tolerance of my many questions, and for his continuous

interest and encouragement.

There are many others to whom I am indebted for their

assistance in this endeavor. To Dr. Mary H. McCaulley, I

would like to express my appreciation for her very valuable

iv









insights concerning the Myers-Briggs personality theory and

for her thoughtful suggestions concerning the study.

My thanks also go to Ms. Vicki Jennings of the Career

Counseling Offices at Santa Fe Community College for providing

assistance in the scoring of the Myers-Briggs Type Indicator.

A very special note of gratitude is extended to Dr. Gerald

B. Standley, author of the numerical method used in this study.

The writer's discovery of Dr. Standley's article on this

intriguing numerical technique was the catalyst for the con-

ceptualization of this project. His advice and encouragement

during the study were deeply appreciated.

I would like to thank Ms. Candy Caputo for the excellent

typing of the manuscript and for maintaining her professional

calm in the midst of my harried declarations that the dead-

line was yesterday.

I wish to acknowledge my parents, Adelaide and Bennett

Ford, for their constant love and support, and for their

ability to instill in me their own natural tendency towards

the quest for knowledge.

And, finally, to my family I wish to express my deepest

appreciation, for they contributed the most. To my children,

Frank and Alison, go very special thanks for their daily gifts

of love which served to brighten each day. To my husband,

Frank, goes a special tribute for his critical reviews of the

text, his gallant attempts at keeping some measure of sanity

in a thoroughly disrupted household, and most of all for his

constant love and encouragement which gave me the support I

needed to complete this project.

v
















TABLE OF CONTENTS


Page


ACKNOWLEDGMENTS . . . .

LIST OF TABLES . . . .

ABSTRACT . . . . . .


CHAPTER ONE


INTRODUCTION .


. . . . . . viii

. . . . . . x

. . . . . . 1


Background . . . . . .
Statement of the Problem . . .
Significance of the Study . .
Instrumentation . . . . .
Research Questions .. . . .
Outline of Procedures . . .
Definition of Terms . . . .

'ER TWO A REVIEW OF THE LITERATE

Theoretical Base . . . . .
Syllogistic Reasoning . . .
Cognitive Style and Cognitive Bias
Myers-Briggs Related Research .


CHAPTER THREE


METHODOLOGY . . . .


Population . . . . . . .
Procedures . . . . . . .
Test Instruments . . . . . .
Statistical Procedures . . . .


CHAPTER FOUR


RESULTS AND ANALYSIS OF THE DATA


Analysis of the Data . . . . . . .
Research Questions . . . . . . .


CHAPTER FIVE


SUMMARY, DISCUSSION, AND CONCLUSIONS


The Study . . . . . . . . . .
Results and Discussion . . . . . . .
Conclusions . . . .
Implications for Instruction .. . .....
Suggestions for Future Research . . . .


CHAP'


URE


. . . 42


I i i










Page
APPENDIX A CATEGORICAL SYLLOGISMS . . . .. 90

APPENDIX B METHODS OF SYLLOGISM ANALYSIS . . 93

APPENDIX C PREFERRED METHODS TEST . . . .. 98

APPENDIX D STUDENT DATA . . . . . . .. 101

REFERENCES . .. . . . ... . . . . 103

BIOGRAPHICAL SKETCH. .. . . . . .... 107


vii
















LIST OF TABLES


Table

1 Distribution of Students by Personality
Type for Group I . . . . . . .

2 Distribution of Students by Personality
Type for Group II . . . . .

3 Results of the Preferred Methods Test .

4 Mean Age of Students by Favorite Method
of Testing Syllogisms . . . . .

5 Sex by Favorite Method of Testing Syllogisms

6 Mean Preference Scores for Type Elements
by Favorite Method . . . . . .

7 Results of Duncan's Multiple Range Test
for MBTI Variable SN for Group I .. ..

8 Results of Duncan's Multiple Range Test
for MBTI Variable SN for Group II . .

9 Linear Discriminant Functions for Predicting
Method N as First, Second, or Third Choice
for Group I . . . . . .

10 Classification Summary for Predicting
Method N from Discriminant Functions
for Group I . . . . . . . .

11 Linear Discriminant Functions for Predicting
Method D as First, Second, or Third Choice
for Group I . . . . . . . .

12 Classification Summary for Predicting
Method D from Discriminant Functions
for Group I . . . . . . . .

13 Linear Discriminant Functions for Predicting
Favorite Method as Method D, N, or R
for Group I . . . . . . . .

14 Classification Summary for Predicting
Favorite Method from Discriminant
Functions for Group I . . . . .


viii


Page


. 49


* 50

S. 56


S 59

. 60


* 62


. 65


S 65



* 68



S 70



S 71



. 72



. 74



S 75









Table Page

15 Classification Summary for Predicting
Method N from Discriminant Functions
for Group II . . . . . . . .. 76

16 Linear Discriminant Functions for
Predicting Favorite Method as
Method D, N, or R for Group II . . . .. 78

17 Classification Summary for Predicting
Favorite Method from Discriminant
Functions for Group II . . . . ... 79
















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


PERSONALITY TYPES AND PREFERRED METHODS OF
ANALYZING CATEGORICAL SYLLOGISMS


By

Cherry Ford May

December, 1984

Chairman: Elroy J. Bolduc, Jr.
Major Department: Subject Specialization Teacher Education

The purpose of this study was to investigate the rela-

tionship between a community college student's personality

type and his choice of method in testing a categorical

syllogism for validity. The Myers-Briggs Type Indicator

(MBTI) was used to assess students' personality types and a

set of three categorical syllogisms was used to determine

each student's order of preference for three methods of

testing syllogisms. The methods investigated were Venn

diagrams, syllogism rules, and a relatively unknown numeri-

cal method. These methods represented three processing

modes: figural (Venn diagram), semantic (syllogism rules),

and symbolic (numerical).

Subjects participating in the study were 56 community

college students enrolled in an introductory logic course

during two consecutive terms. Following a unit on analysis

of categorical syllogisms, each student was given three









syllogisms in symbolic form and directed to test the syllo-

gisms in order according to his preference for the methods.

Independent variables investigated were sex, age, and

the MBTI score. Results showed that the MBTI score on the

Sensing-Intuitive (SN) index was a discriminating factor

in selection of syllogism analysis method. Significant

differences (p < .05) were found with respect to SN between

the means of the group who preferred the diagram method and

the group who preferred the numerical method. The variables

of sex and age were not found to be discriminating factors.

Using stepwise multiple discriminant analysis, functions

were generated which predicted (at a mean correct classifi-

cation rate of 64%) for each student whether a particular

method was his favorite, second favorite, or least favorite

choice. The expected correct rate was only 33.3%. The

variable SN was a predictor in all the functions. Each

function also contained either TF (Thinking-Feeling) or JP

(Judgment-Perception), both of which are MBTI variables.

It was concluded that there does exist a relationship

between certain MBTI type elements and preferred method of

syllogism analysis, and that the relationship can be pre-

dicted.

An unexpected result of significance to educators was

that the little-known non-traditional numerical technique

was selected as the favorite method of analyzing syllogisms.
















CHAPTER ONE
INTRODUCTION

Background

The study of logic originated formally with Aristotle

in the 4th century, B.C., and today the importance of develop-

ing logical reasoning skills is well established. Educators

recognize that, as our world becomes more complex and problems

of conservation, population control, food supply, and other

political, economic, and social problems increase, the

decisions that have to be made become more numerous and the

available options become more complex. The ability to make

good decisions involves reasoning logically.

One current indication of the importance placed by

educators on developing good reasoning skills is the inclusion

on the College Level Academic Skills Test (CLAST) of a large

number of logical ability competencies. The CLAST or "second

year exit test" was part of a series of educational reforms

approved by the Florida Legislature in 1979. The test is used

to determine which sophomores may enter the upper division of

Florida's colleges and universities. Of the approximately 57

competencies on the computations portion of the test, 10 are

of the type that would normally be found in a general or

introductory logic course. In addition, many of the other

competencies require the ability to make logical inferences.









Upper division colleges have indicated their support of

general logic courses by making credit in such courses a

requirement for admittance to the upper division programs.

Among the types or forms of logical reasoning usually found

in introductory logic courses is the categorical syllogism,

which has been analyzed by students of logic since its incep-

tion by Aristotle.

Categorical syllogisms have been used for centuries
as a standard against which human rationality could
be assessed, but they present us with a psychological
anomaly: Otherwise rational students appear to
reason irrationally on such problems. (Revlin,
Ammerman, Petersen, and Leirer, 1978, p. 613)

Although this study focuses on categorical syllogisms,

:he review of research for this investigation includes

studies on other types ol syllogisms (e.g., conditional and

disjunctive) as well as categorical. Research studies on

non-categorical syllogisms were included in the review

because of factors in the studies which were relevant to the

present investigation.

In general, research on syllogistic reasoning has centered

on the difficulty that students have in reaching conclusions

which validly follow from the given statements in the various

types of syllogisms. Several factors that may account for

students' selecting conclusions which do not logically follow

from the premises of a syllogism have been reported in the

literature. Some of the factors have been named for the part

that the extraneous or "surface" material of the argument

plays in the inference process. Such factors include the

"caution hypothesis" (e.g., Woodworth & Sells, 1935), the









"atmosphere effect" (e.g., Woodworth & Sells, 1935; Ceraso &

Provitera, 1971), the effect of personal beliefs or biases

(e.g., Kaufmann & Goldstein, 1967), and the effect of type of

narrative text (e.g., Piper, 1981). In addition, the pre-

sentational form of the task (paper-and-pencil or "application")

has also been investigated (Jansson, 1978).

But in the last fifteen or twenty years, investigation of

errors made in syllogistic reasoning has become centered on

the various meanings attributed to the syllogism statements

by the subjects. Attention has been focused, especially, on

the subjects' interpretations of the premises resulting from

the ambiguity of the word "some" (e.g., Ceraso & Provitera,

1971), of the words "either-or" (e.g., Juraschek, 1978) and

"if-then" (e.g., O'Brien, 1973; Jansson, 1978), and of the

set relations expressed by the premises (e.g., Ceraso &

Provitera, 1971). Since conclusions of syllogisms often can

be shown to follow quite rationally from the premises once the

subject's interpretation is known, these factors of misinter-

pretation of the premises have become of interest to researchers.

Another research area relating to the present study per-

tains to the effects on reasoning ability of individual per-

sonality differences in perception and problem-solving behavior.

Aspects of personality which have been researched include

individual difference variables such as field dependence/

independence and expressed preference for using either a

visual, symbolic, or verbal mode for processing informa-

tion (e.g., Lean & Clements, 1981; Khoury & Behr, 1982;

Perunko, 1982). However, there has been no research found in









the literature on the personality type of the student and its

relationship to his preferred mode of processing information

in the testing of syllogisms for validity.

The majority of the logic studies reviewed by this

researcher have involved subjects who have not experienced

a course in formal logic. Thus, such studies do not

purport to account for the inability of some logic-trained

students to respond with correct answers on tests of syllo-

gistic reasoning. For these students who have had a course

in formal reasoning, the factors which have been suggested

in the literature as responsible for seemingly invalid

reasoning in non-logic-trained students would not apply.

The source of the difficulty exhibited by logic-trained

students must be sought elsewhere.

Statement of the Problem

Investigators in the field of syllogistic reasoning

agree that errors on tests of logic are very frequent. "In

fact, for most syllogisms the modal response is incorrect"

(Erickson, 1978, p. 41). As shown in the preceding section,

many theories have been proposed as to the reasons for the

difficulties which students have in selecting correct

responses on tests of syllogistic reasoning.

The students who participated in the present study re-

ceived instruction in the concepts, definitions, and rules

of formal logic relevant to categorical syllogisms. Thus,

this study controlled for many of the factors previously

mentioned as variables affecting students' responses on tests

of syllogistic reasoning. The factors of personal bias and










belief, and also the type of narrative text, were accounted

for in this study by using abstract rather than concrete

categories in the syllogisms.

The problems of misinterpretation of set relations and

the related misinterpretation of words such as "some" were

accounted for, since the students in this study were taught

the necessary definitions for correct interpretation.

"Atmosphere" and "caution" were also accounted for, because

the students received instruction in the rules for when

negative, affirmative, universal, and particular statements

are logically warranted as conclusions in syllogisms. With

the above variables taken into account, the following ques-

tion is of interest: What other factors might be implicated

in causing difficulty on tasks involving syllogistic reasoning?

The Problem

The basic premise for this study was that there is a

relationship between certain personality traits of the

student concerning his preferred ways of perceiving informa-

tion and the student's choice of mode for processing the

content material. Factors involving a student's way of

perceiving content may determine which mode of processing

the material best promotes his understanding of the con-

cepts and, thus, account for the choice he makes.

The Purpose

The purpose of this study was to determine the relaticn-

ship between a community college student's personality type

and his choice of method in testing a categorical syllogism

for validity. Three methods of syllogism testing were










investigated in this study: the Venn diagram method (to be

referred to as Method D), a numerical method (to be referred

to as Method N), and a method using a set of rules for

categorical syllogisms (to be referred to as Method R).

Each method represents a different processing mode. For

the purposes of discussion, the modes used in this study

will be referred to, using Guilford's (1959) terms for

content classification, as figural, symbolic, and semantic.

Further discussion of Guilford's terminology is found in

Chapter Two of this dissertation.

Significance of the Study

As previously stated the purpose of this study was

to determine the relationship between a community college

student's personality type and his preferred method of

testing a categorical syllogism for validity. Since the

methods of syllogism analysis (testing) used in this

study each represent a different processing mode (figural,

symbolic, or semantic), the results of this study add to

research that has been done on personality types, cogni-

tive styles, and related cognitive biases toward content

processing modes. More generally, this research contri-

butes to the solution of the problem of adapting teaching

strategies to individual learning styles in the classroom,

and advances knowledge in the area of the developing of

logical abilities.

Additionally, this study involves research on a tech-

nique of testing categorical syllogisms for validity









(Standley, 1980) which this researcher has not found in any

standard logic textbook other than Standley's. The tech-

nique is thus virtually unknown, and as such represents a

novel method for analyzing (testing) syllogisms as compared

to the other two standard methods or techniques of syllogism

analysis used in this investigation. Thus, this study yields

data on a logical technique not found in the research litera-

ture, and perhaps will influence other researchers to study

further the area of diverse syllogism analysis techniques

and their relationship to the cognitive style aspect of

personality.

Instrumentation

Two test instruments were used. One test instrument

was written, administered, and graded by the researcher.

It is called the Preferred Methods Test (PMT) and is shown

in Appendix C. The PMT consists of three standard form

categorical syllogisms presented in symbolic form. An

example of such a syllogism is

SAR

RIT

TOS

This syllogism is interpreted to mean (see Appendix A)

All S is R.

Some R is T.

Hence, some T is not S.

The subjects were directed to test the first of the three

syllogisms by their favorite method of analyzing cate-

gorical syllogisms, to test the second syllogism by their









second favorite of the three methods, and to test the third

syllogism by their least favorite method of the three.

The second test instrument used was the Myers-Briggs

Type Indicator (MBTI), Form F (Myers, 1962), a self-

reporting questionnaire which is concerned with people's

basic preferences as to how they perceive and judge. The

MBTI is based on Carl Jung's (1923) theory in which much

apparently random variation in behavior is actually orderly

and consistent, being caused by certain basic differences in

the way people prefer to use perception and judgment (Myers,

1962). According to Myers, perception is understood to mean

the processes by which the individual becomes aware of

things or people or ideas, while judgment is understood to

mean the processes by which individuals reach conclusions

about what has been perceived. In other words, perception

determines what a person sees in his world and judgment

determines what decisions he will reach about it.

The MBTI characterizes individuals along four separate

indices or scales:

1. El (Extraversion or Introversion)

--one's basic orientation to the world. Extraverts

will think, feel, act, and actually live in a way

that is directly correlated with the objective

conditions (people and things) and their demands

(Jung, 1923). Introverts, although aware of

external conditions, choose subjective determi-

nants (concepts and ideas) as the decisive ones.









2. SN (Sensing or Intuition)

--how one receives information about (becomes aware

of) the world. Sensing individuals are realistic,

practical, and like fact and detail. Intuitives

see relationships and possibilities beyond the facts.

3. TF (Thinking or Feeling)

--how one makes decisions (or judges things).

Thinking types weigh facts impartially, objectively,

with logical analysis. Feeling types are more con-

cerned with values and standards than facts.

4. JP (Judgment or Perception)

--one's attitude toward the outer world. Judging

individuals prefer order, objectives, clear plans,

and closure. Perceptive individuals prefer a

flexible, spontaneous way of life, avoiding closure.

An individual's personality type is determined by selec-

ting one preference from each of the four dichotomous scales.

There are sixteen such 4-letter types (for example, INFP or

ENTJ). According to Myers, a person creates his "type" by

using, most often, the processes he prefers and in the area

in which he prefers to use them. The classifications are

described in positive terms by what the individual likes,

not by what he lacks. No one type is considered better than

another. Each type is valuable and in certain situations

even indispensable.

Research Questions

This study was designed to answer the following research

questions:










1. Do students differ in their choice of method for

testing syllogisms for validity?

2. Is there a difference in the ages of the students

in the three method groups (D, N, and R)?

In other words, does the mean age of the students

differ from one method group to another?

3. Do students of the same sex prefer to use the same

method for testing syllogisms for validity?

4. Does personality type (as determined by the Myers-

Briggs Type Indicator) make a difference in which

method of testing syllogisms a student will prefer?

In other words, do students of opposite MBTI type

elements (E-I, S-N, T-F, J-P) prefer different

methods?

5. Is it possible to predict on the basis of the vari-

ables of sex, age, and personality type, which method

of testing syllogisms a student will prefer to use?

Outline of Procedures

Subjects for this study were 56 students enrolled in four

sections of an introductory logic course at Santa Fe Community

College, Gainesville, Florida. This course is taken for

elective credit in humanities or mathematics. Each of the

course sections in which the subjects were enrolled was

taught by the same instructor. The students ranged in age

from 17 to 52; however, 63% of the students were less than

22 years old.

The following procedures were followed in each of the

four sections of the logic course.










1. A unit on the analysis of categorical syllogisms was

taught. Three different methods of testing syllo-

gisms for validity were presented. The methods were

(1) the Venn diagram method (Method D), (2) a

numerical method (Method N), and (3) the syllogism

rules method (Method R). The unit took approximately

five class meetings.

2. At the conclusion of the unit, the Preferred Methods

Test (PMT), consisting of three categorical syllo-

gisms, was administered. Each student was asked to

analyze the first syllogism by the method which he

most preferred, the second syllogism by his next

favorite method, and the third syllogism by his

least favorite method.

3. The Myers-Briggs Type Indicator (Form F) was admin-

istered to each student.

4. Each student was classified as to age, sex, person-

ality type (as determined by the Myers-Briggs Type

Indicator), and his order of preference for the

methods of analyzing categorical syllogisms (as

determined by the PMT).

Definition of Terms

For the purpose of this study, terms are defined as

follows:

A syllogism is a deductive argument consisting of two

premises and a conclusion.

A categorical proposition is a proposition of one of

the following four types:









1. All S is P.

2. No S is P.

3. Some S is P.

4. Some S is not P.

[S and P represent the subject and predicate terms

(classes or categories), respectively, of the propositions.]

A categorical syllogism is a syllogism which contains

only categorical propositions, has exactly three distinct

terms, with each term represented exactly twice.

Analyzing a syllogism means testing a syllogism for

validity.

The Venn diagram method (for analysis of categorical

syllogisms) is a figural method utilizing three circles

which are drawn overlapping each other, each circle repre-

senting one term of the syllogism. The premises of the

syllogism are then represented on the diagram with shaded

areas and "x" marks. If what has been entered on the dia-

gram to state the premises warrants what the conclusion

states, then the syllogism is valid; if not, it is invalid.

The syllogism rules method (for analysis of categorical

syllogisms) is a semantic method which relies on the use of

several rules. If none of the rules is broken, then the

syllogism that the rules are testing is valid. If a syllo-

gism breaks one or more rules, the syllogism is invalid.

The numerical method (for analysis of categorical

syllogisms) is a symbolic method in which the numbers 1, 2,

and 7 are assigned (in any order) to the three terms of the

syllogism. By combining the numbers according to certain






13


rules, the syllogism can be adjudged as valid or invalid.

This method was developed by G. B. Standley (1962) and

later appeared in revised form (Standley, 1980). (Refer to

Appendices A and B for a more detailed discussion of syllo-

gisms and these three methods of syllogism analysis.)

A processing mode is the medium in which information

is processed during the act of problem-solving. The pro-

cessing modes used in this study were figural (visual),

symbolic (numerical), and semantic (verbal).
















CHAPTER TWO
A REVIEW OF THE LITERATURE

This chapter has been divided into four main sections.

In the first section the two components of the theoretical

base for this study are examined. The first component

utilizes a theory of human intellect called the "structure

of intellect" (Guilford, 1959, 1967, 1979). The second com-

ponent of the theoretical base is the theory upon which the

work of Carl Jung (1923) and Isabel Briggs Myers (1962) is

based.

The second section is concerned with the area of syllo-

gistic reasoning in logic. The third section deals with the

personality concepts of cognitive bias and style. Lastly,

there is a section which pertains to the Myers-Briggs Type

Indicator. In each of the last three sections, background

information is presented, followed by a review of selected

studies which pertain to the topic of that section.

Theoretical Base

Structure-of-Intellect Theory

I would maintain that from a rigorous point of view
all human behavior, including creative thinking, is
rational or logical, and it is up to psychologists
to discover the nature of that rationality. All
natural science is founded on this proposition. As
for the intellectual aspects of behavior, I have
proposed the structure-of-intellect (SOI) model as
a logical basis. (Guilford, 1982, p. 151)

The structure-of-intellect model and the theory on

which it is based were the result of a twenty-year investigation

14










by the Aptitude Research Project which began in 1949 at the

University of Southern California (Guilford, 1979). Ten

years after the project began, the structure-of-intellect

model was constructed and reported (Guilford, 1959). In-

depth discussions of the model, research done on structure-

of-intellect theory, and modifications of the model have

subsequently been reported (Guilford, 1967, 1979, 1984).

In the present study, both the original (1959) version of

the model, as well as, according to Guilford (1984), the

most recent version (first reported in 1977) will be discussed.

Guilford (1959), asserts that the "structure of intellect"

is a unified theory of human intellect, which organizes the

known, primary, intellectual abilities into a single system.

These primary, intellectual abilities are known as the com-

ponents or factors of the human intellect. Each factor is

an ability which is needed to do well in a certain class of

tasks. Guilford states that, as a general rule, certain

individuals perform well on tasks of a certain class, but

they may do poorly on the tasks of another class.

The factors are sufficiently distinct so that they can

be grouped on the basis of three classifications. The first

basis for classification is according to the process or

operation performed. Guilford lists five such operations:

factors of cognition, memory, divergent thinking, convergent

thinking, and evaluation. As described by Guilford, cogni-

tion means discovery, rediscovery, or recognition. Memory

refers to retention of what is cognized. Divergent thinking

means thinking in different directions, seeking variety,









while convergent thinking narrows in to one "right" or "best"

answer. In evaluation, decisions are made as to correctness,

suitability, goodness, or adequacy of what we know.

A second way of classifying the intellectual factors,

according to Guilford, is with respect to material or content.

In 1959, the known or demonstrated factors involved three

kinds of content: figural, symbolic, and semantic. Figural

content is material perceived through the senses; for example,

it may be visual, auditory, tactile, et cetera. Symbolic con-

tent refers to letters, digits, and other conventional signs,

usually organized in general systems. Semantic content takes

the form of verbal meanings.and ideas.

A fourth kind of content called behavioral was hypothe-

sized in the original (1959) version of the structure of

intellect, but at that time had no known factors. Behavioral

content has been described by Guilford (1959) as "social

intelligence" and later (1979) as expressive signs or "body

language" which gives information about another individual's

attention, feelings, thoughts, and intentions. Identified

intellectual factors involving behavioral content were in-

cluded in a modified version (see Guilford, 1979, 1984) of

the theory. Also, in this modified version, figural content

was divided into visual and auditory content. However, the

structure-of-intellect theory on which this present investi-

gation is based is that portion of the original theory (see

Guilford, 1959) which contains the three known content classi-

fications--figural, symbolic,and semantic.









Guilford's third way of classifying the factors is by

product categories. There are as many as six different

products associated with the various combinations of opera-

tion and content. The six products are units, classes,

relations, systems, transformations, and implications. The

three types of classifications can be represented by a three-

dimensional model (see Figure 1). Each of the three dimen-

sions of the solid represents one of the three classification

modes. Thus, this model allows for 90 to 120 distinct intel-

lectual factors which are the components of human intelligence.

Not all of the factors have been identified, however.

Guilford (1967) reported that tasks representing many

of these factors are found on standardized tests. For instance,

Guilford points to test items which require filling in blanks

in a series of letters to make a word as examples of a task

which tests the ability to cognizee symbolic units." Syllo-

gistic type tests have been discussed by Guilford (1967) as

possibly testing for factors involving operations of con-

vergent production and evaluation.

The syllogistic tests were first discussed with reference

to "evaluation of semantic relations" in the belief that the

propositions involved in the syllogism state relationships,

but it was decided later that these tests would better relate

to the factor "evaluation of semantic implications." Syllo-

gistic-type tests had also been linked to the factor "conver-

gent production" of semantic implications. But, due to the

fact that the syllogism tests have usually been of the true-

false or multiple-choice type in which the subject does not













CONTENTS

Figural


Semantic


Behavioral

PRODUCTS

Units

Classes
Relations

Systems

Transformations

Implications


Evaluation
.. Convergent Production
-Divergent Production
Memory
-Cognition


OPERATIONS


Figure 1.


The Structure-of-Intellect model
(in its original form). Source:
Cognitive Psychology with a Frame
of Reference (p. 22) by J. P.
Guilford, San Diego, CA: EdITS
Publishers, 1979. Copyright 1979
by EdITS Publishers. Reprinted
by permission.









have to draw his own conclusion, but rather must evaluate

the given conclusions, the interpretation nas been that

such tests are better associated with the factor "evaluation

of semantic implications." Even when syllogistic tests were

utilized in which the subject must draw his own conclusions,

it was decided that such tests could not determine convergent

production separate from the evaluative ability which the

tests also fit (Guilford, 1967).

In discussing the kinds of abilities classified as to

content, Guilford (1959) states that the abilities involving

the use of figural information may be regarded as "concrete"

intelligence. The people who depend most upon these con-

crete abilities include mechanics, machine operators,

engineers (in some aspects of their work), artists, and

musicians. Guilford describes the symbolic abilities and

the semantic abilities as representing two types of

"abstract" intelligence. Both language and mathematics

depend very much on symbolic abilities (although in some

areas of mathematics, figural ability is important). Seman-

tic abilities are important for understanding of verbal

concepts, and hence, are important in all areas where the

learning of facts and ideas is essential.

With respect to education, Guilford contends that each

intellectual factor provides a particular educational goal

at which to aim, and each goal ability then calls for certain

kinds of practice in order to achieve improvement in it.

Guilford further suggests that achieving these goals implies









choice of curriculum and the choice or invention of teaching

methods that will most likely accomplish the desired results.

The present study investigates the relationship between

students' personality types and their preferred methods of

analyzing categorical syllogisms. The methods of syllogistic

analysis chosen for this study were selected to represent the

three known content classifications as described by Guilford

in his 1959 discussion of the structure-of-intellect theory.

The first type of content classification is called

figural and is represented in this study by the Venn

diagram method (Method D). Employing circles, rectangles,

and other markings to present a visual representation of cate-

gorical statements, Method D represents content as perceived

through the senses (in this case, visually). The second type

of content classification is called symbolic, and is repre-

sented in this study by the numerical method (Method N).

Method N utilizes digits to represent the classes of the

syllogism and employs positive and negative signs on the

digits to represent the categorical statements and to analyze

the syllogism. The third classification of intellectual

factors by content is called semantic, and is represented in

this study by the syllogism rules method (Method R). Method

R involves the understanding of a set of verbal rules which

are used in the analysis of the syllogism.

The structure-of-intellect theory forms part of the

theoretical base for this investigation, in that the three

kinds of known content identified in the original model

support the choice of processing modes (and, thus, methods









of syllogism analysis) investigated in this study. This

original theory of the structure of intellect fitted all

known intellectual factors into one of the three content

categories: figural, symbolic, or semantic. Since each of

the three methods of syllogism analysis (Methods D, N, and

R) involves a processing mode which corresponds to one of

the kinds of content, the full range of known content repre-

sentations is made available to the student in the methods

of syllogism analysis. Thus, whichever of the processing

(content) modes is most well developed in the individual

may be the one selected by him in the form of his favorite

method of analyzing syllogisms.

Myers-Briggs Personality Theory

The other part of the theoretical base for this study

involves the theory on which the Myers-Briggs Type Indicator

(Myers, 1962) is founded. As stated by Myers (1962, p. 51),

"Briefly, the theory is that much apparently random variation

in human behavior is actually quite orderly and consistent,

being caused by certain basic differences in mental function-

ing." The basic differences concern the preferences which

people have in the way they like to use the processes of per-

ceiving and judging. These processes constitute a large

portion of the individual's mental activity, according to

Myers.

In Myers-Briggs personality theory there are two dis-

tinct and contrasting ways of perceiving (becoming aware of

things, ideas, or people). One way is by sensing and the

other is by intuition. In the process of sensing, the five









senses are used to perceive information about the world. The

process of intuition uses indirect perception by way of the

unconscious to tack possibilities, relationships, et cetera,

on to the facts perceived.

Myers-Briggs personality theory also defines two dis-

tinct and contrasting ways of judging (reaching conclusions

about what has been perceived). One way uses thinking, a

logical process which is aimed at impersonal finding. The

other way uses feeling, which is a process of appreciation

and bestows on things a subjective value.

In addition to the processes of perception and judgment,

Myers-Briggs theory postulates two contrasting orientations

to life, introversion and extraversion. The introvert is

mainly concerned with the inner world of ideas and concepts,

while the extravert is mainly concerned with the outer world

of people and things. Thus, whenever possible, the intro-

vert directs both perception and judgment on ideas, while

the extravert prefers to direct both processes on his out-

side environment.

Lastly, Myers-Briggs personality theory proposes a pre-

ference between perception and judgment as a way of life, a

way of organizing the surrounding world. In the judging

attitude, one arrives at verdicts and reaches closure on

things. Conversely, in the perceptive attitude one is still

gathering information, waiting for new developments, putting

off reaching decisions. This preference distinguishes between

the judging people who run their lives and the perceptive

people who just live them. Both the perceptive attitude and









the judging attitude must be used, but almost all people

prefer one to the other and feel more comfortable with the

preferred attitude.

The present study is based on the Myers-Briggs person-

ality theory. The contention of this theory is that people

prefer different ways of perceiving (sensing or intuition),

different ways of judging (thinking or feeling), and different

fields (introverted or extraverted) in which to perceive and

judge. People also differ in whether they prefer the per-

ceiving or judging attitude. Thus, it would seem to this

investigator that there should be a relationship between a

person's preferences on each of the Myers-Briggs indices

(ie., EI, SN, TF, and JP), and his preferred method of

perceiving and judging the information presented in an

abstract categorical syllogism. Each of the three methods

of analyzing categorical syllogisms which were investigated

in this study represents a different processing mode or

content classification (either figural, symbolic, or

semantic) for perceiving and judging the content of the

syllogistic statements.

Syllogistic Reasoning

Background and History

Any discussion of syllogistic reasoning should, by

rights, begin with a reference to Aristotle, one of the

greatest philosophers of ancient Greece. Although Aristotle

advanced ideas in every major area of philosophy and science,

he is best known to logicians as the inventor of formal logic

and, more particularly, of the syllogistic form.










In Socrates to Sartre, Stumpf (1966) gives some biogra-

phical information on Aristotle. Born in 384 B.C. in the

town of Stagira on the northeast coast of Thrace, Aristotle

was the son of the physician to the king of Macedonia. At

the age of seventeen Aristotle enrolled in Plato's Academy

in Athens where he studied for twenty years. He left when

Plato died and then he became tutor to Alexander the Great

who at that time was thirteen years old. When Alexander

ascended the throne of Macedonia after his father Philip's

death, Aristotle's tutoring duties were finished. Aristotle

returned to Athens where he founded his own school, the

Lyceum.

At the Lyceum, Aristotle contributed to nearly every

field of human knowledge and, after his death in 322 B.C.,

his treatises on reasoning were compiled into a six-volume

work known as the Organon. Although the word "logic" did

not acquire its modern meaning until the second century

A.D., the subject matter of logic was determined by the

content of the Organon (Copi & Gould, 1972).

The syllogism remained virtually as Aristotle defined

it until the nineteenth century when "modern" logicians

(e.g., DeMorgan, Boole, and Venn) introduced a new view-

point in the interpretation of some propositions. This

new approach served to expand the work of Aristotle, but

little or no research was done concerning the reasoning

process. The frequent errors which are made in the analysis

of syllogisms remained uninvestigated in any depth until the

last fifty years, with the greatest concentration of such









research taking place in the last fifteen or twenty years.

No longer is the failure of students to respond correctly

in solving syllogisms, or in testing syllogisms for validity,

seen as simply an indication of their lack of logical rea-

soning ability, but rather, investigators have begun to look

at the reasoning processes which lead to incorrect solutions.

The need for investigating the errors found in syllo-

gistic reasoning can be shown by noting that syllogisms are

found in numerous and diverse places. Besides their obvious

position in books on logic, syllogisms are found, according

to Mayer and Revlin (1978), in texts on rhetoric and im-

proving thinking ability. They are even incorporated into

games, such as Wff & Proof and Propaganda, and in the games

found in the works of Lewis Carroll. But the syllogism's

long history of use on tests of intelligence emphasizes even

more the need to understand what kinds of errors are being

made, and what specific processes are involved in faulty

reasoning (or the obtainment of incorrect solutions to

syllogisms). If one's ability to solve syllogisms correctly

is being used in the measure of intelligence, then it is

mandatory that we know much more about the processes involved

in syllogistic reasoning.

Logic Studies

Included in this section are studies which represent

several of the factors being proposed in the literature to

account for the incorrect responses given on tests of syllo-

gistic reasoning. The first five studies pertain to

categorical syllogisms while the last four studies involve









either disjunctive or conditional syllogisms. The studies

within each of the two groups are presented in chronological

order.

In one of the earliest American investigations involving

the categorical syllogism, Woodworth and Sells (1935) formu-

lated three hypotheses in their study of students' responses

to syllogisms. Their first hypothesis was that difficulty

arises from the ambiguity of the language in which syllogisms

are expressed. The word "some," as in "Some A is B," means

"at least one and perhaps all" under the definitions of formal

logic. But in the conventional usage of ordinary speech,

"some" usually carries the implication of "more than one,

but less than all." Thus, a person not familiar with formal

logic might think it perfectly correct to infer from "Some

A is B" that "Some (other) A is not B."

Woodworth and Sells' second hypothesis was that of

"caution" or wariness on the part of the subject about accept-

ing universal conclusions or accepting affirmative conclusions.

These researchers report that a larger percent of invalid

particular conclusions are accepted than of universal, and

a larger percent of invalid negative conclusions than of

affirmative.

The third hypothesis proposed by Woodworth and Sells in-

volves the "atmosphere effect." The "atmosphere" of the

premises may be affirmative or negative, universal or parti-

cular, depending on the type of premises. The hypothesis is

that the atmosphere of the premises will be carried over

with a sense of validity to the conclusions. Using combined









data from two experiments, totaling 171 subjects who were

presented the premises of syllogisms and asked to label

the conclusions as valid or invalid, the following results

were noted by Woodworth and Sells (1935). "Examination of

the data from two experiments indicates that nearly all the

acceptance of invalid conclusions can possibly be explained

by these three hypothetical factors" (p. 460).

Emotional value or "affective loading" of the conclusion

was the factor in syllogistic reasoning investigated by

Kaufmann and Goldstein (1967). Thirty-two female subjects

enrolled in an introductory psychology class assessed the

validity of 36 categorical syllogisms varying in affective

loading, quantification, and validity. The instructions on

the test clearly stated the logical meaning of universal

and existential quantification. Results reported by

Kaufmann and Goldstein were that syllogisms with existential

conclusions resulted in more errors than syllogisms with

universal conclusions, and more invalid syllogisms were

incorrectly accepted than were valid ones incorrectly rejec-

ted. Kaufmann and Goldstein also reported that these data

indicate that syllogisms with emotional content may produce

greater wariness of accepting a universal conclusion than if

the syllogism were without affective content.

In another investigation of "atmosphere effect," Begg

and Denny (1969) studied the responses of 33 introductory

psychology students on a 64-item multiple-choice test. Each

test item consisted of two premises and four alternative

conclusions. In preliminary instructions the subjects were









told the logical meaning of "some." The preferred error

tendencies (response tendencies on erroneous conclusions)

for the items were as predicted by the "atmosphere effect,"

with the level of predictive accuracy ranging from 73% to

90% depending on the type of premises. However, as Begg

and Denny point out, this does not imply that the "atmosphere

effect" can be held accountable for the errors. There is

also a possible factor involving faulty interpretation of

the premises which, if used in some syllogisms, would yield

the same incorrect responses as that of the "atmosphere

effect."

The factor of misinterpretation of the premises was

studied by Ceraso and Provitera (1971). These researchers

investigated whether subjects are reasoning properly but

are starting with faulty premises, or whether they are not

reasoning at all (e.g.,just influenced by the "atmosphere

effect"). Eighty students at Rutgers-Newark were recruited

from the campus to use as subjects. The students were

divided into two groups. One group was given traditional

syllogisms and the other was given modified syllogisms.

The modified syllogisms were the same as the traditional

except that the interpretation of the premises was made

explicit. In other words, since a premise of the form

"All A is B" could be given a set identity interpretation

or a set inclusion interpretation, the subjects were told

explicitly for each premise which interpretation to use.

The content of the syllogisms in Ceraso and Provitera's

study dealt with specific attributes of wooden blocks which









the subjects were shown as the premises were being given.

An answer sheet was used which provided the four possible

alternative conclusions for each syllogism. The researchers

concluded from the results of their study that subjects

performing this reasoning task were not responding in a

non-logical way, but were using the logical structure of

the material. By eliminating a potential source of error

(faulty interpretation of the premises), Ceraso and Provitera

found a substantial improvement in the subjects' performance.

Furthermore, the investigators concluded that even though

the subjects still could have dealt with this modified

material in terms of the "atmosphere effect" the evidence

shows they did not do so, and thus probably did not do so

on the traditional syllogisms either.

In a study evaluating a conversion model of formal

reasoning for the model's ability to predict the decisions

made by reasoners when solving concrete and abstract cate-

gorical syllogisms, Revlin et al. (1978) found that natural

language processes in the encoding of the syllogistic pre-

mises are reflected in the reasoners' solutions to the

syllogisms. These researchers held the view that reasoning

errors result primarily from the incorrect way in which

syllogistic premises are encoded (assigned a semantic

reading) and not from a faulty inference mechanism. They

utilized a model of categorical syllogistic reasoning called

the conversion model which, once the students' understanding

of the syllogistic premises is taken into account, shows the

students' decisions to be both predictable and rational. The









major source of error in encoding is said to be illicit con-

version. That is, when the reasoner is told All A is B

he interprets that proposition to mean that the converse

All B is A is also true.

In a study involving conditional syllogisms, O'Brien

(1973) investigated college students' performance on four

common inference patterns (modus ponens, converse, inverse,

and contrapositive). The subjects were tested after com-

pleting an introductory logic course. O'Brien found that

widespread and consistent use of "Child's Logic" [invalid

patterns of inference in which, for example, subjects

construct p q to mean (p r q) v (p q)] persists in

college students. He also found that consistent use of

"Math Logic" (valid patterns of inference) is employed

by very few such students even after completing a college

level course in logic. In addition, it was noted that

scores were substantially lower on class inclusion items

than on corresponding causal items.

Using the same four inference patterns as O'Brien,

Jansson (1978) compared the abilities of adolescents to

handle simple conditional arguments as measured by two

different assessment procedures, namely, written tests and

the Four-Card problem tasks (O'Brien, 1975). The Four-Card

problem tasks were designed to measure application of four

inference patterns (modus ponens, converse, inverse, and

contrapositive). Results of the study indicated that Four-

Card problem tasks were found to be easier for the invalid

principles, whereas paper-and pencil items were easier on









the valid principles. Mastery proportions on the written

tests were similar to those found in other studies (e.g.,

Roberge, 1972).

Juraschek (1978) investigated the use of the logical

connective OR in disjunctive arguments. Testing 266 students

enrolled in a mathematics course for prospective elementary

teachers, he found that students are more likely to assume

an exclusive rather than inclusive meaning to the connective

OR. He also found that using EITHER-OR was more likely to

connote an exclusive meaning than just using OR. Juraschek

says that this is because ordinary language use suggests the

exclusive OR. He suggests that one should be cautious in

judging the logical ability of students when they simply may

be assigning to common words meanings that they find more

natural than the meanings used in formal logic and mathematics.

Piper (1981) examined the effects of three narrative

texts (a fantasy passage, a realistic passage, and a contrac-

tual passage) on the logical performance of subjects in

grades 4, 6, and 12. The test consisted of 27 syllogistic

problems varied for argument type (modus ponens or modus

tollens), for negation, and for conditional statement

(abstract, concrete, and inducement). Two of Piper's con-

clusions were that modus ponens problems were found to be

less difficult than modus tollens, and that negative pro-

blems were more difficult than affirmative ones. Grade 6

performance on the fantasy passages was superior to the

other two groups. Grade 12 performance was superior to the

other two groups on realistic and contractual passages. It









was concluded that a shift of emphasis was necessary away from

structural approaches to the development of reasoning abili-

ties towards models sensitive to the various discourse "worlds"

entered by subjects when working on logical problem tasks.

Cognitive Style and Cognitive Bias

Background

According to Onyejiaku (1982) educational research has

increasingly shifted its emphasis from predictive studies of

success and failure on learning tasks to the understanding of

the cognitive processes which underlie the performance. In-

sight into these cognitive processes could be of utmost

importance in defining instructional treatments for individual

students to maximize their learning potential. It has been

known for some time that no single instructional treatment

will benefit students equally.

Two aspects of personality which have been the focus of

much research are cognitive style and cognitive bias. Cogni-

tive style (e.g., field dependence/independence) can be des-

cribed as the stable, distinct, idiosyncratic preferences

in mode of information-gathering and problem-solving. These

styles are an integral part of one's personality and are

more well developed in some people than in others. As

Onyejiaku (1982) points out "A person's reaction to a stimulus

is, to a large extent, a function of how he perceives, analyzes,

and understands the situation or, in other words, a function

of his cognitive style" (p. 31).

Cognitive bias, as described by Head (1981), is the

individual's expressed preference for verbal, visual, or









spatial modes of working. Guilford (1959) used terms similar

to Head's in discussing the components of the human intellect.

Guilford stated that one way of classifying intellectual

factors is by the kinds of material or content involved:

the content may be figural, symbolic, or semantic. Figural

content is perceived through the senses, e.g., seen, felt,

or heard. Symbolic content is composed of conventional signs

such as digits or letters. Semantic content is composed of

ideas and meanings which are represented verbally. "The

fact that different children respond to the same written

stimulus in different ways raises a number of questions

which are of interest to the classroom teacher and the

educational psychologist" (Lean & Clements, 1981, p. 270).

The following research studies pertain to investigations

of such questions.

Cognitive Style and Cognitive Bias Studies

Lean and Clements (1981) studied 116 engineering students

in Papua, New Guinea. The students were given a battery of

mathematical and spatial tests in addition to an instrument

testing their preferred modes of processing mathematical

information. It was found that students who preferred to

process mathematical information by verbal-logical means

tended to outperform more visual students on mathematical

tests. It was noted by the researchers that the tendency

towards superior performance on mathematical tests by those

students who preferred a verbal-logical mode of processing

mathematical information might be due to a developed ability

to abstract readily and therefore to avoid forming unnecessary









visual images. Statistical analyses did point to the

existence of a distinct cognitive trait associated with

the processing of mathematical information.

Khoury and Behr (1982) investigated the effects of

the individual difference variables of field dependence/

independence and spatial visualization ability on the per-

formance of college students on retention tests in (a) the

pictorial, (b) the symbolic, and (c) the mixed symbolic/

pictorial modes. Ninety-six preservice elementary school

teachers participated in the study. Measures of field

dependence/independence and spatial visualization ability

were obtained on each student. Students were instructed in

whole number addition algorithms based on the counting stick

manipulative aid. Instruction emphasized the use of symboli-

zation, pictorial presentation, and manipulative aids in the

solutions. Three weeks later a retention test was given.

The retention test consisted of three parts which differed

only in the presentational modes of the items. The pictorial

mode was used in Part 1, the symbolic mode in Part 2, and

in Part 3, the presentation alternated between pictorial and

symbolic.

Results of the research using the extreme groups of stu-

dents (upper and lower thirds on the tests for spatial

visualization and for field dependence/independence) showed

that the symbolic mode retention test was the easiest, and

the pictorial mode retention test was the most difficult.

In addition, students of high spatial visualization ability

scored consistently better than students of low spatial









visualization on all three retention test modes. The differ-

ence was highest on the pictorial retention test.

Perunko (1982) examined the relationships that mental

imagery, spatial ability,and analytic or synthetic processing

have to performance on mathematical problems which differ in

the degree to which they involve visual-synthetic or verbal-

analytic concepts and strategies. Eighty-one community college

students enrolled in developmental mathematics classes were

tested for their use of visual and verbal imagery, their

ability to rotate visual and verbal material, and their

preference for an analytic or synthetic processing of visual

and verbal material. Conclusions which are relevant to the

present study are as follows. Students who are able to

correctly rotate the visual figures and/or process the visual

material analytically perform well on the visual and combina-

tion mathematics problems and solve the combination problems

by a visual approach. Those students who do well on the

visual and/or combination problems tend to use a visual

solution approach. Sex-related differences were found

indicating that males score higher on the rotation and

mathematics tests and in the visual mode, whereas females

score higher on the use of imagery and analytic processing

and in the verbal mode.

The aforementioned studies show that students do vary

in their degree of visual imagery, verbal-logical ability,

and spatial ability. Two of the studies indicate that

students have preferred modes of processing mathematical/

logical information.









In an aptitude-treatment interaction study, McLeod,

McCornack, Carpenter, and Skvarcius (1978) investigated

the relationship of the aptitude variable field dependence/

independence to instructional treatments based on two levels

of guidance crossed with two levels of abstraction. One-

hundred-twenty students in four sections of a mathematics

course for prospective elementary school teachers were

randomly assigned to four treatment groups. The four groups

were: (1) maximum guidance with manipulative materials,

(2) minimum guidance with manipulative materials, (3) maximum

guidance with only a symbolic presentation, and (4) minimum

guidance with only a symbolic presentation. The topic taught

to the groups was addition and subtraction of whole numbers

in bases other than ten. Subjects were given a pretest,

two posttests (one symbolic and one using manipulative

materials), two retention tests (a second administration

of the two posttests), and a test designed to measure field

dependence/independence. Results of statistical analyses

showed that there was a significant interaction in two of

the tests of achievement between field dependence/independence

and level of guidance. In the other two tests the interaction,

while not significant, indicated support for the hypothesis

that field-independent students will perform better when

allowed to work independently and that field-dependent

students will learn more when they have extra guidance from

the teacher.

In a study by Onyejiaku (1982) the possible effects of

analytic vs. nonanalytic cognitive styles and two modes of









teaching techniques (discovery vs. expository) on student

performance on mathematics tasks were investigated. Eighty

subjects (40 boys and 40 girls) were selected from two

schools in Ibadan, Nigeria, to comprise the population for

the study. Their ages ranged from 13 to 15. The instruc-

tional materials were teaching units on mensuration-surfaces,

simultaneous linear questions, and parallelograms. Five

instruments were used: (1) a test to measure cognitive

style, (2) a pretest on the material to be taught, (3) a

posttest, (4) a retention test, and (5) a concept transfer

test. Two instructional treatments (discovery method and

expository method) were used. There were four treatment

groups: (1) analytic discovery, (2) nonanalytic discovery,

(3) analytic expository, and (4) nonanalytic expository.

Results showed that a student's cognitive style influences

his performance on mathematics tasks. Generally, analytic

students perform better than nonanalytic students. The more

analytic a boy is the more he is likely to benefit from

expository instruction. Conversely, the more nonanalytic a

boy is the more he is likely to benefit from the discovery

method of teaching. (This distinction between analytic boys

and nonanalytic boys is not as clear-cut with girls.)

Roberge and Flexer (1983) examined the effects of field

dependence/independence and the level of operativity (Piagetian

measures of formal operational thought) on the mathematics

achievement in the upper elementary school grades. Findings

from this study show that both cognitive style and the level

of operational development have a significant effect on the









mathematics achievement of sixth, seventh,and eighth graders.

The analytic abilities displayed by field independent students

and the logical-thinking abilities manifested by high-

operational students had a pronounced influence on their

mathematics achievement. The researchers suggest the need

for future investigations that examine the feasibility of

using instructional strategies and designs that are optimally

suited to the cognitive styles and developmental capacities

of individual learners.

The studies just cited all reflect the current interest

in research on the stable, individual, idiosyncratic prefer-

ences which the individual exhibits when reacting to his

environment. These preferences have been shown to be related

to how well a student performs on various kinds of tests.

In general, students seem to perform better when the tasks

on the tests are matched, in presentation and procedure,

to the students' cognitive preferences.

Myers-Briggs Related Research

Background

The Myers-Briggs Type Indicator (MBTI) is a valuable

instrument for assessing cognitive style. The MBTI is a

self-reporting questionnaire which focuses on the construc-

tive uses of individual differences. Based on the work of

Carl Jung (1923), the MBTI was developed by Isabel Briggs

Myers and Katherine C. Briggs beginning in the early 1940s,

and was published in 1962 as a research tool by the

Educational Testing Service. In 1975, the Consulting

Psychologists Press published the MBTI for professional uses

by psychologists, educators, and other qualified persons.









In People Types and Tiger Stripes, Lawrence (1982)

states that an understanding of type is important to

educators and other professionals concerned with instruc-

tion and guidance. Stressing that type is fundamental,

Lawrence says that the fact that a student may prefer

sensing perception over intuitive perception or an extra-

verted (active) approach to studies over an introverted

(reflective) one is information that some teachers have

used very effectively to improve their instruction.

Studies Utilizing the Myers-Briggs Type Indicator

The study which has used the MBTI in a manner closest

in similarity to this study.was completed by J. A. Novak in

1980. Novak collected data on 283 eighth grade students.

Novak investigated the relationships among the MBTI person-

ality types, cognitive preference orientation, intelligence,

sex, science achievement, and attitudes toward science and

scientists of eighth grade students. The four kinds of data

collected were (1) MBTI, (2) cognitive preference as to

memory, questioning, application,or no preference, (3)

attitude toward science and scientists, and (4) science

knowledge. Novak also obtained data on intelligence and

sex of students. Novak's prediction that MBTI introvert-

intuitive-thinking-perceiving types would prefer a memory,

memory/application, or memory/questioning cognitive preference

orientation was not supported by statistical analysis. Novak

did find statistically significant differences in intelli-

gence between MBTI sensing and intuitive types (in favor

of intuitives) and between MBTI judging and perceiving types









(in favor of perceiving types). Statistically significant

relationships were not found among the variables of MBTI

personality types and cognitive preference orientation,

and sex of students, or between cognitive preference

orientation and intelligence, and sex of students. However,

it was suggested that teachers consider personality factors

and cognitive preference orientation when planning for the

instruction of students.

In another study involving student preference, Miller

(1984) investigated the relationship between students'

personality types as measured by the MBTI, and the type of

mathematical problems they preferred to do. Miller adminis-

tered the MBTI and a set of 24 problems to eighteen above-

average high school students enrolled in a course which

stressed the heuristic processes necessary to solve the types

of problems used in the study. The problems were of four

types: (1) logic, (2) geometry, (3) problems that could be

solved using an inductive strategy, and (4) problems that

could be solved using factors or other properties of the

quantities involved. The students were asked to sort the

set of 24 problems from the one they would most like to do

to the one they would least like to do.

Results of the data analysis indicated that the group,

as a whole, tended to sort the problems in the same manner.

Personality style as measured by the MBTI was not a dis-

criminating factor in determining the outcome of the ordering

process. Results did show that logic problems were preferred

over all other types as demonstrated by their being selected

as choices 1 through 5.






41


Other research that has been done using the MBTI has

been related largely to either career development (e.g.,

McCaulley, 1976, 1978) or to student ability (e.g.,

McCaulley & Natter, 1974; May, 1971).















CHAPTER THREE
METHODOLOGY

This chapter is divided into four sections. The first

section describes the population. In the second section are

found the data collection procedures of the study. Descrip-

tions of the test instruments used for data collection are

the subject of the third section. Lastly, there is a section

describing the statistical procedures.

Population

The students participating in this study were enrolled

in four sections of an introductory logic course at Santa Fe

Community College, Gainesville, Florida, in the winter and

spring terms, 1984. This course is designed to survey some

of the major areas in the study of logical reasoning. Students

receive elective credit in either humanities or mathematics

for this course. There were 56 students (35 males and 21

females) participating in this study. The subjects ranged

in age from 17 to 52. Seven other students were eliminated

from the study for either failing to be present for the

administration of one or both of the test instruments (the

MBTI and the PMT), or for failing to demonstrate competency

in all three methods of analyzing syllogisms for validity.

Procedures

This investigation was carried out in four sections of

the course, Introduction to Logic. All four sections were









taught by the same instructor, namely, the investigator.

The sections were taught in the same manner, following the

procedures which are outlined and discussed in this section.

The procedures which were followed for the purposes of

this study were outlined in Chapter One as follows:

1. A unit on the analysis of categorical syllogisms

was presented. Three different methods (D, N,

and R) of testing syllogisms for validity were

presented to the students.

2. At the conclusion of the unit, the Preferred Methods

Test (PMT) was administered to each student.

3. The Myers-Briggs Type Indicator (Form F) was

administered to each student.

4. Each student was classified as to age, sex, person-

ality type (as determined by the MBTI), and the

order of his preference in selecting methods of

analyzing categorical syllogisms (as determined

by the PMT).

Following is a discussion of each step of the procedure.

The unit on analysis of categorical syllogisms was

prefaced by an introductory unit on general logical reasoning.

The concepts of validity, soundness, consistency, argument

construction, and truth and falsehood in relation to validity

were presented and discussed with the students prior to the

unit on syllogisms. Then, after the students were familiar

with the rudiments of logical reasoning, the four kinds of

categorical propositions were defined and discussed. This

discussion included the logical definition of "some" as










"at least one" and the representation of each of the cate-

gorical propositions in both the traditional symbolic form

and the Boolean symbolic form. For instance, the A-form

(universal affirmative) categorical proposition, such as

"All D is C," would be written "DAC" in traditional symbolic

form and would be written"DC=d'in Boolean symbolic form.

For the purposes of this study, however, the propositions of

the syllogisms were presented in traditional symbolic form.

Next, the students were taught the valid inferences which

can be made from the relationships on the Square of Opposition

and from the operations of conversion, obversion,and contra-

position. These inferences were discussed from both the

Aristotelian (existential) viewpoint and from the Boolean

(hypothetical) viewpoint. When the Aristotelian viewpoint

is taken, all classes mentioned in the syllogism are assumed

to have at least one member. This is known as the existential

assumption. From the Boolean viewpoint, however, only the

particular propositions presuppose the existence of at least

one member of each class; in the universal propositions no

assumption of existence is made. Neither viewpoint is con-

sidered better than the other; which viewpoint is taken

usually depends on whether or not each class in the syllogism

has members.

In the present study, abstract categories for the terms

(or classes) of the propositions in the syllogisms were used.

Since the use of abstract categories does not make implicit

the existential assumption of the Aristotelian viewpoint, the

more general Boolean or hypothetical viewpoint was chosen for

use in this investigation.









Following the study of the categorical proposition, the

categorical syllogism was defined. The component parts of

the syllogism and its form in terms of mood and figure were

discussed. The students were told that only 15 of the pos-

sible 256 syllogistic forms were unconditionally valid, but

the students were not given a list of the valid forms (see

Appendix A).

The Venn diagram method of testing categorical syllo-

gisms for validity (Method D) was then taught. The differ-

ence between Venn diagrams and Euler circles (which are

often referred to as Venn diagrams) was briefly explained.

Next, the categorical rules method (Method R) was taught.

The logical notion of "distribution" of terms was, of neces-

sity, discussed at this point in order to explain and employ

rules number two and three. Lastly, the numerical method

(Method N) was taught. (See Appendix B for an explanation

of these three methods.)

The presentation of each of these three methods took

approximately one to one and one-half class periods. Follow-

ing the discussion of each method, quizzes were given to

ascertain that each student could employ the particular method

correctly. In order to establish competency in the three

methods, students were given the opportunity to retake the

quizzes and to receive extra help on the methods. A brief

review session on the three methods was held and then the

Preferred Methods Test (PMT) was administered.

The PMT was scored by the investigator and the order of

preference for the three methods was recorded for each student.










The preference order was recorded by three letters, one for

each method, with the first letter representing the students'

favorite method, the second letter representing his second

favorite method,and the last letter representing his least

favorite method. Examples of students' preference orders

are DNR, NRD, et cetera.

The MBTI was administered to the students and each

response sheet was hand-scored independently by at least two

different people (including the investigator). This was

done to verify the accuracy of the reported scores. The

students were told that the results of the MBTI would be

used in a study that was being done, and that the results

of the study would be used in the future to improve the

teaching of the logic course. Lastly, the sex and age of

each student was recorded.

Test Instruments

The Preferred Methods Test

The PMT (see Appendix C) is a test instrument designed,

administered,and graded by the investigator. It consists

of three categorical syllogisms presented in standard

syllogistic form (ie., the order of the statements is (1)

major premise, (2) minor premise, (3) conclusion). Each of

the syllogisms contains only abstract categories with each

category represented by an alphabetic letter. Each cate-

gorical statement is written using traditional symbolization

(e.g., DAC) as opposed to Boolean symbolization (DC=0).

Abstract categories and symbolic form were employed in

the presentation of the syllogisms on the PMT, so as to









control for the variables of faulty encoding and "belief-

bias" theory as previously discussed in Chapter Two.

Faulty encoding occurs when information in the statements

is given an incorrect semantic reading (ie., misinterpreted)

by the subject. By using symbolic form which defines a non-

ambiguous interpretation for each of the four types of

categorical statements, the variable of faulty encoding can

be eliminated from the factors which might cause incorrect

answers in the analysis of the syllogism. In like manner,

by using abstract categories, the "belief-bias" theory can

be eliminated, since the abstract classes, A, B, C, et

cetera, would not, under normal conditions, evoke emotional

responses from the subject and, thus, would not cause

"affective loading."

The instructions to the student were to work syllogism

number one by his favorite of the three methods (D, N, or

R) of analyzing categorical syllogisms, to work syllogism

number two by his second favorite method, and to work syllo-

gism number three by his least favorite method. Space was

provided on the test copy for the student's written response.

The student's responses were then recorded as to which method

he used for each of the syllogisms.

The Myers-Briggs Type Indicator

The MBTI is a self-reporting personality preference in-

ventory using a modified version of the dichotomous scales

suggested by Jung. The four scales are extraversion or

introversion (EI), sensing or intuition (SN), thinking or

feeling (TF), and judgment or perception (JP). Using one










letter from each of the four scales, sixteen unique person-

ality types (such as ENTP or ISTJ) can be defined.

The MBTI was designed to discriminate among these sixteen

types, which reflect subjects' reporting of their basic per-

sonality preferences with respect to judgment and perception.

The personality type of each student is included as part of

Appendix D. In addition, the distributions of each type and

each type element are given in Tables 1 and 2.

Scoring the MBTI

The MBTI may be scored by computer or by hand. In the

present study the MBTI was scored by hand. To ensure the

accuracy of the scoring procedure, each MBTI was scored at

least twice, including once by the investigator. The results

of scoring the MBTI can be given as four preference scores,

one for each of the four indices: EI, SN, TF, and JP. The

score for each index is represented by a letter showing the

direction of the reported preference, followed by a number

showing the reported strength of the preference (Myers, 1962).

Two keys are required for each index, with separate sets of

keys used for each sex on the TF scale.

In this study, for the purpose of the statistical analy-

ses, continuous scores rather than preference scores were

used. The continuous score for an E, S, T, or J score is 100

minus the preference score. For an I, N, F, or P score, the

continuous score is 100 plus the preference score. Thus, for

each individual, four numerical scores are obtained, one for

each index. The continuous scores for each student partici-

pating in this study are shown in Appendix D.










Table 1

Distribution of Students by Personality Type
for Group I

(N = 28)


SENSING TYPES
with THINKING with FEELING


INTUITIVE TYPES
with FEELING with THINKING


ISTJ ISFJ INFJ INTJ

N= 1 N= 1 N= 1 N= 2
%= 3.6 %= 3.6 %= 3.6 %= 7.1





ISTP ISFP INFP INTP

N= 2 N= 1 N= 1 N= 4
%= 7.1 %= 3.6 %= 3.6 %=14.3





ESTP ESFP ENFP ENTP

N= 0 N= 0 N= 3 N= 5
%= 0 %= 0 %=10.7 %=17.9





ESTJ ESFJ ENFJ ENTJ

N= 5 N= 1 N= 1 N= 0
/o= 17.9 o%= 3.6 %/= 3.6 O%= 0


53.6
46.4

39.3
60.7

67.9
32.1

42.9
57.1

17.9
28.6
28.6
25.0

28.6
10.7
21.4
39.3

28.6
10.7
46.4
14.3

28.6
39.3
17.9
14.3

28.6
32.1
17.9
21.4










Table 2

Distribution of Students by Personality Type
for Group II

(N = 28)


SENSING TYPES
with THINKING with FEELING


INTUITIVE TYPES
with FEELING with THINKING


ISTJ ISFJ INFJ INTJ

N= 3 N= 1 N= 1 N= 0
%= 10.7 %= 3.6 %= 3.6 %= 0





ISTP ISFP INFP INTP

N= 2 N= 3 N= 0 N= 5
%= 7.1 %= 10.7 %= 0 %=17.9





ESTP ESFP ENFP ENTP

N= 0 N= 2 N= 3 N= 2
%= 0 %= 7.1 %=10.7 %= 7.1





ESTJ ESFJ ENFJ ENTJ

N= 3 N= 2 N= 1 N= 0
%= 10.7 %= 7.1 %= 3.6 %= 0


E 13 46.4
I 15 53.6

S 16 57.1
N 12 42.9

T 15 53.6
F 13 46.4

J 11 39.3
P 17 60.7

IJ 5 17.9
IP 10 35.7
EP 7 25.0
EJ 6 21.4

ST 8 28.6
SF 8 28.6
NF 5 17.9
NT 7 25.0


32.1
25.0
35.7
7.1

21.4
32.1
28.6
17.9

21.4
21.4
32.1
25.0










Statistical Procedures

Overview

There were five research questions posed in Chapter I

of this study. In order to discuss those questions the

following definitions will be used:

Group D: the group of students who preferred Method D

for the testing of syllogisms.

Group N: the group of students who preferred Method N

for the testing of syllogisms.

Group R: the group of students who preferred Method R

for the testing of syllogisms.

Method group: Group D, Group N, or Group R.

The following statistical procedures were used to analyze

the data. Descriptive statistics were employed to determine

the percentage of students in Group D, Group N, and Group R.

A one-way analysis of variance was done to determine if the

average age for the students in each method group differed

significantly.

An exact conditional test of independence (Agresti &

Wackerly, 1977) was done to determine if the proportion of

males within each method group was similar or different.

Descriptive statistics were used to determine if students

of different type elements (E-I, S-N, T-F, J-P) preferred

different methods. In addition, a stepwise discriminant

analysis was run to evaluate each of the variables of per-

sonality type (or type element), sex, and age for its ability

to predict, for each student, the method that he was most

likely to prefer.










Discriminant Analysis

Discriminant analysis is useful in classifying individuals

into groups on the basis of their scores on tests or other

data. The discriminant function is a regression equation

with a response (dependent) variable that represents group

membership. Discriminant analysis can be distinguished from

regression analysis, in that discriminant analysis involves

a nominal response variable, whereas regression analysis

entails a continuous response variable (Marks, 1982).

When only two groups are used, the discriminant analysis

is a multiple regression analysis with 0 and 1 being the two

values of the dependent variable. Using several variables,

and values of 0 and 1 as the dependent variable, the regres-

sion equation would be solved in the usual manner to obtain

the coefficients. The resulting equation, the discriminant

function, maximally discriminates the members of the sample

according to the group to which each member belongs. The

function is used for predictive purposes. Of course, the

validity of predicting to new samples relies on the compar-

ability of the new sample with the original.

In the present study three classification groups (D, N,

and R) rather than the usual two groups were used. The pro-

cedure for three or more groups is to seek the linear com-

bination of the variables that will maximize the differences

between the groups relative to the differences within the

groups (Kerlinger & Pedhazur, 1973).










The independent variables can be considered together in

the construction of the discriminant function or they can be

considered one at a time. The latter way is known as step-

wise discriminant analysis and was the procedure employed

to answer Question Five of the research questions. According

to Kleinbaum and Kupper (1978), this procedure is similar to

stepwise multiple regression in that one variable is added

to the function at each step, this variable being the one that

results in the most significant F-value after adjusting for the

variables already included in the model. Variables are added

one at a time until no further significant gain in discrimina-

tion can be achieved by the addition of more variables to the

discriminant function. This procedure allows for the examina-

tion at every step of both the variables which have been in-

cluded and those being considered for inclusion. This is

important since a variable which entered the function early

in the procedure may later become superfluous due to the

relationship between it and other variables already in the

model. The retaining of superfluous variables, as is done in

discriminant analysis which is non-stepwise (ie., all of the

variables are "forced" into the discriminant function), can

actually lead to a loss of discriminatory power (Kleinbaum &

Kupper, 1978).
















CHAPTER FOUR
RESULTS AND ANALYSIS OF THE DATA

The purpose of this study was to determine the relation-

ship between a community college student's personality type

and his preferred method of testing a categorical syllogism

for validity. Previous chapters have established a rationale

for this study, presented a theoretical base and a review of

the literature pertinent to the study, and outlined the

methodology. This chapter will present the results of the

study and a statistical analysis of the data. The results

are organized into five sections, each section relating to

one of the research questions posed in Chapter One.

Analysis of the Data

Since the data were collected during two consecutive

terms (winter and spring, 1984), they were analyzed separate-

ly as two groups. For the purposes of discussion, the

subjects participating in the study in the winter term are

referred to as Group I and the subjects from the spring term

are referred to as Group II. All statistical analyses were

done using the IBM main-frame computers at the University

of Florida. The results pertaining to each research

question will be discussed for Group I and for Group II.

The two groups turned out to be quite different and results

of the pooled data were not found to be significant. Con-

sequently those results will not be presented. Differences

between groups will be shown throughout this chapter.










Data for analysis were obtained through the use of the

Myers-Briggs Type Indicator (MBTI) and a test instrument

called the Preferred Methods Test (PMT) which was designed

by the investigator. These two instruments were adminis-

tered to 56 students (28 students each in Group I and Group

II). Appendix D contains, for each subject in the study,

the individual's age, sex, and his results on both the MBTI

and the PMT.

Research Questions

Question One

Three methods of testing syllogisms for validity--Method

D (Venn diagram method), Method N (numerical method), and

Method R (rules method)--were presented to the students who

participated in this study. At the conclusion of the unit

on the analysis of syllogisms, the students were given the

Preferred Methods Test (PMT) and asked to specify their

favorite method, their second favorite, and their least

favorite method. The order of preference was recorded for

each student (e.g., DNR, RDN, et cetera). The question to

be answered was as follows: Do students differ in their

choice of method for testing syllogisms for validity?

To answer question one, the percentage of students who

chose Method D as their favorite method, the percentage who

chose Method N, and the percentage who chose Method R were

computed. In like manner, the percentages were computed for

the numbers of students who chose each of the three methods

as their second favorite, and as their least preferred. These

data for Group I and Group II are found in Table 3. An










Table 3

Results of the Preferred Methods Test


Choice


Method First Second Third

n % n % n


Group I


D 9 32.14 12 42.86 7 25.00

N 13 46.43 9 32.14 6 21.43

R 6 21.43 7 25.00 15 53.57


Group II


D 10 35.71 6 21.43 12 42.86

N 11 39.29 12 42.86 5 17.86

R 7 25.00 10 35.71 11 39.29


comparing
Group I


Note: Chi-square was not significant for
percentages of students for either
(p < .30) or Group II (p < .30).










examination of the data shows that each method was selected

as the favorite method by at least 21% of the subjects in

each group. Thus, students did differ in their choice of

method. There was a tendency for students to select Method

N as their favorite method (46.4% of Group I and 39.3% of

Group II) and to select Method R as their least favorite

(53.6% of Group I and 39.3% of Group II).

Additionally, a chi-square test was done on the data for

both Group I and Group II to determine if the percentage of

students differed for the three methods. The null hypothesis

tested was


H : P = P = PR'


where PD' PN, and PR are the percentages of students who prefer

Methods D, N, and R, respectively. There were no significant

differences (p < .30) found between any of the three method

groups for Group I or Group II. Thus, the percentage of

students does not differ significantly for the three methods.

Question Two

The second of the research questions concerned the ages

of the students in the study. An examination of the data

showed that the range of ages in Group I was 35 years (age 17

to age 52), and the range of ages in Group II was 17 years

(age 18 to age 35). In Group I, 18 (64.29%) of the 28 stu-

dents were less than 22 years old. In Group II, 17 (60.71%)

of the 28 students were less than 22 years old.

The question concerning age was the following: Does

the mean age of the students differ from one method group to









another? The statistical procedure used to answer this

question was a one-way analysis of variance. The null hypo-

thesis to be tested was


HO: MD = MN = MR'


where MD, MN, and MR are the mean ages for students who select

Method D, N, and R, respectively, as their favorite. The

analysis of variance procedure did not show any significant

differences between the mean ages of any of the three groups

D, N, and R (favorite method groups) for either Group I

(p < .91) or Group II (p < .48). Therefore, the null hypo-

thesis was not rejected for either Group I or Group II. The

mean ages for Group I, Group II, and the favorite method

groups in both Group I and Group II are found in Table 4.

Question Three

The third research question to be answered concerned

whether students of the same sex prefer the same method of

syllogism analysis. Table 5 displays, for Group I and

Group II, the number and percentage of students by sex who

prefer each of the three methods of testing syllogisms.

The null hypothesis to be tested was


HO PD PN R= R'


where PD is the percentage of males in Group D, PN is the

percentage of males in Group N, and PR is the percentage of

males in Group R.

Since some of the cell sizes were too small (n < 5)

for the usual chi-square test to be valid, an exact










Table 4

Mean Age of Students by Favorite Method
of Testing Syllogisms


Favorite
Method n % of Group Mean Age


Group I


D 9 32.14 24.22

N 13 46.43 22.62

R 6 21.43 23.00


Total 28 100.00 23.21


Group II


D 10 35.71 21.00

N 11 39.29 23.27

R 7 25.00 22.42


Total 28 100.00 22.25


Note: ANOVA was not significant for comparing ages in
either Group I (p < .91) or Group II (p < .48).










Table 5

Sex by Favorite Method of Testing Syllogisms


Favorite Sex
Method

Female Male Total


n % n % n %


Group I


D 3 10.71 6 21.43 9 32.14

N 6 21.43 7 25.00 13 46.43

R 2 7.14 4 14.29 6 21.43


Total 11 39.29 17 60.71 28 100.00


Group II


D 3 10.71 7 25.00 10 35.71

N 4 14.29 7 25.00 11 39.29

R 3 10.71 4 14.29 7 25.00


Total 10 35.71 18 64.29 28 100.00









conditional test of independence (Agresti & Wackerly, 1977)

was used to test the hypothesis. This test is similar to

chi-square, but is designed to be used on small samples.

The Wackerly-Agresti test is an extension of Fisher's exact

test, but is not restricted to 2x2 tables. The Wackerly-

Agresti statistic was used in the test, and an examination

of its test value showed that the statistic was not signi-

ficant for either Group I (p < .79) or Group II (p < .89).

Thus, the null hypothesis was not rejected for either group.

Question Four

The following question was investigated in this section:

Does personality type make a difference in which method of

syllogism analysis a student will prefer? In other words,

do students of opposite MBTI type elements prefer different

methods? Distributions of type elements by favorite method

are shown in Table 6. Mean preference scores for each type

element by favorite method are also shown in Table 6.

When the data were examined in terms of frequencies it

was noted that in several cases (El for both Group I and II,

and TF and JP for Group I) one method was preferred by stu-

dents of one type element, while the students of the oppo-

site type element preferred two methods equally (see Table 6).

The only scales on which students of opposite type elements

distinctly preferred different methods were SN in Group I

and SN, TF, and JP in Group II.

However, when strength of preference (in terms of mean

preference scores) was also taken into account, certain

tendencies appeared stronger. On the SN scale with respect










Table 6

Mean Preference Scores for Type Elements
by Favorite Method


Favorite Method
Type
Element
D N R


mean mean mean
n n n
score score score

Group I


E 4 16.5 8 30.5 3 20.3
I 5 30.6 5 27.0 3 24.3

S 1 1.0 9 20.6 1 35.0
N 8 22.3 4 14.5 5 15.0

T 8 19.5 8 16.3 3 10.3
F 1 19.0 5 21.8 3 13.0

J 3 24.3 7 25.3 2 13.0
P 6 27.0 6 16.3 4 18.0


Group II


E 5 11.8 5 18.2 3 13.7
I 5 29.0 6 33.0 4 33.5

S 6 24.0 5 7.0 5 22.6
N 4 15.5 6 36.7 2 26.0

T 4 15.5 7 18.4 4 34.0
F 6 13.3 4 16.5 3 17.0

J 3 27.7 5 17.8 3 23.7
P 7 32.1 6 33.3 4 23.0









to both S and N, the strongest preference for a particular

method was found with the highest frequency for that method

(with one exception in Group I). This finding occurred in

both Group I and Group II (see Table 6).

Since the tendency towards preference for a certain

method seemed to become clearer when frequency of preference

was examined together with strength of preference, mean

continuous scores were used in the statistical analysis for

this question. It should be noted that under some circum-

stances the use of mean continuous scores can have drawbacks

(Myers, 1962). Namely, frequency of preference and strength

of preference can become confounded with no clear information

as to either. In this study, however, separate examinations

with respect to frequency and strength indicated that mean

continuous scores used judiciously would not present a pro-

blem in these data. In fact, these scores yield more

information concerning the relationship of type element to

favorite method than the examination separately of strength

(using mean preference scores) and frequency.

Therefore, a one-way analysis of variance followed by

Duncan's multiple range test (when applicable) was utilized

to examine whether the mean scores for the four preference

variables (EI, SN, TF, and JP) were similar for each of the

three methods. The null hypothesis tested was


H : MD = M = MR'


where MD, MN, and MR are the mean continuous scores for each

method group with respect to a given preference variable.









The null hypothesis of no differences in the mean scores

of the three method groups, could not be rejected in either

Group I or Group II for the variables EI, TF, and JP. An

examination of the results for Group I with respect to the

variable SN showed a significant difference (p < .05) between

the means of Group D and Group N. Significant differences

(p < .05) were also found in Group II with respect to the SN

variable between the means of Group D and Group N, and between

the means of Group R and Group N. Thus, the null hypothesis

of no significant differences between the means of the three

method groups was rejected for the SN variable in both Group

I and Group II. The results of Duncan's multiple range test

for the SN variable are shown in Tables 7 and 8.

Question Five

Once the four preference variables of Myers-Briggs

personality theory and the variables of sex and age had been

investigated, the next step was to determine whether these

variables could be used to predict which method of syllogism

analysis a student would prefer. Stepwise discriminant

analysis was the procedure used to obtain the predictive

rules or discriminantt functions." The discriminant function

consists of predictor variables based on measurements obtained

on the individuals and a response variable which defines the

groups to which the individuals are assigned. In this study,

the predictor (independent) variables were sex, age, El

preference, SN preference, TF preference, and JP preference,

while the response (dependent) variable was method of syllo-

gism analysis.










Table 7

Results of Duncan's Multiple Range Test for MBTI
Variable SN for Group I


Favorite Method


D R N


n

Mean SN Score


Duncan Grouping


9

119.67


6

106.67


90.23


Note: Means not connected by a common line are
significantly different (p < .05).









Table 8

Results of Duncan's Multiple Range Test for MBTI
Variable SN for Group II


Favorite Method


N D R


n

Mean SN Score

Duncan Grouping


11

116.82


91.80


91.29


Note: Means not connected by a common line are
significantly different (p < .05).










A discussion of discriminant analysis was presented in

Chapter Three. In brief, discriminant analysis presupposes

two populations (or groups) to which individuals are to be

assigned, and measurements for each individual on p correlated

random variables X1, X2, . X. The procedure in dis-

criminant analysis is to form a linear combination of these

variables, for instance,


L = 1X1+ 32X2+ . + pXp


and then to assign a new individual to either of the two

groups on the basis of the value of L obtained (Kleinbaum &

Kupper, 1978). When there are more than two groups to which

individuals are to be assigned (as in this investigation)

more than one discriminant function is needed for the assign-

ment. Moreover, since the discriminant analysis for this

study utilized a stepwise procedure, not every variable

necessarily appears in the discriminant functions. Only

those variables meeting a certain criterion (p < .15) for

predictive ability are used.

According to Marks (1982), the assumptions for perform-

ing discriminant analysis are that the response or dependent

variable must be nominal (or be treated as nominal), that

the independent variables or factors are considered on a

continuous scale, and that each independent variable is

assumed to have a normal distribution. Although these are

the classical assumptions for discriminant analysis, cate-

gorical independent variables can be included in this model









through the proper use of dummy variables (Marks, 1982).

These assumptions are made for the data in the present study.

The results of the analysis of the Group I data will be

given first. An examination of each of the variables as

possible predictors of whether a student chose Method N as

his favorite, second favorite, or least favorite method

determined the following variables (in order of predictive

strength) to be important: SN, sex, and JP. The discriminant

functions for the data of Group I for Method N are given in

Table 9. The numbers across from "First Choice" in row 1

of Table 9 are the constant and the coefficients of the

variables SN, sex, and JP, respectively. Thus, the dis-

criminant function which best predicts Method N as first

choice (favorite method) is


Y1 = -10.79458667 + 0.14290670 (SN) 0.05241970 (sex)

+ 0.09287194 (JP).


Now, using the data for Student Number One (see Appendix D),

the value of the response variable Y1 can be computed

(coding sex as: M = 1, F = 0) as follows:


Y1 = -10.79458667 + 0.14290670 (73) 0.05241970 (1)

+ 0.09287194 (51)

= 4.32165167.

Likewise, the values for Y2 and Y3 (the response variables

for the functions which best predict Method N as second

choice and third choice, respectively) can be computed

using the numbers from the second and third rows in Table

9 as follows:

















Table 9

Linear Discriminant Functions for Predicting Method N
as First, Second, or Third Choice for Group I


Coefficients of Predictor Variables

Ranking of Response
Variable (Method N) Constant SN Sex JP


First Choice -10.79458667 0.14290670 -0.05241970 0.09287194

Second Choice -17.22839808 0.18335173 -1.20846870 0.12005299

Third Choice -15.73585505 0.20182943 1.86778098 0.06542500









Y2 = -17.22839808 + 0.18335173 (73) 1.20846870 (1)

+ 0.12005299 (51)

= 1.07051200.

Y3 = -15.73585505 + 0.20182943 (73) + 1.86778098 (1)

+ 0.06542500 (51)

= 4.20214932.

Thus, since the value of Y1 is larger than either Y2 or

Y3, the analysis classifies Student Number One as choosing

Method N as his first choice (favorite method). This agrees

with Student Number One's actual first choice (see Appendix

D). Hence, the discriminant functions correctly classified

Student Number One as to his preference for Method N. When

similar computations were performed on the data for the rest

of the students, a classification summary (see Table 10)

shows that the functions correctly predicted (classified) the

choices of 68% of the students as to whether they selected

Method N as their favorite, second favorite,or least favorite

method. On the basis of chance alone, correct predictions

would be expected to occur in only 33.3% of the cases.

An examination of the results of the analysis with

respect to Method D showed that variables TF and SN (in order

of predictive strength) were predictors of Method D's posi-

tion on an individual's preference list. Thus, TF and SN

were used to form the discriminant functions (see Table 11).

Again, the functions correctly predicted the choices of 68%

of the students as to their preference for Method D as

favorite, second favorite, or least favorite method (see

Table 12). The results of the analysis with respect to













Table 10

Classification Summary for Predicting Method N from
Discriminant Functions for Group I


From Classified into Method N
Method N

First Choice Second Choice Third Choice Total


n % n % n % n


First Choice 8 61.54 3 23.08 2 15.38 13 100.00

Second Choice 1 11.11 7 77.78 1 11.11 9 100.00

Third Choice 1 16.67 1 16.67 4 66.67 6 100.00


Total 10 35.71 11 39.29 7 25.00 28 100.00


Note: The functions correctly predicted the choices with respect to
Method N of 68% of the students.

















Table 11

Linear Discriminant Functions for Predicting Method D
as First, Second, or Third Choice for Group I


Coefficients of Predictor Variables


Ranking of Response
Variable (Method D) Constant- TF SN


First Choice -21.83368459 0.22159782 0.20791753

Second Choice -19.33484743 0.25945851 0.15342524

Third Choice -24.58938269 0.31889931 0.14514857














Table 12


Classification Summary for Predicting Method D
from Discriminant Functions for Group I


Classified into Method D
From
Method D
First Choice Second Choice Third Choice Total


n % n % n % n %


First Choice 6 66.67 2 22.22 1 11.11 9 100.00

Second Choice 3 25.00 8 66.67 1 8.33 12 100.00

Third Choice 1 14.29 1 14.29 5 71.43 7 100.00


Total 10 35.71 11 39.29 7 25.00 28 100.00


Note: The functions correctly predicted the choices with respect to
Method D of 68% of the students.









Method R did not yield any variables of sufficient predictive

strength to allow for the formation of useful discriminant

functions.

When each of the variables was analyzed for its ability

to predict an individual student's favorite method, the vari-

ables SN and TF (in order of strength) were found to be pre-

dictors. Table 13 displays the discriminant functions which

were produced for predicting which of the three methods of

testing syllogisms a student would choose as his favorite.

The functions in this case correctly predicted the choices

of 64% of the students as to their favorite method of testing

syllogisms (see Table 14). This is as opposed to a 33.3%

prediction rate on the basis of chance alone.

An examination of the results of the discriminant analysis

of the Group II data produced the following results. Of the

six variables--age, sex, El preference, SN preference, TF

preference, and JP preference--the variables SN and JP (in

order of strength) were found to be predictors in determining

whether a student would select Method N as his favorite, his

second favorite, or his least favorite method. Using SN and

JP as predictor variables, 71% of the students were correctly

classified as to where Method N was placed on an individual's

preference list (see Table 15). This is as opposed to a

33.3% correct classification which would be expected by chance.

This analysis of Method N in Group II is the first situa-

tion where the covariance matrices for the three different

groups (choice 1, choice 2, or choice 3) were not similar.

In such cases the discriminant analysis uses a pooled error
















Table 13

Linear Discriminant Functions for Predicting Favorite
Method as Method D, N, or R for Group I


Coefficients of Predictor Variables
Response Variable
(Favorite Method)
Constant SN TF


Method D -22.09164251 0.23685856 0.18683210

Method N -19.06237085 0.16465069 0.23650226

Method R -22.76445068 0.20070121 0.23803394












Table 14


Classification Summary for Predicting Favorite Method
from Discriminant Functions for Group I


From Classified into Favorite Method
Favorite
Method
D N R Total


n % n % n % n %


D 8 88.89 0 0.00 1 11.11 9 100.00

N 4 30.77 7 53.85 2 15.38 13 100.00

R 2 33.33 1 16.67 3 50.00 6 100.00


Total 14 50.00 8 28.57 6 21.43 28 100.00


Note: The functions correctly predicted the choices with respect to
favorite method of 64% of the students.













Table 15


Classification Summary for Predicting Method N
from Discriminant Functions for Group II


From Classified into Method N
Method N
First Choice Second Choice Third Choice Total


n % n % n n %


First Choice 9 81.82 2 18.18 0 0.00 11 100.00

Second Choice 5 41.67 6 50.00 1 8.33 12 100.00

Third Choice 0 0.00 0 0.00 5 100.00 5 100.00


Total 14 50.00 8 28.57 6 21.43 28 100.00


Note: The functions correctly predicted the choices with respect to
Method N of 71% of the students.









variance from all three groups rather than the individual

covariance matrices. In this situation the equations become

too complex to display easily, and, thus, do not appear in

these results. If they were to be used prospectively, the

computations would have to be done on computer (Kendall &

Stuart, 1968, p. 266 and p. 282). For Method D and Method

R, no variables of sufficient predictive strength were pro-

duced in the discriminant analysis to allow for the

formation of useful discriminant functions.

When each of the variables was analyzed for its ability

to predict an individual's favorite method, the variables SN

and JP (in order of strength) were found to be predictors.

Thus, discriminant functions were produced by the analysis

for predicting which of the three methods of testing syllo-

gisms a student would choose as his favorite. The functions,

in this case, correctly predicted the choices of 54% of the

students as to their favorite-method of syllogism analysis.

The functions generated by the discriminant analysis to

predict favorite method from Group II data are found in

Table 16, and the corresponding classification summary is

found in Table 17.
















Table 16

Linear Discriminant Functions for Predicting Favorite
Method as Method D, N, or R for Group II


Coefficients of Predictor Variables
Response Variable
(Favorite Method)
Constant SN JP


Method D -8.46876217 0.08533209 0.07972013

Method N -11.33997792 0.16276173 0.03330362

Method R -7.51537912 0.10460652 0.05442800













Table 17


Classification Summary for Predicting Favorite Method
from Discriminant Functions for Group II


From Classified into Favorite Method
Favorite
Method
D N R Total


n % n % n % n


D 5 50.00 3 30.00 2 20.00 10 100.00

N 1 9.09 7 63.64 3 27.27 11 100.00

R 2 28.57 2 28.57 3 42.86 7 100.00


Total 8 28.57 12 42.86 8 28.57 28 100.00


Note: The functions correctly predicted the choices with respect to
favorite method of 54% of the students.
















CHAPTER FIVE
SUMMARY, DISCUSSION, AND CONCLUSIONS

The Study

This study was designed to investigate the relation-

ship between a community college student's personality type

and his choice of method in testing a categorical syllogism

for validity. Subjects used in the investigation were 56

community college students enrolled in an introductory logic

course. Half of the students (Group I) were enrolled during

the winter term, 1984, and half (Group II) were enrolled

during the spring term of the same year.

Two test instruments were utilized in the study: the

Myers-Briggs Type Indicator (MBTI) and the Preferred Methods

Test (PMT). The MBTI was used to determine the students'

personality types. A self-reporting personality inventory,

the MBTI aims to ascertain an individual's basic prefer-

ences along four dichotomous indices (Myers, 1962). The

indices are

El (Extraversion or Introversion)

SN (Sensing or Intuition)

TF (Thinking or Feeling)

JP (Judgment or Perception)

An individual's personality type is described by a four-

letter combination (INTJ, ESTP, et cetera), where each letter

reflects the individual's reported preference on a particular









index of the MBTI. The eight letters denoting preference are

referred to as type elements.

The PMT, consisting of three categorical syllogisms which

the students analyzed by means of three different syllogism-

testing methods, was employed to determine the order of each

student's preference for the methods. The PMT was designed

and developed by the investigator to obtain information as to

a student's favorite, second favorite, and least favorite

method of testing syllogisms. The three methods investigated

in this study were the Venn diagram method (Method D), a

numerical method (Method N), and the syllogism rules method

(Method R). Each method represented a different processing

mode, either figural, symbolic, or semantic. Each student's

order of preference was recorded as three letters (e.g.,

DNR, RDN) representing the order in which he preferred the

methods from favorite to least favorite.

A theoretical framework for this study was discussed in

Chapter Two. Theory for this study was drawn mainly from two

sources. One source is the personality theory which forms

the basis for the MBTI. This theory, based on the work of

Carl Jung, was developed by Isabel Briggs Myers. According

to Myers (1962), personality types are patterns which indi-

cate the way people prefer to perceive and judge, the world

they prefer to perceive and judge in, and the kind of process

(perception or judgment) they prefer to use. The scores of

the MBTI generate 16 such personality types, each with its

own excellence and valuable contributions (McCaulley, 1976).









The second source of theory on which this investigation

was based is J.P. Guilford's (1959) personality theory, a

factor analytic approach to personality and intelligence.

Guilford's part of the framework for this study consists of

his structure-of-intellect model which contains content

classifications for the identified factors or components of

the intellect. Three types of content in the model are

figural, symbolic, and semantic. The processing modes

investigated in this study are defined by Guilford's content

classifications. These three classifications or processing

modes are represented in this study by three methods of

syllogism analysis: the Venn diagram method (figural), a

numerical method (symbolic), and the syllogism rules method

(semantic).

Results and Discussion

There were five questions posed in Chapter One of this

study. The results of the analysis of the data were pre-

sented in Chapter Four. The first question investigated

whether students differ in their choice of method for test-

ing syllogisms for validity. The data showed that each of

the three methods was chosen by at least 21% of the subjects

in Group I and in Group II. Thus, the students did differ

in their choice of method. This result was substantiated

by a chi-square test which showed there were no significant

differences between any of the three method groups for

Group I or Group II.

The second question involved the relationship of student

age and choice of method. An analysis of the data showed that









there were no significant differences in the mean ages for

the three method groups. However, since most of the stu-

dents were in their late teens and twenties, with only a

relatively few students above age 35 (three from Group I,

none from Group II) the results concerning age should be

regarded cautiously when generalizing to populations with

a large percentage of students over age 35.

In order to answer the third question, the relationship

of sex to method of syllogism analysis was examined. The

results of the statistical analysis indicated that the

methods favored by males are not different from those

favored by females.

The fourth question under consideration in this investi-

gation concerned whether students of opposite MBTI type

elements prefer different methods of syllogism analysis.

The data were examined in terms of strength of MBTI scores

as well as frequency of MBTI preference. For the statistical

procedures which were used, mean continuous scores, which

combine strength of preference and frequency of preference,

were employed. The results of these statistical procedures

(one-way analysis of variance and Duncan's multiple range

test) confirmed the findings which were already indicated

by inspection of Table 6. Thus, the use of mean continuous

scores accorded the investigator a stronger statistical base

from which to report the following findings concerning the

relationship of certain MBTI type elements to preferred

method of syllogism analysis.









Results of the statistical procedures showed that, in

both Group I and Group II with respect to the SN variable,

Group N (those who preferred Method N) differed signifi-

cantly from one or both of the other two method groups in

choice of method of syllogism analysis. The results also

showed that the Sensors (S) in Group I chose a different

method from the Sensors in Group II, and that the Intui-

tives (N) in Group I chose a different method from the

Intuitives in Group II. The Sensors in Group I preferred

Method N while the Sensors in Group II preferred Method D

or Method R. The Intuitives in Group I preferred Method

D while in Group II the Intuitives preferred Method N.

These preferences were noted both in the frequency table

for the methods (Table 6) and in the statistical analysis

employing Duncan's multiple range test (see Table 7).

This difference in the choices of the Sensors in the

two groups and the difference in the choices of the Intui-

tives in the two groups may be a result of differences in

the terms in which the students were enrolled. Group I

students were enrolled during a 15-week regular term.

Classes met every other day. Group II students were en-

rolled in a seven-week term. Classes met every week day.

Thus, the learning pace was different for the two terms.

Since Sensors are characteristically precise, detailed

learners, who prefer to move step-by-step through a new

experience, it would seem that Sensors would learn best under

a schedule which allowed them time to go through new pro-

cedures thoroughly before moving on to other material. Thus,









the 15-week terms would appear to be more conducive to

sensory learning than would the short seven-week terms.

In contrast, Intuitives work in bursts of insight and

enthusiasm, and, once the main concept of the new material

is grasped, become impatient to move on to other material.

Thus, Intuitives may prefer a fast-paced seven-week term.

These characteristics of the Sensors and the Intuitives

with respect to the learning pace of the term may have had

some bearing on their choice of method.

It is possible, too, that students who enroll in the

short term are different from those students who enroll in

the regular term. The short terms (offered in late spring

and summer) are often considered optional "summer" terms

offered for students who want to complete their 64 credit

hour program in less than the usual two years. Thus, those

students enrolled in the short terms may be more motivated

(intellectually, financially, et cetera) than those who opt

to attend only the regular terms (offered in the fall and

winter). The students enrolled in the short terms may be

students who feel more capable of handling a fast-paced

term than those who enroll only for regular length terms.

Those enrolled in the short term may also be motivated

financially to finish their formal education and obtain a

monetarily rewarding job as quickly as possible. These

and other reasons may account for the differences between

Group I and Group II. Further research is needed to investi-

gate these differences fully.










In the analysis of the data with respect to Question

Five, stepwise discriminant analysis (Marks, 1982; Kleinbaum

& Kupper, 1978) was used to determine if the variables of sex,

age, and MBTI scores could be used to predict the method of

syllogism analysis that a given individual would prefer. This

statistical procedure proved to be highly informative and

yielded results which were both interesting and significant.

Predictive discriminantt) functions were generated by

the discriminant analysis procedure. In Group I, for each

of the two methods, N and D, a set of functions was obtained

for predicting the method as favorite, second favorite, or

least favorite for each student. A third set of functions

predicted each student's favorite method. The mean rate of

correct classification (prediction) for Group I was 67%.

In Group II, functions were obtained for predicting

Method N as favorite, second favorite, or least favorite

method for each student. Another set of functions predicted

each student's favorite method. The mean rate of correct

classification for Group II was 63%. The mean expected

correct classification rate in both groups would be only

33.3% on the basis of chance alone.

The variable SN was a predictor in all of the functions

of both groups. In addition, either JP or TF appeared in

each function. The variable sex was the only other variable

to appear, and it appeared only in the functions used to

predict Method N as first, second, or third choice in Group

I.









Conclusions

Analysis of the data yielded results which supported the

basic premise of this study--that there is a relationship

between certain personality traits of the student concerning

his preferred ways of perceiving information and the stu-

dent's choice of mode for processing the content material.

Not only has such a relationship been shown, but the statis-

tical procedure of stepwise discriminant analysis produced

discriminant functions which demonstrate that for the two

groups in this study the method of analysis which was chosen

by a student was predictable with a rate which was approxi-

mately twice the chance prediction rate. These results

indicate that a definite relationship between the variables

of MBTI type and preferred processing mode does exist and

that it is predictable.

An additional finding in this study which has parti-

cular significance for teachers is that Method N, the non-

traditional technique of analyzing syllogisms, was the

technique chosen as the favorite by more students than any

other method. Most textbooks include Method D and Method

R as traditional ways of testing syllogisms for validity,

but Method N (the numerical method) is not found in standard

introductory logic texts. The fact that Method N was the

preferred method indicates that traditional approaches to

problem-solving are not necessarily the ones which students

choose when given an option. Since it is assumed that

students learn best when using methods which they prefer,

this finding suggests that teachers should consider a









variety of problem-solving methods, not just the standard

ones, in their instructional planning.

Implications for Instruction

In recent years, teachers have been encouraged to use a

variety of presentational modes (laboratory demonstration,

lecture, media presentation, et cetera) to enhance the

effectiveness of their instruction, but little has been said

with regard to the processing modes (visual, figural, or

semantic) that students prefer to use as they solve problems.

The results of this study show that students do have a

preference as to which processing mode they prefer for solving

logic problems syllogismss). This would seem likely to be

true of other content areas as well. Thus, teachers should

endeavor to present problem-solving methods which represent

as many processing modes as possible. This would afford

students maximum opportunity to work within their preferred

cognitive style areas, thus enabling them to perceive and

evaluate problems under conditions most conducive to

successful problem-solving.

Since the MBTI has been shown in this study to provide

information on personality type which allows prediction of

which method a student will prefer to use, teachers should

make use of the MBTI in obtaining very useful information as

to the ways a student prefers to solve problems (and, thus,

probably solves them best). This will help to promote in-

struction which is best suited to the personality type

(preferences) of the student.









Suggestions for Future Research

Following are suggestions for future research studies:

1. Use students all from the same term or from similar

terms (ie., all regular or all short terms) to control for

the observed differences in the terms.

2. Use a different content area, such as mathematics

(as opposed to logic), to determine if similar results are

obtained. An example of the use of different processing

modes in mathematics, for instance, would be to use both

graphing (visual) and algebraic (symbolic) methods to solve

a system of two linear equations in two unknowns. Other

content areas could be considered as well.

3. Include a survey questionnaire or conduct an

interview with each student to determine why the student

preferred one method and disliked another.

4. Replicate the study to investigate further the

observed differences between Sensors and Intuitives with

respect to each other and with respect to term length.




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