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This is to certify that the

thesis entitled
An Empirical Investigation of The
Behavioral Dimensions of Four
Tests of Learning Disabilities

presented by

Jerry Blickman Crittenden

has been accepted towards fulfillment

of the requirements for

Ph.D. degree in Education

 

Major professor

Date WC ‘7

 

 

 

 

 

 

 

I.

 

 

 

ABSTRACT

AN EMPIRICAL INVESTIGATION OF THE BEHAVIORAL DIMENSIONS
OF FOUR TESTS OF LEARNING DISABILITIES

BY

Jerry Blickman Crittenden

Diagnosis of learning disabilities in children requires
the use of a number of time-consuming individually administered
tests. These tests are based upon tasks designed by the author
to conform to the test's theoretical dimensions or factors,
but these factors are often inconsistent with empirical data.
The major objective of the present study was to identify the
dimensions which underlie four tests used for the diagnosis
and remediation of learning disabilities. The tests used in
this study were: the Illinois Test of Psycholinguistic Abili-
ties, Revised Edition (ITPA); the Marianne Frostig Developmen-
tal Test of Visual Perception (DTVP); the Wepman Auditory Dis-
crimination Test (WADT); and the Purdue Perceptual Motor Survey
(PPMS).

A theoretical framework for hypothesizing a factor struc—
ture for this test battery came from Guilford's Structure of
Intellect Model and his Matrix of Psychomotor Abilities. Six—
teen dimensions were hypothesized to explain the factorial
composition of the 28 sub—tests in the test battery.

Data collected from 305 disadvantaged kindergarten children
were submitted to Principal Axis Factor Analysis with Varimax

Rotation. The resulting factor analyses were interpreted for

 

Jerry Blickman Crittenden

a Four-Test Battery on 93 $5, a Three-Test Battery (excluding
the PPMS) on 305 Ss, and each test for 305 $5. In addition,

a Two-Way Analysis of Variance and Multiple Regression Analyses
were done, the former to determine the extent to which experi-
mental controls for age and sex were present in this study,

and the latter to identify a set of sub-test variables that
predict I.Q.

The results showed the factorial nature of this battery
of tests was best represented by nine dimensions described by
Guilford. These were: (a) Cognition of Sematic Relations
(CMR); (b) Convergent Production of Semantic Relations (NMR);
(c) Memory for Symbolic Systems (MSS); (d) Cognition of Figural
Systems (CFS); (e) Evaluation of Symbolic Units (ESU); (f)
Trunk Strength and Limb Flexibility; (g) Limb Impulsion and
Gross Coordination; (h) Limb and Gross Precision; and (i)
Memory for Figural Units (MFU).

The factorial nature of the individual tests in the
battery is best explained as follows: (a) the ITPA is repre-
sented by the first three dimensions above; (b) the DTVP is
represented by the fourth dimension listed above; (c) the WADT
is represented by the fifth dimension above, and (d) the PPMS
is represented by the remaining four dimensions given above.

The nine sub-tests of this battery most highly associated
with nine factors were, respectively: (a) Visual Reception;
(b) Verbal Expression; (c) Auditory Sequential Memory; (d)
Spatial Relations; (e) the WADT; (f) Angels-in-the-Snow;

(g) Jumping; (h) Identification of Body Parts; and (i) chalkboard.

 

Jerry Blickman Crittenden

These nine sub-tests should provide the same factorial data

the entire battery would when administered to disadvantaged 53.
Also, these sub—tests appear to reduce significantly the time
needed to gather data representative of the battery's factorial
nature.

A comparison of the hypotheses and the empirical data
resulted in the confirmation of one hypothesis. Confirmation
was determined by the degree of congruence between the variables
predicted to associate with a hypothetical factor, and those
associated with its empirically determined counterpart. However,
the empirical factor structure had its associated variables
loaded with the empirical factors in a manner which demonstrated
a psychologically meaningful relationship. These results seemed
to mitigate the overprediction that resulted in the hypothetical
factor structure.

The results of the Two—Way Analysis of Variance showed
significant F-Ratios for age and sex on two factors. Age
appeared to affect the results of the DTVP testing when the
55 were twelve months apart in age. Main effects resulted for
sex and age on the factor loaded by the ITPA's reception,
association, and closure sub—tests. Males and females differed
significantly on those variables, and as age increased the 85'
scores increased.

It was shown that four sub-tests seemed to predict I.Q.
better than all others. These sub-tests were: (a) Auditory
Association, (b) Auditory Sequential Memory, (c) Grammatic

Closure, and (d) Spatial Relations.

 

Jerry Blickman Crittenden

The results of this investigation led to the conclusion
that a factorial model of the intellectual and psychomotor
abilities present in disadvantaged Ss probably should contain
at least six intellectual abilities and three psychomotor
abilities. While the emphasis of this study is on the structure
of the tests, it also appears possible that the disadvantaged
85 do not attain the ability skills necessary to adequately
differentiate the underlying dimensions of this battery of
four tests. Furthermore, the results suggested that a different

model of ability dimenSions may exist for the disadvantaged Ss.

 

AN EMPIRICAL INVESTIGATION OF THE
BEHAVIORAL DIMENSIONS OF FOUR TESTS

OF LEARNING DISABILITIES

BY

Jerry Blickman Crittenden

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

College of Education
Department of Elementary and Special Education

1969

 

DEDICATION

This study, such as it is, is fondly dedicated to my
mother, who did not see its completion, but who was always
sure I would finish what I set out to do.

ii

 

 

 

ACKNOWLEDGEMENT

I would like to thank my dissertation committee chairman,
Dr. Clessen Martin, for the help he gave me in completing this
study. I would also like to thank the members of my committee:
Dr. William Hicks, Dr. John Jordan, Dr. Jean LePere, and Dr.
Ruth Brend. Especial thanks go to the "Little Mother" of Spe-
cial Education doctoral students, Mrs. Vivian Stevenson, for
smoothing the rough road a doctoral candidate travels. Dr.
Jane Bonnell and Mrs. Joan Webster provided immeasurable service
in resolving problems during the data collection in the Grand
Rapids Public Schools. To Mr. Robert Cross, who helped to
recruit my examiners, and to Dr. Frank Heger, who trained
them and otherwise gave wise counsel, I give thanks. The
13 examiners who did the testing deserve my gratitude because
this study would not have been completed without them. And
to my two sounding boards for wild ideas and wise advice, Drs.
William Lashbrook and Joseph Ascroft, go special thanks for
seeing my foibles and follies and protecting me from them.
My typists, Mrs. Carole Winely and Mrs. Joan Lingle, who
read rough copy beautifully and type rapidly, were gems. And,
to the two secretaries, in the Grand Rapids Public Schools,
Mrs. Helen Cameron and Miss Jean Brown, go my profoundest
thanks for the thousand phone calls received and made to keep
my study on its schedule. To Burt Rodee, who suffered and
commisserated with me during our years together as graduate
students, goes thanks for many timely and needed favors.
Nearly last and certainly not least, I owe much to the patience
and forebearance of my family; my wife, Rae, and my children,
Steven and Trisa, during the graduate grind. Everyone, who
has had this experience, knows that without the support of
his immediate family, a doctoral student would not be able
to complete the degree. Grateful thanks to all these persons
is little enough for the benefits derived by me from having
known all these friendly dedicated peOple.

i

 

TABLE OF CONTENTS

Page
DEDI CAII‘IOIq O O Q 0 O I O O I I C O O C I O O I O b O I I ii
ACKNOWLEDGEMENT . . . . . . . . . . . . . . . . . . . . iii
LIST OF TABLES. O O 0 O I O O I O I I I I C O 0 I I O 0 vi

LIST OF FIGURES O D O I U . I O O O O 0 . O I D D I C ' Vii

CHAPTER I PROBLEM STATEMENT . . . . . . . . . . . . . . 1
Test Descriptions. . . . . . . . . . . . . . . . . 2
The Illinois Test of Psycholinguistic
Abilities. . . . . . . . . 2
The Frostig Developmental Test of Visual
Perception . . . . . . . . . . . . . . . 8
The Purdue Perceptual Motor Survey. . . . . . 9
The Wepman Auditory Discrimination Test . . . 12
Review of Research . . . . . . . . . . . . . . . . 13
General Theoretical Models — The Structure
of Intellect . . . . . . . . . . . . . . 13
General Theoretical Models — Psychomotor
Abilities. . . . . . . . . . . . . . . . 14
ITPA Factor Studies . . . . . . . . . . . . . l6
DTVP Factor Studies . . . . . . . . . . . . . 21
PPMS Factor Study . . . . . . . . . . . . . . 23
WADT. . . . . . . . . . . . . . . . . . . 25
Summary of Research Review. . . . . . . . . . 25
Hypothesized Factor Structure. . . . . . . . . . . 25

CHAPTER II METHODOLOGY AND PROCEDURES

Subjects . . . . . . . . . . . . . . . . . . 30
Instrumentation and Procedures . . . . . . . . . . 32
Examiner Training. . . . . . . . . . . . . . . . . 33
Data Collection. . . . . . . . . . . . . . . . . . 34
Statistical Analyses . . . . . . . . . . . . . . . 34

CHAPTER III RESULTS

Factor Analyses: Introduction . . . . . . . . . . 38
Factor Analyses: Three-Test Battery . . . . . . . 39
Factor Analyses: The ITPA . . . . . . . . . . . . 50
Factor Analyses: The DTVP . . . . . . . . . . . 57
Factor Analyses: Four— Test Battery. . . . . . . . 62

iv

1
_
1

 

Table of Contents (cont.)
Factor Analyses: The PPMS . . .
Factor Analyses: Summary. . . .
TWO-Way Analysis of Variance:
Multiple Regression Analysis:

Delete and Least Squares

CHAPTER IV DISCUSSION AND CONCLUSIONS

0 o o 0 o 0 0

Age and Sex . .
Least Squares
Add Programs . .

Hypotheses Confirmation: A Comparison of the
Hypothesized Factor Structure and the
Empirical Factor Structure. . . . . . . . .

Limitations of the Study . . . . . . . . . . . .

Implications for Future Research . . . . . . . .

Sumary. O O I I O O C C O O I O C O O O U 0 O O O

BIBLIOGRAPHY. I C O O O I D O O O O O O I O O C C O O 0
APPENDIX. 0 I C C O O I O O O C O O O Q l l O I C O O 0
l a. Means and Standard Deviations for Four
Test Battery. . . . . . . . . . . . . . .
b. Intercorrelation Matrix of All Variables
for Four Tests. . . . . . . . . . . . . .
c. Means and Standard Deviations for Three
Test Battery. . . . . . . . . . . . . . .
d. Intercorrelation Matrix for Three
Test Battery. . . . . . . . . . . . . . .
. Intercorrelation Matrix for the PPMS. . .
Intercorrelation Matrix for the ITPA. . .
g. Intercorrelation Matrix for the DTVP. . .
2 a. Intercorrelation Matrix for the PPMS
(Roach and Kephart) . . . . . . . . . . .
b. Varimax Rotation for PPMS (Roach and

Kephart) a O o o o c o a a o o c o o o o c

Page
77
89
94

96
118
118
120
125

130

130

131

132

133
134
135
136

137

138

 

Table

10

ll

12

13

14

15

16

LIST OF TABLES

Matrix of Psychomotor Abilities.;. . . . . . .
Correspondence of PPMS Tasks in Each of the
Author's "Major Area of Performance" to the
Writer's Factor Analysis of the PPMS
Intercorrelation Matrix. . . . . . . . . . . .

Hypothesized Factor Atructure of Four Tests
of Learning Disabilities . . . . . . . . . . .

Composition of Sample-Groups for Analysis. . .
Abbreviations Used in the Data Report. . . . .
Varimax Rotation Factor Loadings of All
Variables for Three Tests (Five Factor

Solution). . . . . . . . . . . . . . . . . . .

Factor I Five Factor Solution on Three-Test
Battery. 0 O O O O O I O O O O O I I O C O I .

Factor II Five Factor Solution on Three-Test
Battery. 0 O I O I I O O O O I C O I O O I C I

Factor III Five Factor Solution on Three—Test
Battery. 0 I I O I O O O I I O O I O I 0 O I I

Factor IV Five Factor Solution on Three—Test
Bsttery. . . . . . . . . . . . . . . . . . . .

Factor V Five Factor Solution on Three-Test
Battery I I I O I I O I I 0 O I O O 0 I I l I O

Varimax Rotation Factor Loadings of All
Variables for the ITPA (Three-Factor

SOlution C U U C O O O I I O O C C C 0 I I I I
Factor I Three-Factor Solution of the ITPA . .
Factor II Three—Factor Solution of the ITPA. .
Factor III Three-Factor Solution of the ITPA .

Varimax Rotation Factor Loadings of All
Variables for the DTVP (Two Factor—Solution)

0

vi

Page

17

24

26

31

40

42

43

45

46

48

59

52

53

55

56

58

Table

17
18
19

20

21

22

23

24

25

26

27

28

29

30
31
32
33
34

35
36

LIST OF TABLES (Cont'd.)

Factor I Two-Factor Solution of the DTVP. . . .
Factor II Two-Factor Solution of the DTVP . . .

Varimax Rotation Factor Loadings of All
Variables for Four Tests (Nine-Factor Solution)

Factor I Nine-Factor Solution on Four—Test
Battery I I Q I I I I I I I I I I o I I I I I I

Factor II Nine-Factor Solution on Four-Test
Battery I I I I I I I I I I I I I I I I O I I 0

Factor III Nine-Factor Solution on Four—Test
Battery I I I I I I O I O I I I I I I I O I I I

Factor IV Nine-Factor Solution on Four—Test
Battery I D I I O I I I I I I I I I I I I I I I

Factor V Nine—Factor Solution on Four-Test
Battery 0 O I I I O I C I I O O O I U I I Q I 0

Factor VI Nine—Factor Solution on Four-Test
Battery I I I I I O I I I I I I I I I I I I I I

Factor VII Nine-Factor Solution on Four-Test
Battery I I I I I I I I I I I I I O I I I I I I

Factor VIII Nine—Factor Solution on Four—Test
Battery I I I I O C O I I I I I O I I I I I I I

Factor IX Nine-Factor Solution on Four—Test
Battery I I I I I O I I I I I I I I I I O I I I

Varimax Rotation Factor Loadings of All
Variables for the PPMS (Four—Factor Solution) .

Factor I Four-Factor Solution on the PPMS . . .
Factor II Four-Factor Solution on the PPMS. . .
Factor III Four-Factor Solution on the PPMS . .
Factor IV Four—Factor Solution on the PPMS. . .

A Summary of the Factor Structure of the
Four Tests. I I 0 I I I I I I I I I I I I I O I

Two-Way Analysis of Variance Factor I . ._. . .
Two—Way Analysis of Variance Factor V . . . . .

vii

Page
59
61

63

64

66

67

69

7O

72

73

75

76

79
80
81
83

84

86
92

93

 

LIST OF FIGURES

Figure Page

1 Changes in Sub-test Nomenclature for the

Revised Edition of the ITPA . . . . . . . . . . . 3
2 Three-Dimensional Model of the ITPA . . . . . . . 5
3 The Structure of Intellect. . . . . . . . . . . . 15

4 A Comparison of the Hypothesized Factor Structure
and the Empirical Factor Structure. . . . . . . . 99

viii

CHAPTER I

PROBLEM STATEMENT

 

What are the factors which underlie four of the major
diagnostic tests of learning disability? Presumably, each of
the theoretically derived sub-tests represents a distinct
dimension. The major question of the present study is: would
an empirical analysis of the data obtained through administer-
ing these tests support such an assumption? An examination of
the recent history of the learning disability movement in edu-
cation discloses many divergent theories (Bateman, 1966) con-
cerning the diagnosis and remediation of learning disability.
These theories have given rise to numerous measures such as
the Illinois Test of Psycholinguistic Abilities (ITPA), the

Marianne Frostig Developmental Test of Visual Perception

 

(DTVP), the Wepman Auditory Discrimination Test (WADT), and

 

the Purdue Perceptual Motor Survey (PPMS). These tests of

 

learning disabilities present a variety of tasks assumed to

be of diagnostic and remedial value. The tasks often do not
factor according to the theory underlying them when subjected
to a rigorous analysis. That they do not is supported by
considerable evidence: Meyers, 1968; Sprague, 1963; Hueftle,
1967; Thams, 1955; and others. This lack of congruity between
hypothesized dimensions and empirical dimensions represents a

crucial failure in test validity.

The major purpose of this investigation was to establish
the dimensions which underlie a battery of four tests of
learning disability. These dimensions permit parsimonious
description of the abilities assessed by the battery. In
addition, their identification assures the selection of the
smallest possible set of tasks which will yield data comparable
to that obtained by the present battery. An analysis of the
items comprising the factors found as a result of the present
study may be used as a model for a comprehensive test for
learning disabilities.

Before stating the a priori hypotheses regarding the manner
in which the tasks were predicted to cluster, a description of
the tests and a research review are necessary. The former
provides prima facie evidence and the latter empirical sub-
stantiation for the rationale supporting these a priori

hypotheses.

Test Description

The Illinois Test of Psycholinguistic Abilities (ITPA) (See
Figure I)

The Illinois Test of Psycholinguistic Abilities (ITPA)

 

developed by McCarthy and Kirk (1961) provides information
about a child's psycholinguistic capabilities. Psycholinguis—
tic deficiencies found by this diagnostic battery become the
basis of a specific remedial program for the child. Currently
the authors have developed tests for ten psycholinguistic
abilities (Kirk, McCarthy, and Kirk, 1968). These tests,

based upon a theoretical model proposed by the authors

Sub-test Nomenclature

 

Revised Edition (1969)

 

Auditory Reception

Visual Reception

Visual Sequential Memory
Auditory Association
Auditory Sequential Memory
Visual Association

Visual Closurea
Verbal Expression

Grammatic Closure

Manual Expression

Figure 1.

Experimental Edition (1961)

 

Auditory Decoding

Visual Decoding

Visual Motor Sequencing
Auditory Vocal Association
Auditory Vocal Sequencing

Visual Motor Association

Vocal Encoding
Auditory Vocal Automatic

Motor Encoding

Changes in Sub-test Nomenclature for

the Revised Edition of the ITPA

 

Note - In the research review, this writer changed
the sub-test names to conform with the new

nomenclature.

aA new test added to the Revised Edition.

 

(see Figure 2), are derived from Osgood's elaborated extension
of Hull's formulations regarding psycholinguistic abilities.
Each psycholinguistic ability, proposed by Kirk, has three
dimensions, derived from the theoretical model, which are as
follows:

1. Channels of Communication. These are the routes
through which the content of communication flows.
Included here are the modalities through which sense
impressions are received and the forms of expression
through which a re5ponse is made. The channels may
include various Combinations of sensory input and
response output. The major modes of input are auditory
and visual; those of output are vocal and motor.

2. Psycholinguistic Processes. In analyzing behavior
which occurs in the acquisition and use of language,
three main processes are considered: (a) the receptive
process, that is, that ability necessary to recognize
and/or understand what is seen or heard; (b) the ex-
pressive process, that is, those skills necessary to
express ideas or to respond either vocally or by
gesture or movement; (c) an organizing process which
involves the internal manipulation of percepts, con-
cepts, and linguistic symbols.

3. Levels of Organization. The degree to which
habits of communication are organized within the in-
dividual determines the level of functioning. Two
levels are postulated in the clinical model of the
ITPA: (a) the representational level, which requires
the more complex mediating process of utilizing
symbols which carry the meaning of an object; (b)
the automatic level, in which the individual's habits
of functioning are less voluntary but highly organized
and integrated. (Kirk, McCarthy, and Kirk, 1968. Page 7.)

The ten tests used in the ITPA are not an exhaustive set
of psycholinguistic abilities. Kirk and McCarthy indicated
that the testing of some abilities will have to await develop-
ment of suitable task techniques (1961; page 7). This obser-
vation was confirmed by the revised ITPA edition of Fall, 1968.
It added one additional and two supplemental skills at the

automatic level. The new test, visual closure, is described

EXPRESSIVE PROCESS

  
   
 
     
  
       

ORGANIZING PROCESS
RECEPTIVE PROCESS

REPRESENTATIONAL LEVEL

 
 
 

vusuAl
gechON

AUTOMAIIC LEVEL

AUDITORY STIMULI VOCAL RESPONSE

VISUAL STIMULI MOTOR RESPONSE

' Auditory Closure, Grammatic Closure, and Sound Blending subtext:

Figure 2. Three-Dimensional Model of the ITPAa

 

aAfter Kirk, McCarthy and Kirk; 1968. Page 8.

below.

Each of the ITPA sub-tests can be summarized as follows:

Test 1.

Test 2.

Test 3.

Test 4.

Test 5.

Auditory Reception (Auditory Decoding» or the compre-
hension of the spoken word,is tested by the use of

a controlled vocabulary test. The S answers yes

or no to such questions as Do you eat.... Do you
rain.... Do bananas telephone.... Do Chateaux chastise?
Visual Reception (Visual Decoding) or comprehension

of pictures and written words,is assessed by the S
being shown a stimulus picture (e.g. a shoe) and then
selecting from a set of pictures the one most meaning-
fully related.

Visual—Sequential Memory_jvisual-Motor Sequencing), or
the ability to reproduce a symbol or object sequence
previously seen, is assessed by having the S dupli-
cate the order of a sequence of objects or geometric
figures presented to him. Cardboard blocks with the
objects and figures are arranged in a particular order,
mixed, then the S restores the sequence.

Auditory Association (Auditory-Vocal Association), or

 

the ability to relate spoken words, is tested by an
analogies test (e.g., John is a boy: Mary is a .)
The S must supply the appropriate word.

Auditory-Sequential Memory (Auditory-Vocal Sequencing),

 

or ability to repeat a sequence of symbols previously
heard, is tested through the use of digit repetition.

The S repeats a series of digit sequences from two

Test 6.

Test 7.

Test 8.

Test 9.

to seven digits in length.

Visual Association (Visual-Motor Associatiom, or the

 

ability to relate meaningful visual symbols, requires
the S to choose by pointing to that object or pic-
ture which meaningfully relates to a stimulus object
or picture (e.g., a shoe - balL sock: a spoon - car,
cup).

Visual Closure, is the ability to identify a common
object (e.g. dog, bottle, fish, shoe, hammer and
saw) from an incomplete visual presentation. Five
paper strips are presented to the S independently,
one strip for each of the objects in the sub-test.
On each strip is a scene with many pictures incom-
pletely presented and the S points out the objects
as quickly as possible. An example would be the tail
or hindquarters of a dog displayed against the back-
ground of a fence. The S should be able to inte-
grate these into completed dogs in his mind.

Verbal Expression (Vocal Encoding), or the ability
to express ideas in oral language, is assessed by
the S describing stimulus objects, such as a ball
or block, in terms of its name, qualities, color,
use, value, etc.

Grammatic Closure (Auditory-Vocal Automatic), or the

 

capability to predict future linguistic events from
past experience, is assessed by the S providing a

completion to a test statement (e.g., This is a bed:

Here are two .)

Test 10. Manual Expression (Motor Encoding), or the ability

 

to use gestures expressively, is assessed by showing
the S a stimulus object and having him supply a
motion for manipulating the object (e.g., drinking

from a cup or hammering with a hammer).

The Developmental Test of Visual Perception (DTVP)

The Marianne Frostig Developmental Test of Visual Per—
ception (DTVP) developed by Frostig, et a1. (1964) assesses
defects in five types of visual perception. These are: (a)
eye—hand coordination; (b) figure-ground perception; (c) form
constancy; (d) position in space; and (e) spatial relationships.
These distinct types were postulated fromthe clinical experience
of Dr. Frostig and her associates. Their postulations were
supported by research showing the relatively independent develop-
ment of the areas (Frostig, et al.; 1964). This test was not
intended to assess all visual perceptual abilities, but rather
only those felt to be of relevance to school performance. The
items in the test yield measures (the perceptual quotient and
perceptual age) which are indicative of the visual perceptual
age of a young child who has taken the test. Further, the
sub-tests provide profiles indicating weaknesses which occur
in visual perception, and these can be used to establish a
specific remedial program designed to correct the deficiency
areas.

Each of the sub-tests can be described as follows:

 

Test 1.

Test 2.

Test 3.

Test 4.

Test 5.

Eye-Motor Coordination requires the S to draw

 

straight and curved lines between increasingly narrow
boundaries, or to draw a straight line from an object
or point to a similar object or point.

Figure-Ground has the S discriminate between
intersecting and overlapping shapes, and find hidden
geometric figures.

Constancy of Shape has the S discriminate geometric
figures of different shadings, sizes and positions
among other shapes on a page.

Position in Space assesses directionality by having

 

the S mark the object or figure which is either
oriented in a different direction from the others
in its group, or matches a stimulus object exactly
relative to its position in space.

Spatial Relationships has the S copy patterns by

 

linking a series of dots with pencil lines. The S
is shown a figure made by connecting dots with lines
and is required to reproduce the figure as accurately

as possible.

The Purdue Perceptual Motor Survey (PPMS)

 

The Purdue Perceptual—Motor Survey (PPMS) developed by

Roach and Kephart (1966) qualitatively assesses the perceptual-

motor abilities of children in the early grades. The authors

state its purpose as follows:

The Perceptual-Motor Survey was designed primarily
to detect errors in perceptual-motor development.
To date it is a qualitative scale which designates

 

 

 

10

areas for remediation. The survey was not designed

for diagnosis, per se, but to allow the clinician

to observe perceptual-motor behavior in a series of

behavioral performances. (Roach and Kephart, 1966;

page 11.)

The survey contains 22 items that are divided into 11 sub-
tests purported to measure some aspect of the individual's
perceptual-motor development. The authors noted that the sub-
tests can be divided into three major aspects: (a) laterality;
(b) directionality; and (c) perceptual-motor matching. Further,
they indicated that the sub-tests will be included in any com-
bination of those three aspects (Roach and Kephart, 1966).

In scoring the PPMS, the authors complicated this pro-
cedure by grouping the items and sub-tests into five major areas
of performance which were listed as: (a) Balance and Posture;
(b) Body Image and Differentiation; (c) Perceptual-Motor Match;
(d) Ocular Control; and (e) Form Perception.

Each of the 11 sub—tests may be described as follows:

Test 1. The Walking Board is an elevated two by four board 12

 

feet in length on which the S is requested to walk
forward, backward and sideways.

Test 2. Jumping is a series of jumping, hopping, and skipping
tasks which are performed by the S using both feet,
one or the other of his feet, or rhythmically using
his feet.

Test 3. The Identification of Body Parts is a series of commands

 

given the S to touch body parts (e.g., shoulders,
hips, elbows, mouth, etc.).

Test 4. The Imitation of Movements is a series of unilateral

 

 

Test 5.

Test 6.

Test 7.

Test 8.

ll

bilateral, and contralateral movements the S
imitates while facing the examiner. These movements,
using the arms extended to the sides, resemble
semaphore signalling.

The Obstacle Course is three tasks in which the sub-

 

ject steps over a stick placed at knee height between
two chairs, ducks under the stick placed at shoulder
height, and passes between the end of the stick and

a wall without touching either the wall or stick end.
The Kraus-Weber consists of two tasks from a familiar
physical strength and muscular fitness test. A
pillow is placed under the hips of the S in both
tasks. In one, he must raise his body off the floor
from the waist up for a specific time. In the other,
he must raise his legs off the floor for the same
time period (e.g., ten seconds).

The Angels-In-The-Snow is another series of tasks

 

which the S performs while lying on his back on a
floor. The examiner points to a specific arm or leg,
or combination of the two limbs, and instructs the S
to move the extremities to various positions while
maintaining contact with the floor with the limbs.
The Chalkboard consists of four tasks which the S
must perform by using chalk and a board. The first
two concern the drawing of circles, first with one
hand, and then simultaneously with both hands. The

last two tasks require the drawing of vertical and

 

Test 9.

Test 10.

Test 11.

 

12

horizontal lines. First, the s connects two X's
with a straight horizontal line. Then, he draws
vertical lines, simultaneously and bilaterally, from
X's placed on the board, considerably above his head,
to the board bottom.

Rhythmic Writing is a series of writing tasks in
which the S reproduces a pattern that the examiner
places on a blackboard. There are eight patterns

or motifs for reproduction (e.g.,_jj_r1J“LI1_,
antenna, pbphpb, etc.).

Ocular Pursuits is a series of tasks using a pen-
1ight and occluder (eye cover) in which the S's
ability to follow the light beam is assessed for
binocular and right—left monocular vision.

The Visual Achievement Forms are seven tasks which
the S completes by reproducing geometric forms
(e.g., circle, cross, square, triangle, horizontal
diamond, vertical diamond, and divided rectangle).

This test is also called Developmental Drawings.

The Wepman Auditory Discrimination Test (WADT)

 

The Wepman Auditory Discrimination Test (WADT), developed

by Wepman (1958), is a method for determining a subject's

ability to recognize fine differences between English speech

phonemes.

The author notes that it measures only the ability

to hear accurately. Two comparable forms have been developed.

Each form consists of 30 word—pairs, each word-pair differing

 

 

13

by a single phoneme, and ten word-pairs in which there is no
difference among any of the word pairs. The phonemes contrasted
belong to the same articulatory category (e.g., stops, etc.)

and the word-pairs are equated for length. The latter cautions
eliminate discriminations on the basis of contrasting articula-
tory category, or contrasting length, and force a choice on

the basis of the differing auditory characteristic (Wepman,
1958).. The word—pairs are matched for familiarity using the

Lorge-Thorndike Teacher’s Word Book of 30,000 Words. The

 

word—pairs which are not different provide a check against
guessing. The examiner reads the word-pairs aloud to the S,
whose back is turned to him. The S replies, "same" or "dif-
ferent," to each word-pair, depending upon his discrimination
ability. Examples of the word-pairs used in this brief test

are web-wed, shake—shape, thread-shred, thimble-symbol, etc.

Review of Research

 

General Theoretical Models - The Structure of Intellect
Underlying this review is the basic assumption that the
reader is familiar with one purpose of factor studies, which
is to explain data simply and meaningfully (Harman, 1967).
An effort has been made by the investigators reviewed here, to
identify specific ability factors. This procedure has ample
precedent in the literature, best exemplified by the work of
J. P. Guilford (1958; 1966; and 1967). No exhaustive review
of Guilford's research will be presented, but it is necessary

to present summaries of two of his theoretical models.

14

The first is a multifactor model of intelligence called
the Structure of Intellect-SI (Guilford, 1959). The SI is
relevant here because several investigators in this review have
employed this model to describe their factors, and because it
provides a simple classification scheme for abilities. Guilford
has proposed a three dimensional model to identify the factors
of intelligence or intellect (See Figure 3). These dimensions
are operations, content, and products. Each intellectual
component or factor can be identified by a three letter code
(trigram) specifying: (a) one of the five operations or pro—
cesses of intellect (e.g., cognition, memory, divergent think—
ing, convergent thinking, and evaluation); (b) one of the four
content areas (e.g., figural, symbolic, semantic, and behavioral);
and (c) one of six products of intellect (e.g., units, classes,
relations, systems, transformations, and implications). Using
this model as a theoretical basis for describing intelligence
factors, Guilford identified and classified tasks representing
the specific factors he needed to verify. He has presented a
summary of SI factors and associated tasks for the interested

reader (Guilford, 1966 and 1967).

General Theoretical Models-Psychomotor Abilities

 

Guilford (1958) also presented a theory of psychomotor
abilities similar to his SI model. He reviewed the literature,
and as a result classified the empirical data into theoretical
psychomotor ability factors, based upon a two dimensional matrix.

The first dimension, part of the body involved, includes: the

 

 

OPERA TIONS

Co-nltlon

Memor -

Diverenl Production - -

Conver-ent roduction - -
va uatlon - ..l. I

S stems
Transformations \

Im llcatlons
CONTENTS ‘
Fi ural
S mSoIlc
S

emantlc

Behavig [Q1
\

 

 

 

 

 

 

 

 

 

 

Figure 3. The Structure of Intellecta

 

aAfter Guilford, 1966. p. 21.

 

16

gross body, trunk, limbs, hand, and finger parts. The second
dimension, type of ability, includes: strength, impulsion
(“rate at Which movements are initiated from stationary po-
sitions"), speed, static precision ("the accuracy with which
bodily positions can be held"), dynamic precision ("precision
of directed movements"), coordination, and flexibility. His
psychomotor ability matrix is reproduced in Table l. and will,
be used in the present study as a simple classification scheme

for factors.

ITPA Factor Studies

 

A number of factor analytic studies have been conducted
of the ITPA. These studies were summarized by Meyers (1968),
who presented a synthesis of 16 factor studies of the
ITPA. The latter studies are grouped according to their utility
in the identification of ability factors on which specific ITPA
sub-tests appear saturated. Using the SI code as well as general
descriptive names, Meyers concluded that the ITPA best measures
three factors. The first, a verbal comprehension factor,
whose SI label is Cognitive—Convergent Semantics (C—NM), satu—
rates with the ITPA sub-tests of Grammatic Closure and Auditory
Association. The remaining two factors are visual-motor di-
mensions. The first of these, "vocal motor expression" or,
by SI label, Convergent Production of Semantic Relations (NMR),
loads with the Visual Reception, Manual Expression, and Verbal
ExpresSion sub—tests. The final visual motor factor, whose SI

label is Cognition of Semantic Relations (CMR), is saturated

 

 

 

 

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18

by the Visual Sequential Memory sub—test. Meyers posits four
other factors in his Synthesis which show less reliability than
the three above. He suggests these to be tentative factors,
pending further confirmation. His criteria for establishing
the validity of the first three factors were: (a) substantia-
tion through his own synthesis of ITPA factor research, and
(b) related factor research in the literature which confirmed
the existence of those factors. Critical reservations should
be held regarding the comparability of factors from different
analyses. Nunnally (1967) has indicated a procedure for such
comparison. However, this writer feels the use of SI labels
and Meyers' technique of grouping his studies somewhat miti-
gates this reservation. His work represents a major contri-
bution to understanding the factorial composition of the ITPA.
Hueftle (1967), in an investigation not reported by
Meyers, studied the factor structure of three instruments:
the ITPA, Frostig's DTVP, and the WISC. Meyers used 50 sub-
jects, who were drawn in a random stratified sample, based on
paternal educational levels, disregarding race, creed, sex,
and intelligence. He did separate analyses for each test,
as well as one for the 26 variables included in his research.
He presented nine factors, four of which are relevant to the
present discussion. His second factor, visual—hand, was
loaded by ITPA variables. Hueftle's third factor, an auditory
visual memory cluster, was also loaded heavily with ITPA variables.
The fifth factor, which was loaded most heavily with the DTVP,

represented a collapsing of two factors which appeared in the

 

 

19

separate DTVP analysis. Factor nine was comparable to a
quasi-unique (author's term) factor generated by the separate
ITPA analysis and was similar to J. S. Cohen's (1949) Freedom
from Distractibility factor. It appears that the ITPA accounted
for three of the factors reported by Hueftle with the DTVP form-
ing the other one.

A critique of the Hueftle study could not overlook the
following points. Factors generated from heterogeneous samples
are questionable and the composition of Hueftle's population
was not homogeneous (Guilford, 1952; Nunnally, 1967). The DTVP
and the ITPA were standardized on non—Black populations which
casts doubt on the validity of Hueftle's scores (McCarthy and
Kirk, 1961; Frostig, et al., 1963). Finally, the ratio of
subjects to variables should be at least ten to one in order
to calculate stable loadings and factors (Nunnally, 1967).

The authors of the ITPA originally interpreted the experi—
mental edition as having six factors accounting for 86% of the
variance (McCarthy and Kirk, 1963). This interpretation, using
unrotated data, was somewhat tenuous because the first factor
was loaded by all nine sub-tests, in excess of .8 for each sub-
test. These extremely high loadings on the first factor, a
general linguistic ability dimension, cast doubt on the meaning
of successive factor values. Furthermore, this first factor
accounted for 72% of the variance, while the remaining five
factors could each account for only 3% or less. Interpretation

of factors accounting for such small amounts of variance may be

20

questioned because of the magnitude of the first factor. Their
factor interpretation casts serious doubt on the McCarthy and
Kirk conclusions and leads to characterization of the ITPA as
an unifactorial test.

The acceptance of the factor interpretation by McCarthy
and Kirk ignores the fact that the ITPA is a nine dimension
test (presently ten) and only six factors appeared in their
analysis. This observation suggests the need for further re-
search on the factor structure of the ITPA.

Kirk and Paraskevopoulos (1969) will release in late May,
a book discussing the standardization of the revised edition of
the ITPA. It is assumed that the factor structure of the ITPA
will be part of their analysis.

Center (1963) correlated the ITPA with an achievement test
and found that the seven sub—tests loaded on four factors. Two
of the sub-tests divided their variance between two factors.

On the basis of these results it appears that the sub-tests do
not correspond to the theoretical model. Center called for
further research using factor methods to clarify the problems
of implementing Osgood's model at the automatic and representa—
tional level.

Using the SI model, Loeffler (1963) hypothesized seven
ability dimensions. He factored 32 tests labelled with appro-
priate SI codes, including the ITPA. Six dimensions factored
out with the sub-tests of the ITPA loading on five of the abilities.
The second factor, verbal comprehension, loaded with the ITPA

Grammatic Closure sub-test. All the test variables in the

 

21

verbal comprehension factor were classified either as Convergent
Production of Semantic Units (NMU) or Cognition of Semantic
Units (CMU). The third factor, fluency, whose SI label Divergent
Production of Semantic Units (DMU), was represented by the ITPA
Verbal Expression sub-test. Figural reasoning, factor four,

was loaded by Visual Association and Visual Reception. The
latter was classified as Cognition of Figural Classes (CFC)

and the former as Cognition of Figural Relations (CFR). Ime
mediate memory for symbolic units (Auditory), factor six, loaded
with the sub-test, Auditory Sequential Memory. Its SI label

was Memory of Symbolic Units (MSU). The final test, Visual
Sequential Memory, loaded on factor seven, immediate memory

for figural units (Visual). Memory for Figural Units (MFU)

was its SI label.

DTVP Factor Studies

 

Two studies using the DTVP were published by Corah and
Powell (1963) and Sprague (1963). The latter investigator
correlated the DTVP with achievement measures. Sprague's
results showed four sub—tests loading on two factors. The
Eye-Motor Coordination and Figure-Ground sub-tests loaded
.4 on a factor accounting for 5%% of the common factor variance.
The Position in Space and Spatial Relations sub—tests contri—
buted substantially larger loadings on their factor. These
two variables were interpreted as a space relations factor

accounting for 10.4% of the variance.

 

 

22

Corah and Powell (1963) compared the DTVP with the following

tests: the Full-Range Picture Vocabulary Test (FRPV), an in-

 

telligence measure; the Ghent Overlapping Geometric Figures Test

 

19§£)' a measure of form discrimination; and a form constancy
task (FC). They concluded that two factors could explain the
greater share of the variance accounted for in the analysis.
These two factors were labelled general intelligence and develop-
mental change in perception. Corah and Powell suggested that
the perceptual quotient (PQ - Total score on test) should be
given more attention as a good measure of the latter factor.
The meaning of the results, using sub-test scores, was question-
ed because of reliability problems associated in the use of
difference profiles. As age increased, individual sub-test
scores became more reliable, and it was concluded that scatter
analysis of the sub-tests for this reason was questionable.

One implication of Corah and Powell's study is that the
DTVP is a unifactorial test. This conclusion is supported by
two sources. Hueftle's study, cited above, identified a factor
on which the DTVP loaded almost exclusively, and Corah and
Powell observed that the PQ (total score on test) should be
given more attention as a measure of their second factor.

A final note regarding the DTVP's status as a unifactorial
or multifactorial test was offered by Frostig, et a1 (1964).
They wrote in reference to the P0:

The use of any unitary measure of perceptual function

may suggest that it expresses some common trend or factor.
But the five sub—test scores are based on the assumption

 

23

that essentially five different and relatively inde—

pendent abilities are tested and may subsequently be

differentially trained. (page 481).

The two remaining instruments used in the present study
appear not to have been the subject of published factor analytical

studies.

PPMS Factor Study

 

This writer did factor analyze the intercorrelation matrix
(Table 2) in the Manual for the Purdue Perceptual Motor Survey
(PPMS) by Roach and Kephart (l966)1. Six clusters appeared with
factor loadings between .54 and .83. Three tasks did not load
on any cluster. These tasks were the obstacle course, the Kraus
Weber, and the Angels-in—the—Snow. The six clusters and their
tasks were: (a) the Walking board tasks; (b) the Chalkboard
tasks; (c) the Ocular Pursuits tasks; (d) the Developmental
Drawing tasks; (e) the Rhythmic Writing tasks; and (f) Jumping,
Identification of Body Parts, and Imitation of Movements.

Factor three, ocular pursuits, accounted for 26% of the
variance. This was the largest share with the other factors
each sharing between 5 and 8%. The total amount of the variance

explained by the factor analysis was 61%.

 

1The authors maintain the PPMS items are not factorially
pure (1966; page 70), although there are striking simi—
larities between the factor structure above and the PPMS
"major areas of performance" (Re: page 9-10 of this
discussion and note Table 2 on the following page).

 

24

 

 

 

Table 2. Correspondence of PPMS Tasks in Each of the
Authors' "Major Area of Performance" to the
Writer's Factor Analysis of the PPMS
Intercorrelation Matrix.
Roach-Kephart's
Major Areas of
Performance PPMS Tasks Factor
1. Balance and posture Walking board One
Jumping
2. Body image and Identification
differentiation of body parts Six
Imitation of
movements
Obstacle course
Kraus—Weber ] Omitted
Angels-in-the-Snow tasks
3. Perceptual—motor Chalkboard Two
match
Rhythmic writing Five
4. Ocular pursuits Ocular pursuits Three
5. Developmental drawing Developmental Four
(Visual Achievement drawing

Forms)

 

 

25

M

The Wepman Auditory Discrimination Test (WADT) appears to
be a unifactorial test because all 40 items are of a similar
nature. Presumably, Memory of Symbolic Units (MSU) would be

an appropriate SI label and category for this test.

Summary of Research Review

 

In summary, of the four instruments, one — the ITPA — has
been subjected to the most complete factor study. The results
suggest that it is at least a three factor test. Considerable
doubt exists about the factorial status of the DTVP, PPMS, and

the WADT.

Hypotheses

The preceding two sections have brought together from three
sources most of what is known about the factors underlying the
battery of tests used in the present investigation: (a) A clear
description of the nature of the tasks encompassed by each sub—
test was given; (b) The research inconsistencies apparent with-
in each test's factorial construction were noted; and (c) two
systems were presented, both elaborated upon by J. P. Guilford,
for the classification of tasks into a hypothetical factor
structure. These three sources were used to develop in tabular
form this writer's hypothesized factor structure for the battery
of tests (Table 3).

The 16 hypothesized factors parsimoniously explain the nature

of the tasks included in this battery. Hypothesized factors 1 - 3

26

 

 

 

 

by that model.

Table 3. Hypothesized Factor Structure of Four Tests of learning Disabilities.
Hypothesized
Factor Name Common Research Factor.
and Code Name Test(s) Source Status.
1. Cognition of Semantic Semantic ITPA Aud. Rec. Meyers Confirmed
Relations (CMR ) Relations ITPA vis. Assfn. (1968)
2. Convergent Production Semantic ITPA Vis. Rec. Meyers Confirmed
of Semantic Rela- Correlates ITPA Verb. Exp. (1968)
tions (NMR) ITPA Man. Exp.
b3. Cognition-Convergent Verbal ITPA Aud. Asa'n Meyers Confirmed
Semantics (C-NM) Comp. ITPA Grams. Close. (1968)
4. Memory for Symbolic ITPA Aud. Seq. Men. Meyers Tentative
Systems (M55) (1968)
5. Memory for Figural ITPA Via. Seq. Mam. Meyers Tentative
Systems-visu ual (1968)
(Mrs-v
6. Cognition of Figural Spatial DTVP Pos. in Sp Sprague Tentative
Systems (CPS) Orient. DTVP Spat. Rel (1968)
7. Cognition of Figural DTVP Eye Mot. Coord. Sprague Tentative
DTVP Fig. Grnd (1968)
(CPU-v) DTVP Cons. Shape
8. Memory for Symbolic WADT
Units (MSU)
c9. Trunk-Strength PPMS Krause-Weber Guilford
(1958)
10. Limb-Thrust PPMS Jumping
ll. Static-Balance PPMS Walk Bd
12. Arm Steadiness PPMS Chalkbd
13. Arm Aiming PPMS Indent Bod Pts
PPMS Imit. Move.
14. Gross Bodn PPMS Obstacle Cse
Coordination PPMS Angels-in-Sno
15. Ocular Pursuit PPMS Ocular Pursuits
°16. Memory for Figural Memory-Motor PPMS Rhythm Writing
Units (MFU) PPMS Develop Drwngs
(Visual Achievement
Forms)
a According to research reported.
b Author‘s use of Guilford's SI model deviates from accepted practice by using two
operations and not designating a produc
c Factors 9-14 are hypothesized using the task descriptions contained in Guilford
(1958).A11 are tentative statu
d Factor 15 is hypothesized because its existence appears consistent with the
Psychomotor Ability Matrix.
e Factor 16 used the SI model because the required tasks seemed more adequately described

27

were strongly substantiated by Meyers' research. Hypothesized
factors 4 and 5 are tentative but Meyers suggested that it is
reasonable to expect their presence. It appears that five
factors explain the nature of the present ITPA if these hypoth-
eses are confirmed. Hypotheses 6 and 7 predict the DTVP struc-
ture as a two factor test. This is consistent with Sprague's
results_but questions those of Hueftle and Corah and Powell.
The decision to predict two factors results from differences
seen in the nature of the tasks as described by Frostig and
their similarity to the two SI factors by which they are
classified. Hypothesized factor 8 explains the WADT because
the task description from the SI model most closely resembles
the WADT task.

Hypothesized factors 9 - 14 were classified as a result
of their similarities to Guilford's description of tasks repre-
senting the psychomotor abilities he proposed as separate
psychomotor functions. Factor 15, ocular pursuits, appears to
be an eye-motor coordination cluster not identified by Guil-
ford's model but consistent with its structure. It loaded
separately in the PPMS analysis reported, and it is predicted
to load separately in the hypothesized factor matrix. Finally,
hypothesized factor 16 combines two tasks which loaded separately
in the PPMS analysis but whose description matches the SI task
by which they are coded.

In conclusion, 16 factors werelrypothesized, at a maximum,

to parisimoniously explain the data derived from four tests of

 

28

learning disabilities-—the ITPA, the DTVP, the WADT, and the

PPMS. These 16 hypotheses are:

Hypothesis 1.

N
s

Hypothesis

Hypothesis 3.

Hypothesis 4.

Hypothesis 5.

Hypothesis 6.

Hypothesis 7.

m
e

Hypothesis

LO
0

Hypothesis

Hypothesislfl.

The ITPA sub-tests, Auditory Reception and Vis-
ual Association, associates with a semantic
relations dimension whose label is Cagnition

of Semantic Relations.

The ITPA sub-tests, Visual Reception, Verbal
Expression, and Manual Expression, associates
with a semantic correlates dimension whose
label is Convergent Production of Semantic
Relations.

The ITPA sub—tests, Auditory Association and
Grammatic Closure, associates with a verbal com—
prehension dimension whose label is Cognition
Convergent Semantics.

The ITPA sub-test, Auditory Sequential Memory,
associates with a symbolic memory dimension
whose label is Memory for Symbolic Systems.

The ITPA sub-test, Visual Sequential Memory,
associates with a figural memory dimension whose
label is Memory for Figural Systems-~visual.

The DTVP sub-tests, Position in Space and
Spatial Relations, associates with a spatial
orientation dimension whose label is Cognition
of Figural Systems.

The DTVP sub—tests, Eye—Motor Coordination,
Figure-Ground, and Form Constancy, associates
with a figural recognition dimension whose
label is Cognition of Figural Units—visual.

The WADT associates with a symbolic memory
dimension whose label is Memory for Symbolic
Units.

The PPMS sub-test, Kraus-Weber, associates with
a psychomotor ability dimension whose label is
Trunk-Strength.

The PPMS sub- -test, Jumping, associates with a
psychomotor ability dimension whose label is
Limb- Thrust.

 

Hypothesis

Hypothesis

Hypothesis

Hypothesis

Hypothesis

Hypothesis

11.

12.

13.

14.

15.

29

The PPMS sub-test, Walking Board, associates
with a psychomotor ability dimension whose
label is Static Balance.

The PPMS sub-test, Chalkboard, associates
with a psychomotor ability dimension whose
label is Arm Steadiness.

The PPMS sub-tests, Identification of Body
Parts and Imitation of Movements, associates
with a psychomotor ability dimension whose
label is Arm Aiming.

The PPMS sub-tests, Obstacle Course and
Angels-in-the-Snow, associates with a psy-
chomotor ability dimension whose label is
Gross Bodily Coordination.

The PPMS sub—test, Ocular Pursuits, associates
with an eye muscle coordination dimension
whose label is Ocular Pursuits.

The PPMS sub-tests, Rhythmic Writing and Visual
Achievement Forms, associates with a figural
memory dimension whose label is Memory for
Figural Units.

 

CHAPTER II

METHODOLOGY AND PROCEDURES

 

The procedures used in the study are presented in this
chapter. Sample selection, examiner training, instrumentation,

and procedures, etc. are discussed in detail.

Subjects

The 55 used in this study were disadvantaged kinder-
garten children from the Grand Rapids public and parochial
school systems. They are participating in an CEO Study of
Disadvantaged Children (Ericson, McMillan and Bonnell, 1968
et. seq.). The children were classed as disadvantaged under
two OEO criteria. These criteria relate the number of persons
in a family to their combined income to determine if a person
may be described as disadvantaged. As examples of this: The
poverty level for a family of four is thirty-two hundred
dollars, for a family of five persons the corresponding income
level is thirty—seven hundred dollars, and a family of more
than five may earn up to five hundred dollars more to support
each additional member of the family. Of the 327 55 available
in the original subject pool, 22 83 did not complete the basic
three-test battery composed of the ITPA, the DTVP, and the WADT.

The Ns used in each statistical analysisare reported in Table 4.

30

31

 

 

 

Table 4. Composition of Sample-groups for Analyses.a

Sex 3—Test Sample 4-Test Sample I.Q. Sample
Male 148 40 105
Female 157 53 103
Total N 305 93 208

——

 

aAll Ss drawn from original

S pool of 305.

 

32

Because of time limitations, examiner shortage, and
scheduling difficulties it was decided to administer the
PPMS to a sample of 100 85. An additional conflict with
another testing schedule reduced the N for this factor study
to 93 Ss.

A third group of 208 Ss‘whose Stanford Binet I.Q. was
known constituted the final sample used for analysis in this
study.

The age range for the Ss in the three samples above was

62-84 months, with a mean of 68 months and S.D. of four months.

Instrumentation and Procedures

 

The battery of tests used in this study is described in
Chapter I. During the administration and scoring of these
tests,the procedures outlined in the respective test manuals
were followed as closely as possible. A sample pre—test in-
dicated the necessity to modify two tests during the data
collection. Descriptions of these modifications follow:

1. The WADT was recorded on tape in the MSU Speech
Laboratory. Copies of this tape were made to
assure a standard administration of the test. All
55 were given the test on identical tape recorders.
This procedure is contrasted with the usual
administration in which the examiner reads the
word—pairs aloud at an intensity and frequency
which varies from examiner to examiner and from
word—pair to word-pair.

2. The PPMS Rhythmic Writing Sub-test is not

 

33

intended for children under eight. After brief
experimentation by this investigator, it was
decided that the 85 were capable of responding
to the first three motifs. These results are
included in the data.
Otherwise, the test administration and scoring procedures
recommended by each test author were strictly followed during

the study.

Examiner Training

 

Because of the large number of Ss and the length of the
total test battery, 13 examiners were recruited to aid in the
data collection. All the examiners were senior college students
majoring in Education or Psychology. Their training began with
an introduction and discussion of the test theory and test
materials. Each examiner was given a set of the test materials
for familiarization purposes. An added recommendation was
given that the examiners practice on neighborhood children.
The examiners then observed an administration of the test by
a qualified psychometrician. These observations were followed
by supervised administrations in which the examiners did the
testing. The writer and the psychometrist were available for
consultation on any problems of administration and scoring.

In addition, the writer periodically observed all examiners
during the data collection. In this manner, serious efforts

were made to standardize procedures of data collection.

34

225a Collection

The 85 were located in 32 Public and Parochial Schools in
Grand Rapids. Each S was administered each test individually.
Earlier plans to test in groups did not prove practical because
of limited testing space in the schools. Also, the Ss became
distracted by the presence of peers.

The S's responses were recorded on the test forms and
keypunched by sub-test scores using a numeric code on IBM
data cards. Each S was differentiated from the other 85

by a three—digit identification Code.

Statistical Analyses

 

All computer analyses used in this study were completed
on the MSU CDC 3600 computer.

The major objective of this study was to determine the
underlying dimensions of the four tests used for assessing
learning disabilities. To achieve this objective, the data
were submitted to principal Axis Factor Analysis with Varimax
Rotation. The particular program used was developed by the
MSU Computer Institute for Social Science Research (1967). To
make the resulting analyses more readily interpreted, they were
rotated orthogonally using the varimax method. The cut—off
index for determining the number of factors to be rotated was
an eigenvalue of 1.000. This index is accepted routinely in
factor research as an appropriate level for determining the

number of factors to be rotated.

35

Separate factor analyses were performed to determine the
empirical factor structure for the following:

1. The ITPA, the DTVP, and the WADT for 305 Ss;

2. The ITPA, the DTVP, the WADT, and the PPMS for 93 SS;

3. The ITPA for 305 Ss;

4. The DTVP for 305 Ss; and

5. The PPMS for 93 Ss.

Lange (1969) studied the question of stable factor loadings
and concluded that a minimum N of 400 is needed. However, in
all present analyses except #2 and #5, a minimum subject-vari-
able ratio of 10:1 was imposed on the data (Nunnally, 1967).

The suggested ratio proposed assures stable factor loadings.
Other factor research on meaningful factor loading levels
suggests a minimum N of 200 Ss (Guilford, 1954). These criteria
were also met by the present study.

Exceptions to the criteria described above were analyses
#2 and #5. These exceptions were necessary because of a con-
flict in scheduling. To complete the additional 85 would have
required delay in the Spring test program of the school systems
involved. Despite this difficulty, it was felt that useful
information would be wasted if the PPMS analyses across the
tests and individually were not completed. Subsequent inter-
pretation of these analyses presented in the results, will
take into account the failure to meet the subject-variable ratio
criterion.

In addition to the factor analyses, the data were subjected

to analytical routines which were felt to strengthen the assump-

 

36

tion of homogemfity for the samples, and to determine the use-
fulness of the sub-tests as predictor variables.

An analysis of variance routine for unequal Ns was em-
ployed to determine the effects of age and sex on the samples.
The 3-Test sample was divided into three age groups of one-half
year intervals. This alternative was taken after it was found
that the Ns could not be divided into three month intervals
consistent with the norms reported in the ITPA and DTVP test
manuals. The three month Ns would have been too small for
meaningful analysis. The presence of non-significant cell
differences lendssupport to the assumption of sample homogeneity.
Further, non-significant differences due to age would bring into
question the value of the tests included in the battery as de-
velopmental indices.

Finally, multiple regression analyses routines were used
to determine the ability of the following independent variables
to predict I.Q.: sex, age, the sub-test scores of the ITPA,
the DTVP, and the WADT.

Two step-wise regression programs were employed to identi-
fy the predictor variables (MSU Agricultural Research Station,
1967, 1968). These were the Step-wise Deletion of Variables
From a Least Squares Equation (LSDel) Routine and the Step-wise
Addition of Variables To Form a Least Squares Equation (LSAdd)
Routine. Each procedure is essentially the reverse of the other.

The general procedure used in the LSDel Routine begins with
a multiple regression equation using as predictors all the in—

dependent variables, then deleting the variables one at a time.

 

37

The order of deletion is determined by the amount of variance
accounted for by each independent variable. The variables
eliminated are those which account for less than a predeter-
mined amount of variance. Each of the retained variables
accounts for variance in excess of that amount. The level

of significance chosen for both routines was .05.

The LSAdd Routine begins with the independent variable
contributing the most variance to the multiple correlation.
Then variables are added in order of the magnitude of the
variance accounted for until all variables are added.

These two routines identify the major predictor variables
in terms of variance contribution to the criterion prediction.

The method employed above is fully described by TenBrink (1968).

 

CHAPTER III

RESULTS
The data analyses, reported here, are the results of six
factor analyses, a two-way analysis of variance, and two
stepwise multiple regression analyses. Factor analyses are
reported for a Three-Test Battery, comprised of the ITPA, the
DTVP, and the WADT, as well as for a Four—Test Battery, which
included the latter three tests and the PPMS. In addition,

separate factor analyses for each test are reported.

Factor Analyses: Introduction

 

The basic technique employed in this study was that of
factor analysis. The major hypotheses relate to the number
of underlying dimensions or factors which appear to explain
parsimoniously the set of the sub—test variables.

Means, standard deviations, and intercorelation matrices
were computed and are presented in Appendix I. The inter—
correlation matrices were submitted to Principal Axis Factor
Analysis with Varimax Rotation. The number of factors to be
rotated was determined by an eigenvalue of 1.000.

The interpretation of the separate factors in the factor
solutions presented below depends on two considerations:

(a) The strength of the association of a particular variable

38

 

39

with its factor as measured by the factor loading; and (b) The
consistency with which particular variables associated on the

same factor.

Factor Analyses: Three-Test Battery

 

Table 5 contains a listing of the sub—test variables and
the abbreviations used in the subsequent data analysis tables.

The analysis for the Three-Test Battery was done by sub—
mitting the intercorrelation matrix for the three tests to
Principal Axis Factor Analysis with Varimax Rotation. The
results are presented in Tables 6-11.

The solution which best explained the dimensionality of
the 17 sub-test variables included in this analysis contained
five factors. This solution accounted for 59% of the factor
variance across the Three-Test Battery. One factor, Factor III,
accounted for 7% of this factor variance. The remaining four
factors each accounted for at least 10% of the factor variance
(Table 6).

Every factor in this solution was loaded with variables
whose minimum factor loadings were .50. The decision to use
factor loadings of .50 was an arbitrary one made by the inves-
tigator. Other studies have employed smaller variable values,
but it was felt that a variable accounting for at least 25% of
the factor variance, a factor loading of .50, would contribute
to the interpretation of the factor. In addition, each factor
had one variable associated with it which loaded at least .70.

The sample size used to obtain this solution exceeded the

 

40

TABLE 5

Abbreviations Used in the Data Report

 

 

Test Variables
The Illinois Test of Psycholinguistic Abilities (ITPA)

1 AR — Auditory Reception

VR - Visual Reception

VSM - Visual Sequential Memory
Auditory Association
ASM - Auditory Sequential Memory
Visual Association
Visual Closure
Verbal Expression
GC - Grammatical Closure
Manual Expression

S

O\ooa~1mtns-OJN
<:<'<
{1103’
I II

E

 

The Frostig Developmental Test of Visual Perception (DTVP)

11 EMC - Eye-Motor Coordination
12 FG - Figure-Ground

13‘ FC — Form Constancy

l4 PIS - Position in Space

15 SR - Spatial Relations

 

The Wepman Test of Auditory Discrimination (WADT)

l6 DIFF - Different Word-Pairs
l7 SAME - Same Word~Pairs

 

The Purdue Perceptual Motor Survey (PPMS)

18 WE ~ Walking Board

19 JP — Jumping

20 IBP - Identification of Body Parts
21 IM - Imitation of Movements
22 OC - Obstacle Course

23 KW - Kraus-Weber

24 AIS - Angels-in-the—Snow

25 CB - Chalkboard

26 RW - Rhythmic Writing

27 OP - Ocular Pursuits

28 VAF - Visual Achievement Forms

 

41

subject—variable ratio criterion discussed in Chapter II.

The five sub-test variables of the Frostig loaded on
Factor I, Visual Perceptual Relations (Table 7). This set
of sub-test variables accounted for 17% of the factor variance
in the three test solution. The variables having the highest
loadings were the Figure-Ground and Spatial Relations sub-tests
which had loadings of .73 and .74 respectively. These vari-
ables each accounted for at least 49% of the factor variance
associated with the factor.

It will be recalled that a factor loading is the measure
of association of a variable with a factor. In variance terms,
the factor loading is the square root of the variance. To
obtain an estimate of the factor variance accounted for by a
variable it is necessary only to square the loading and read
the resulting figure as a percentage. A variable with a load—
ing of the magnitude of .70 is generally considered to have a
high association with the factor on which it loads.

The remaining sub-tests, Eye—Motor Coordination, Form
Constancy, and Position in Space, had substantial factor load—
ings (nearly .60) with Factor I. The association of these
five sub-tests appears quite clear here. However, when the
DTVP was analyzed separately, the Form Constancy variable formed
a separate factor. This inconsistency was minimized to some
extent because the factor did not meet the eigenvalue cri-
terion. Further, the interpretation of a univariable factor

is quite difficult. It is recommended that at least two

42

TABLE 6

Varimax Rotation Factor Loadings of All Variables for
Three Tests on a Five Factor Solution.a

 

 

 

 

 

Factors

Variables I II III IV V
1 AR —.58
2 VR —.75
3 VSM .50

4 AA -.49
5 ASM .77
6 VA -.64
7 VC -.62

b8 VE .85
9 GC

10 ME .83

11 EMC .58

12 PG .73

13 FC .59

14 PIS .59

15 SR .74

16 DIFF .76

17 SAME -.77

Eigenvalues 5.1546 1.4358 1.3122 1.1029 1.0210

% Var Accounted

for by Factor 17 10 07 ll 14

 

Total Var accounted for by Five Factor Solution 59%

 

an = 305

bThis variable did not load above .50 on any factor.

Factor I.3

43

TABLE 7

Principal Axis Factor Analysis with
Varimax Rotation for all Variables on Three Tests.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
11 EMC .58 .26 .47
12 PG .73 .23 .59
13 FC .59 .17 IV .39
14 PIS .59 .28 IV .49
15 SR .74 .23 v .66
Eigenvalue 5,1545
% Var acct'd
for by Factor 17 59%

 

aFive factor

b

N

= 305

solution

 

44

variables be associated with a factor before any attempt is
made to interpret it. Factor I,as presented in Table I is
probably the best characterization of the Frostig Test vari—
ables.

The ITPA sub-test variables, Verbal and Manual Expression,
loaded together on Factor II, VerbaleManual Expression (Table
8). These two variables had factor loadings of .85 and .83
respectively. Factor loadings of this magnitude usually in-
dicate a very high degree of association. A comparison of the
variable's secondary factor loading with the primary loading
is an indication of the degree Of association. Therefore,
since the secondary loadings were .14 and .11 respectively,
the comparison showed that the sub-test, Verbal Expression,
accounted for 69% of its primary factor variance but less
than 2% of its secondary factor variance. Similarly,

Manual Expression accounted for 68% of its primary factor
variance but less than 2% of its secondary factor variance.
These two variables loaded on the same factor in every analysis
performed in this study. Because of the high loadings on
Factor II and the consistency with which these variables loaded
on this factor, it was felt to be the most stable factor iden-
tified in this study.

Factor III, Auditory Discrimination, was defined by the
two Wepman sub—tests (Table 9). DIFFERENT word—pairs had a
factor loading of .76, while SAME word—pairs had a loading of

.78. These two sub—tests were not associated in the Four—Test

Factor II.a

45

TABLE 8

Principal Axis Factor Analysis with

Varimax Rotation for all Variables on Three Tests.

 

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
8 VB .85 .14 IV .76
10 ME .83 .11 I .72
Eigenvalue 1,4353
% Var acct'd
for by Factor 10 59%
aFive factor solution

bN

= 305

 

Factor III.a

46

TABLE 9

. Principal Axis Factor Analysis with
Varimax Rotation for all Variables on Three Tests.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
16 DIFF .76 .40 IV .79
17 SAMH -.78 .28 IV .76
Eigenvalue 1.3122
% Var acct'd
for by Factor 7 59%

 

aFive factor solution

bN

= 305

 

47

analysis to be presented later. However, the data presented
in Table 9 were more reliable because they were based on a much
larger sample. '

Visual Sequential Memory, an ITPA sub-test, loaded on
Factor IV (Table 10). Its loading of .50 was the minimum
level for accepting a variable for interpretation with a
factor. The other sub-test which loaded on this factor was
Auditory Sequential Memory and its loading was .77. The
variables, Auditory Sequential Memory and Visual Sequential
Memory, had their highest loadings on the same factor, in the
separate ITPA analysis presented below. These two sub-tests
appeared to measure the same abilities in the auditory and
visual channels described in the ITPA theoretical model in
Chapter I. Together, these variables accounted for 11% of
the factor variance across the factor solution. Since these
two tests measured a type of serial learning ability, Factor
IV was labelled a Serial Learning factor.

Five ITPA sub-test variables comprised Factor V, Auditory-
Visual Understanding (Table 11). The Visual Reception sub—
test had a factor loading of .75 on this factor. Two other
sub-tests, Visual Association and Visual Closure, had sub-
stantial factor loadings, .63 and .62 respectively. The
remaining two variables, Auditory Reception and Auditory
Association, had factor loadings of .58 and .49 on Factor V.
The latter factor loading was below the minimum level accepted
in this study for interpretation; however, this variable

consistently loaded on this factor in all subsequent analyses.

Factor Iv.a

48

TABLE 10

Principal Axis Factor Analysis with

Varimax Rotation for all Variables on Three Tests.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal— Factor
Loading Loading ity Solution

3 VSM .50 .32 I .46
5 ASM .77 .11 V .62

Eigenvalue 1.1029

% Var acct'd

for by Factor 11 59%

 

a . .
Five factor solution

bN

305

Factor V.a

49

TABLE 11

Principal Axis Factor Analysis with

Varimax Rotation for all Variables on Three Tests.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
1 AR .58 .38 IV .52
2 VR .75 .14 IV .53
4 AA .49 .47 IV .63
6 VA .63 .24 I .51
7 VC .62 .39 I .56
Eigenvalue 1.0210
% Var acct'd
for by Factor 14 59%

 

a . .
Five factor solution

bN

= 305

50

The other four variables, Auditory Reception, Visual
Reception, Visual Associations, and Visual Closure, also
clustered together in the separate ITPA analysis. In
addition, the sub-test variable, Grammatic Closure, while
it did not have a factor loading sufficiently large for in-
terpretation here, . did associate with these variables in
the subsequent analyses of the ITPA. The association of
Grammatic Closure with this set of variables probably means
it should be considered part of Factor V. It is assumed
that these six sub-test variables of the ITPA probably
comprise the Auditory-Visual Understanding factor identified
here.

In summary, the five factor solution presented here
probably describes the clustering of these 17 sub-tests in
the most parsimonious manner. The acceptance of this solution
has much to recommend it empirically because all the factor

analytic criteria were met in this solution.

Factor Analyses: The ITPA

 

The following analysis yielded a three-factor solution
for the ten ITPA sub—test variables. The ITPA intercorrela-
tion matrix was submitted to Principal Axis Factor Analysis
with Varimax Rotation.1 The number of factors to be rotated
was determined by an eigenvalue of 1.000. The three factor

solution accounted for 59% of the factor variance and each

 

1See Appendix 1.

51

factor contributed at least 17% of the factor variance (Table
12). This solution was also consistent with the Three—Test
solution just presented which showed the ITPA sub-test varia—
bles loading on three factors (Tables 12-15).

The third factor presented below has an eigenvalue of
.9879 which is slightly below the criterion for determining
the number of rotated factors used for interpretation.
Because this three-factor solution was consistent with the
previous discussion of the Three-Test Battery, this factor
was interpreted.

Table 13 presents Factor I, Auditory-Visual Understand—
ing, which had six variables loading on it. The sub—test,
Visual Reception had a factor loading of .66 and Visual
Association had a factor loading of .68. Visual Closure had
a factor loading of .75 associated with Factor I above. The
remaining three sub-tests, Auditory Reception, Auditory
Association, and Grammatic Closure had factor loadings of
.56, .56, and .50, respectively, with Factor I. These same
six variables clustered together on the same factor through—
out all analyses. Without exception, the three sub-tests,
Auditory Reception, Auditory Association, and Visual Asso-
ciation, clustered together in each analysis. The Visual
Reception and Visual closure sub-tests had factor loadings
associated with the three sub—tests above on all the analyses
except one. On the Four—Test analysis, Visual Reception and

Visual Closure, did not cluster with the variable set above;

52

TABLE 12

Varimax Rotation Factor Loadings of All Variables for
the ITPA on a Three Factor Solution.a

 

 

 

 

 

 

Factors
Variables I II III
1 AR .56
2 VR .66
3 VSM .55
4 AA .56
5 ASM . 87
6 VA .68
7 VC .75
8 VB .85
9 CC .50
10 ME .84
Eigenvalues 3.6111 1.2642 .9879
% Var accounted
for by Factor 24 l7 l7

 

Total Variance accounted for by Three-Factor Solution 59%

 

aN = 305

 

53

TABLE 13

Factor I.a Principal Axis Factor Analysis with b
Varimax Rotation for all Variables on the ITPA Test.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
1 AR .56 .38 III .49
2 VR .66 .11 III .45
4 AA .56 .51 III .64
6 VA .68 .19 II .51
7 VC .75 -.07 II .57
9 GC .50 .46 III .53
Eigenvalue 3,5111
% Var acct'd
for by Factor 24 59%

 

aThree factor solution

bN = 305

 

54

however, they did load together on another factor. The final
sub-test variable, Grammatic Closure, did not load on the
Three-Test analysis, but it was consistently associated with
this variable set in the remaining two analyses.

Two sub-tests comprised Factor II, Verbal-Manual Expres-
sion (Table 14). Both of these variables, Verbal Expression
and Manual Expression, had strong factor loadings on this
factor. The former was .85 and the latter was .84. It was
noted previously that this variable setwaspmobably the most
stable one occurring in the present study, because these
variables were associated together on all analyses and they
had high factor loadings on Factor II.

The sub-tests, Auditory Sequential Memory and Visual
Sequential Memory, were associated with Factor III, Serial
Learning (Table 15). The variable, Auditory Sequential
Memory, had a factor loading of .87 on this factor, and
Visual Sequential Memory had a factor loading of .55. The
decision to interpret this factor despite its eigenvalue of
.9879 was based upon three reasons in addition to the one
cited previously. First, both of these sub-tests, Auditory
Sequential Memory and Visual Sequential Memory, did not have
sufficiently large factor loadings on the Four—Test analysis
to include them for interpretation. However, on all other
analyses they associated together with one factor. Second,
it was pointed out previously that these sequential memory
variables appeared to be measuring the same ability in terms

of the ITPA theoretical model presented in Chapter 1. Finally,

55

TABLE 14

Factor II.a Principal Axis Factor Analysis with
Varimax Rotation for all Variables on the ITPA Test.

 

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
8 VB .85 .15 III .76
10 ME .84 .11 I .72
Eigenvalue 1.2642
% Var acct'd
for by Factor 17 - ' 59%

 

aThree factor solution

bN = 305

56

TABLE 15

Factor III.a Principal Axis Factor Analysis with
Varimax Rotation for all Variables on the ITPA Test.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
3 VSM .55 .27 II .44
5 ASM .87 —.09 II .76
Eigenvalue .9879
% Var acct'd
for by Factor 17 59%

 

aThree factor solution

bN

= 305

 

57

the two analyses on which this serial learning dimension appeared
were based upon data from 305 Ss. The factor loadings based
upon the large sample were more stable than the loadings
obtained from the other analyses. In view of these consider—
ations, Factor III, Serial Learning, was retained.

In summary ,the three factor solution for the ITPA
sub—test variables has demonstrated dimensions which show sta-
bility and consistency across all analyses and a strong variable

association with the respective factors presented above.

Factor Analyses: The DTVP

 

The DTVP intercorrelation matrix was submitted to
Principal Axis Factor Analysis with Varimax Rotation as were
the previous analyses.1 All relevant criteria for suitable
analysis were met by the data. One important exception was
that a two—factor solution was presented in Tables 16—18 but
the interpretation was that the variables show a unidimensional
nature.

Four Frostig sub—test, Eye—Motor Coordination, Figure-
Ground, Position in Space, and Spatial Relations, comprised
Factor I, Visual Perceptual Relations (Table 17). Eye—Motor
Coordination had a factor loading of .80 and Spatial Rela-
tions had a factor loading of .75. Both of these variables
appeared to have a strong association with this factor. The
remaining two variables, Figure-Ground and Position in Space,

had moderate factor loadings of .66 and .63 reSpectively.

 

JSee Appendix 1.

58

TABLE 16

Varimax Rotation Factor Loadings of All Variables for

the

DTVP on a Two-Factor Solution.

 

 

 

 

 

 

Factors

Variables I II

1 EMC .80

2 PG .66

3 FC .89

4 PIS .63

5 SR .75
Eigenvalues 2.4398 .8662
% Var Accounted
for by Factor 41 26

 

Total Variance accounted for by Two—Factor Solution 66%

 

a

N

305

59

TABLE 17

Factor I.a Principal Axis Factor Analysis with b
Varimax Rotation for all Variables on the DTVP Test.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
1 EMC .80 -.21 II .68
2 PG .66 .44 II .62
4 PIS .63 .32 II .50
5 SR .75 .38 II .70
Eigenvalue 2.4398
% Var acct'd
for by Factor 41 ‘ 66%

 

aTwo factor solution

bN = 305

 

60

These two sub-tests and the Spatial Relations sub—test had
secondary factor loadings which indicated a mild association
with Factor II of this solution. This was taken to mean that
their nature would become clearer if these two DTVP factors
were collapsed together. In addition, it must be noted that all
five Frostig sub-tests were associated with One factor in the
Three-Test analysis previously presented. This evidence
appeared to support the assumption that this testwas unifactorial
in nature. Further evidence is presented in the Four-Test
analysis on which Form Constancy, the variable that comprised
Factor II of this solution, did not load with any factor.

Factor II, Form Constancy, was associated with the Form
Constancy sub-test (Table 18). The factor loading for this
variable was .89. However, the decision to interpret the
Frostig variables as a unidimensional set was determined by
the eigenvalue associated with this factor which was .8662.

This latter figure was considerably below the cut-off value

of 1.000. Furthermore, it has been noted that a factor with
only one loading is difficult to interpret. Ideally, at least
two variables should load on a factor before that factor can be
interpreted.

To summarize, the analysis of the DTVP revealed that this
test was unidimensional. This interpretation was consistent

with that suggested in the research review presented in Chapter I.

Factor II.a

61

TABLE 18

Principal Axis Factor Analysis with
Varimax Rotation for all Variables on the DTVP Test.

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
3 FC .89 .10 I .81

 

 

 

 

 

 

Eigenvalue .8662

% Var acct'd
for by Factor 25

 

aTwo factor solution

bu = 305

66%

Factor Analyses: Four-Test Battery

 

The results of the factor analysis for the Four—Test
Battery are presented in Tables 19-28. It appeared that the
best solution was a nine factor one where these nine factors
accounted for 64% of the factor variance. Every factor,
except Factor IX, had one variable with a factor loading of
.70 (Table 19).

The four test analysis was performed in the same manner
as the preceding)” All the criteria for factor analysis were
met with the single exception being that of the subject—
variable ratio criterion. However, these data were considered
important enough to include despite the failure to meet the
sample size.

Three PPMS sub-tests comprised Factor I, Body Coordina—
tion (Table 20). They were Walking Board, Kraus-—Weber, and
Angels-in-the-Snow. Two of the variables, Walking Board and
Angels—in-the-Snow were strongly associated with the factor
and had respective factor loadings of .71 and .77. The
remaining variable, Kraus-Weber, had a factor loading of .63.
The interpretation of this set of sub-test variables was
difficult to make without the subsequent separate PPMS factor
analysis also being considered. The latter analysis has shown
the Kraus-Weber and Angels-in-the—Snow variables continuing to
associate in a more interpretable factor. The Walking Board
sub-test associated with another set of variables which was
also more amenable to interpretation. Despite the magnitude

of the factor loadings associated with this factor it was

 

1See Appendix 1.

 

63

TABLE 19

Varimax Rotation Factor Loadings of All Variables for
Four Tests on a Nine Factor Solution.

 

 

 

 

 

Factors
Variables I. II III IV v VI VII VIII Ix
1 AR .69
2 VR —.53
3 VSM
4 AA .79
5 ASM
6 VA .49
7 vc "78
8 VE .64
9 so .72
10 ME .76
b11 EMC «77
c12 PG
13 FC
14 PIS '80
15 SR '59
16 DIFF -.54
17 SAME -72
dl8 WB .71
19 J
20 IBP “-80
21 IM ‘62
22 cc '59
23 KW .63
24 AIS .77
25 CB ’-52
26 RW
27 op -71
28 VAF ‘-69

Eigenvalues 5.369 2929 2.002 1.603 L492 1.427 1.183 1.105 1.066
% Var acct'd

 

 

for by Factor 7 ll 7 7 6 8 8 6 5
Total Variance accounted for by Nine Factor Solution 64%
an = 93

bThis Variable did not load above .50 on any factor.
CThis Variable did not load above .50 on any factor.
dThis Variable did not load above .50 on any factor.

64

TABLE 20

Factor I.a Principal Axis Factor Analysis with
Varimax Rotation for all Variables on Four Tests.

 

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
18 W8 .71 .28 IV .72
23 Kw .63 .32 Ix .66
24 AIS .77 .18 VIII .71
Eigenvalue 5.3694
% Var acct'd
for by Factor 7 64%

 

aNine factor solution

bN=93

assumed that the solution offered by the separate PPMS factor
analysis was probably the more interpretable one. The reason
for this was the simplicity of interpretation and the continued
association of the KrauseWeber and Angels—in-the-Snow sub-tests
in that solution.

Table 21 shows four ITPA sub-test variables associated
with Factor II, Auditory-Visual Understanding. These sub—tests
were Auditory Reception, Auditory Association, Visual Associa-
tion, and Grammatic Closure. The second and fourth variables
were strongly associated with this factor, and their factor
loadings were .79 and .72 respectively. Auditory Reception
had a substantial factor loading of .69 associated with Factor
II but the remaining variable, Visual Association, had a factor
loading of .49 which was just below the .50 level used in this
study to interpret a factor. However, as has been pointed out
in the previous analyses of the Three-Test Battery and the
ITPA, these variables clustered together consistently.

Three sub-test variables were associated with Verbal-Manual
Expression, Factor III, of this solution (Table 22). Two of
these variables demonstrated a strong and consistent associa-
tion on the same dimension. These variables were the ITPA
sub-tests, Verbal Expression and Manual Expression. The former
had a moderate factor loading of .64 associated with this factor,
and the latter had a fairly strong factor loading of .76. The
final variable which appeared to be related to Factor III was
the Wepman sub—test, DIFFERENT word—pairs with a factor loading

of .54.

 

 

66

TABLE 21

Factor II.a Principal Axis Factor Analysis with
Varimax Rotation for all Variables on Four Tests.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct.
Loading Factor High Communal— Factor
Loading Loading ity Solution
1 AR .69 .35 VIII .67
4 AA .79 .25 I .74
6 VA .49 .28 III .56
9 GC .72 .17 VII .61
Eigenvalue 2.6286
% Var acct'd
for by Factor 11 ' 64%

 

aNine factor solution

bN=93

 

67

TABLE 22

Factor III.a Principal Axis Factor Analysis withb
Varimax Rotation for all Variables on Four Tests.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
1 VB .64 .40 II .72
10 ME .76 .23 II .68
16 DIFF -.54 -.38 IV .68
Eigenvalue 2.0020
% Var acct'd
for by Factor 7 64%

 

aNine factor solution

IDN=93

 

 

68

In the previous discussion of the Three-Test analysis,
the two Wepman sub-tests loaded together. Because of the con-
sistent association of the first two variables, Verbal Expres-
sion and Manual Expression, it appeared that the association
of the present three variable set was due to the relatively
small sample size employed in the Four-Test analysis.

The other Wepman sub-test variable, SAME word-pairs,
and a PPMS variable, Ocular Pursuits, were related with Factor
IV, Recognition of Sameness (Table 23). The associated factor
loadings were .72 and .71 respectively. Although these factor
loadings were strong ones, the variables appeared to be less
related when the separate PPMS and Three-Test Analyses were
considered.

The Wepman variable SAME word-pairs, associated with its
opposite sub-test in the Three—Test analysis. This seemed to
be the most fruitful explanation for the factor association
of the variable set.

The Ocular Pursuits sub-test in the PPMS analysis, present-
ed next, associated with three other sub-tests and offered a logi-
cal explanation for their association. Like the Factor III above,
this dimension, Factor IV, seemed to be the result of the rela-
tively small number of subjects employed in the present analysis.

The Frostig sub—test, Eye—Motor Coordination, was associated
witfli a univariable dimension, Factor V, which was labelled Eye-
bhotOJ: Coordination (Table 24). Its factor loading was .77, but
Since: only a single variable loaded on this factor interpretation

is digEficult. Previous analyses have shown this DTVP variable

69

TABLE 23

Factor IV.a Principal Axis Factor Analysis with
Varimax Rotation for all Variables on Four Tests.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
17 SAME .72 .37 II .70
27 OP .71 .25 IX .67
Eigenvalue 1.6027
% Var acct'd
for by Factor 7 ' 64%

 

aNine factor solution

bN=93

70

TABLE 2 4

Factor V.a Principal Axis Factor Analysis with
Varimax Rotation for all Variables on Four Tests.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
11 EMC .77 .14 VII .65
Eigenvalue 1.4915
% Var acct'd
64%

for by Factorfi

 

aNine factor solution

bN=93

 

71

to be related to a unidimensional factor comprised of the other
DTVP variables.

Three PPMS variables, Identification of Body Parts,
Chalkboard, and Visual Achievement Forms, loaded on Factor
VI, Visual Body Orientation (Table 25).

The first sub-test, Identification of Body Parts had a
strong factor loading of .80 associated with this factor. In
the PPMS analysis, presented next, Identification of Body
Parts was associated with two other PPMS variables which
appeared to offer a more suitable interpretation for the fac—
torial nature of this variable.

The other two PPMS sub—tests related to Factor VI,
Chalkboard and Visual Achievement Forms, had factor loadings
of .52 and .69 associated with Factor VI. These two variables,
in the separate PPMS analysis, were related to two other sub—
tests which presented a logical and interpretable variable
set. One reason for assuming the separate PPMS factor analysis
yielded a better factor interpretation was that the number of
83 used approximated the subject-variable ratio criterion
previously discussed.

Factor VII, a spatial relations dimension, had two DTVP
variables related to it. These were the Position in Space
sub-test and the Spatial Relations sub—test (Table 26). The
former was strongly associated to the dimension with a factor
loading of .80, while the latter had a factor loading of .59.

The association of these two variables, Position in Space and

Factor VI.a

72

TABLE 25

_ Principal Axis Factor Analysis with
Varimax Rotation for all Variables on Four Tests.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
20 IBP .80 .17 II .72
25 CB .52 .40 I .71
28 VAF .69 .29 VII .63
Eigenvalue 1.4270
% Var acct'd
for by Factor 8 64%

 

aNine factor solution

b

N = 93

Factor VI.a

73

TABLE 26

Principal Axis Factor Analysis with
Varimax Rotation for all Variables on Four Tests.

 

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
14 PIS .80 .15 II .69
15 SR .59 .46 V .64
Eigenvalue 1.1831
% Var acct'd
for by Factor 8 64%
aNine factor solution

bN

= 93

74

Spatial Relations, was confirmed by the Three—Test and DTVP
analyses previously discussed. The Four-Test solution did not
load two other DTVP variables, Figure-Ground and Form Con—
stancy, in this factor analysis. It was noted that Eye-Motor
Coordination, the remaining DTVP sub-test, appeared to be a
univariable dimension associated with Factor V of this solu—
tion. The omission of two sub—tests and separation of Eye-
Motor Coordination in this solution suggested that the best
factorial association of these five variables was to be found
elsewhere. This assumption strengthened the earlier conclu-
sion that this set of variables was factorially associated.

Two associated ITPA variables, Visual Reception and
Visual Closure, comprised Factor VIII, Visual Understanding
(Table 27). Visual Closure had a strong factor loading of
.78 associated with this dimension. The other sub-test,
Visual Reception, had a factor loading of .53. These two
variables were consistently associated in the previous analyses,
and although the remaining variables generally associated
with them were not loaded on this factor, the consistency of
their related status could not be disregarded. Factor VIII
seemed to support the belief that these two variables were
substantially associated.

The final factor in this Four-Test solution was comprised
of PPMS variables, Imitation of Movements and Obstacle Course.
Factor IX, limb-trunk control (Table 28), was the only factor
in the present nine factor solution which had variables asso-

ciated with it that did not load in excess of .70. Imitation

Factor VIII.a

75

TABLE 27

Principal Axis Factor Analysis with

Varimax Rotation for all Variables on Four Tests.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
2 VR .53 .45 II .57
7 VC .78 .12 I .66
Eigenvalue 1.1054
% Var acct'd
64%

for by Factor 6

 

aNine factor solution

b

N = 93

 

Factor IX.a

76

TABLE 28

Principal Axis Factor Analysis with
Varimax Rotation for all Variables on Four Tests.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
21 IM .62 .32 V .62
22 0C .59 -.26 V .52
Eigenvalue 1.0657
% Var acct’d
64%

for by Factor

7

aNine factor solution

b

N = 93

 

77

of Movements had a factor loading of .62, while Obstacle

Course had a factor loading of .59. In addition, the PPMS
analysis also showed Imitation of Movements and Obstacle

Course loading on different dimensions. While the loadings

of these variables on their respective factors were not high

in the PPMS analysis, they were interpretable. This was not
the case in the present analysis. Again, the separate PPMS
analysis was the most valid, in that it approached the sub-
ject-ratio criterion proposed in Chapter II, and the variables
associated with the factors were interpretable.

The factor solution for the Four—Test Battery yielded
nine factors from the 28 variables. This solution appeared
to best describe the factor structure of the battery.
However, the interpretation was limited by the difficulties
which have been discussed. An increase in the sample size
would have resulted, in all probability, in a shift in the
factorial composition to conform with the previous analysis

of the Three—Test Battery.

Factor Analyses: The PPMS

 

The PPMS factor analysis which is presented in Tables
29-33 was performed in the same manner as the preceding
analyses. The intercorrelation matrix for the eleven sub-
test variables was submitted to Principal Axis Factor Analy-

sis with Varimax Rotation.l The eigenvalue criterion for

 

1See Appendix 1.

 

78
determining the number of factors to be rotated was, again,
1.000. Each factor which resulted from the four factor solu-
tion had at least one variable associated with it that loaded
in excess of .70 (Table 29). The total factor variance accounted
for was 62%. Each dimension accounted for a share of the
factor variance which exceeded 10%.

As with the Four—test analysis, the subject-variable
ratio criterion was not met. However, because of the reduc-
tion of variables in the intercorrelation matrix, the resul-
tant analysis approximates this criterion. At least 110 Ss
were needed to meet the minimum requirements of this factor
analysis, but only 93 55 were included. However, the solution
presented here probably offers a better explanation of the
factorial nature of the eleven sub—test variables than did the
previous analysis because it did approximate the requirements
for an adequate number of subjects.

The Kraus-Weber and Angels-in-the-Snow sub-tests loaded
Factor I, Trunk-Limb Coordination (Table 30). They both had
strong factor loadings of .80 on this factor, and both were
also associated in the Four-Test analysis. The strength and
consistency of the association of these variables seemed to
indicate that these variables were related to the same under-
lying dimension, although a final conclusion about their factor-
ial nature should await a more rigorous analysis.

The variables, Jumping and Obstacle Course, were related
to Factor II, Muscle Control (Table 31). Jumping was strongly

associated because its factor loading was .77, while the

 

79

TABLE 29

.Varimax Rotation Factor Loadings of All Variables
for the PPMS on a Four Factor Solution.a

 

 

 

 

 

 

Factors
Variables I II III IV
1 WB .55
2 J .77
3 IBP .72
4 IM .49
5 0C .64
6 KW .80
7 AIS .80
8 CB .74
9 RW .62
10 OP .76
11 VAF .51
Eigenvalues 3.3502 1.3309 1.0829 1.0279
% Var accounted
for by Factor 17 14 12 18

 

Total Variance accounted for by Four Factor Solution 62%

 

80

TABLE 30

Factor I.3 Principal Axis Factor Analysis with b
Varimax Rotation for All Variables on the PPMS Test.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next var acct
Loading Factor High Cemmunal- Factor
Loading Loading ity Solution
6 KW .80 .12 IV .65
7 AIS .80 .23 II .71
Eigenvalue 3.3502
% Var acct'd
62%

for by Factor 17

 

aFour factor solution

bN=93

a
Factor II.
Varimax Rotation for all Variables on the PPMS Test.

81

TABLE 31

Principal Axis Factor Analysis with

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
2 J .77 .12 I .63
5 0C .64 .09 III .42
Eigenvalue 1.3309
% Var acct'd
for by Factor 14 62%

 

aFour factor solution

b

N

= 93

82

Obstacle Course variable had a factor loading of .63. These
two variables presented a difficult interpretation problem
in the Four-Test analysis. The first variable, Jumping,
failed to load above .50 on any factor, but its association
with Factor II seemed to indicate a relationship. The Ob-
stacle Course variable became more interpretable in this
solution. Both variables appeared to be logically associa-
ted in this analysis and were easier to interpret in this
solution.

Factor III, Body Balance Orientation (Table 32), had
Walking Board, Identification of Body Parts, and Imitation
of Movements associated with it. Identification of Body
Parts had a factor loading of .72. The Walking Board had a
loading of .55, but the last variable, Imitation of Movements,
had a factor loading of .49. Imitation of Movements loaded
with the Obstacle Course variable on the Four—Test analysis
but as noted above, the latter sub—test had a substantial
factor loading on Factor II. The separation of these two
variables made interpretation easier because they appeared to
be logically associated in this solution. The three variables,
Walking Board, Identification of Body Parts, and Imitation of
Movements, associated on Factor III. All involved balance
and body orientation in a vertical plane. The sub-test
descriptions from Chapter I supported this observation.

The final four sub-tests of the PPMS appeared to be re—
lated to Factor IV, Visual Reproducibility (Table 33). The

sub-tests, Chalkboard and Ocular Pursuits, had factor loadings

83

TABLE 32

Factor III.a Principal Axis Factor Analysis with
varimax Rotation for all Variables on the PPMS Test.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
1 WB .55 .41 IV .75
3 IBP .72 .31 II .65
4 IM .49 .46 I .50
Eigenvalue 1.0829
% Var acct'd
for by Factor ' 62%

 

aFour factor solution

bN=93

Factor IV.a

84

TABLE 33

Principal Axis Factor Analysis with
Varimax Rotation for all Variables on the PPMS Test.

 

 

 

 

 

 

 

 

 

 

Variable's Factor 2 Total
Variable Factor Next High of Next h Var acct
Loading Factor High Communal- Factor
Loading Loading ity Solution
8 CB .74 .29 I .65
9 RW .62 .43 I .63
10 GP .76 .19 II .62
ll VAF .51 .43 II .59
Eigenvaluel.0279
% Var acct'd
for by Factor 13 62%

 

aFour factor solution

b

= 93

85

of .74 and .76, respectively, on this factor. Rhythmic Writing
had a factor loading of .62 associated with Factor IV. The
final variable, Visual Achievement Forms, had a factor loading
of .51. The Chalkboard and Visual Achievement Forms were asso-
ciated in the Four-Test analysis. Ocular Pursuits in a pre-
vious analysis loaded on a factor with a Wepman variable. In
this analysis, it presented a stronger association. Rhythmic
Writing did not load in excess of .50 in the Four—Test solution.
It appeared that this set of four sub-tests presented a more
reasonable factor association because all these variables in-
volved visual tasks. This fact seemed to account for the
apparent association among these variables.

The 11 sub-test variables of the PPMS best fit the four
factor solution presented above. This solution was more
economical than the one discussed in the research review.1
It should be recalled that the authors maintained that the
PPMS items were not factorially pure (Chapter I), and tentative
acceptance of this factor solution provided a PPMS dimensional

model which was not available before.

Factor Analyses: Summary

 

A tabular summary of the dimensions found in this study
is presented in Table 34.

The WADT was not submitted to separate factor analysis,
because it was felt that a test with only two generated sub-
tests was not amenable to factor analysis. Furthermore, the

character of the two generated sub—tests were such that it

 

1See Appendix 2.

86

TABLE 34

A Summary of the Factor Structure

of the Four Tests

 

 

Factor Name

 

and
Associated Common Associated Sub-Test
SI Code Name Variables

l. Auditory Visual Semantic Auditory Reception,
Understanding. Relations Visual Reception,
Cognition of Auditory Association,
Semantic Rela- Visual Closure,
tions (CMR) Visual Association,

Grammatic Closure.

2. Verbal Manual Semantic Verbal Expression,
Expression. Con- Correlates Manual Expression.
vergent Produc—
tions of Semantic
Relations (NMR)

3. Serial Learning. Auditory Sequential
Memory for Sym- Memory, Visual Sequen-
bolic Systems (MSS) tial Memory.

4. Visual Perceptual Spatial Eye-Motor Coordination,
Relations. Cogni— Orientation Figure-Ground, Form
tion of Figural Constancy, Position in
Systems (CFS) Space and Spatial

Relations.

5. Auditory Discri- Symbolic Wepman Auditory
mination. Evalua- Identification Discrimination Test.
tion of Symbolic
Units (ESU)

6. Trunk-Limb Flex- Kraus-Weber, Angels-in—
ibility and Strength the-Snow.

7. Limb Impulsion Jumping, Obstacle
and Gross Coordina— Course.
tion

8. Limb and Gross Walking Board, Iden-
Precision tification of Body

Parts, and Imitation
of Movements.

9. Visual Reproduc- Visual Chalkboard, Rhythmic

ibility. Memory Memory
for Figural Units
(MFU)

Writing, Ocular Pur—
suits, and Visual
Achievement Forms.

 

87

appeared they were measuring the same factor. The assumption
that the WADT was unidimensional was based upon inspection of
the Four-Test and Three-Test analysis. In the former analysis,
the two WADT sub-test variables, DIFF and SAME, loaded on
separate factors which were difficult to interpret (Tables 7.
and 8). When reanalyzed in the Three-Test case, these two
variables loaded on the same factor(Table 17). Also, the
variables that were associated with these two in the Four-Test
analysis presented a clearer factor structure after being
separated from the WADT sub-test variables (Tables 16 and 24).
It was assumed that the WADT was a unifactorial test of
auditory discrimination.

The analyses showed the ITPA best fits a three—dimensional
model. When each analysis was compared, three associated
variable sets appeared consistently: (a) the Auditory Recep-
tion, Auditory Association, Grammatic Closure, Visual Recep-
tion, Visual Association, and Visual Closure sub-tests were
on one dimension; (b) the Auditory and Visual Sequential
Memory sub—tests were on another dimension; and (c) the Verbal
Expression and Manual Expression sub-tests were on the third
dimension. It was assumed that the ITPA was a three dimen—
sional test. These dimensions were auditory-visual compre-
hension, auditory-visual serial learning, and verbal-manual
expression.

In the separate analyses, the DTVP yielded fairly consis-

tent results. Despite its loading on the final analysis as a

88

two dimensional test, the most satisfactory assumption was
that the DTVP was a unidimensional test of visual perception.
This decision represented the best explanation of the three
factor analyses in which the DTVP was a part.

The analysis of the PPMS suffered from a failure to meet
the subject-variable ratio criterion, because only 93 55 were
administered this test. Despite this shortcoming, several
similarities between the Four-Test analysis and the separate
PPMS analysis presented above led to the conclusion that the
PPMS was a four-dimensional test. The Four-Test analysis
indicated the PPMS loaded on four factors, three of which
contained two variables that were associated in the separate
PPMS analysis. The latter result produced the most acceptable
solution. The abilities associated with those four dimensions
were: (a) trunk strength and limb flexibility in a horizontal
plane; (b) limb impulsion and gross coordination; (c) limb
and gross precision in a vertical plane; and (d) visual coordi—
nation and reproducibility. These abilities provided the
best labels for the factors.

It was apparent that the factorial structure underlying
this battery of tests was best represented by nine dimensions.
These nine factors appeared to provide a parsimonious explana-
tion of the underlying dimensions of the 28 sub—test variables,
because the latter were consistent and easily interpreted across

the analyses. Finally, because the sample was fairly large,

 

89

these results were quite stable.

Two-Way Analysis of Variance: Age and Sex

 

Tables 35 and 36 present the results of a two by three
analysis of variance for sex and age effects. Factor scores
for each of five dimensions were derived from the Three-Test
Solution which was chosen because it appeared to best rep-
resent the factorial nature of the sub—test variables. The
DTVP and the WADT were unidimensional tests while the ITPA
was tridimensional. The ITPA's first dimension was comprised
of the Reception, Association, and Closure sub-tests. The
Verbal and Manual expression sub—tests loaded on another di-
mension while the third factor loaded the Sequential Memory
variables. The use of standard scores for analysis of
variance does not affect the results as Nunnally (1967 points
out, because, "...the results of a particular analysis of
variance would be the same whether the analysis started with
raw scores, deviation scores from the grand mean, or standard
scores from the grand mean. The different ratios of variance
would be the same regardless of which type of scoring was
used" (p. 106).

Factor scores are standardized scores (EEO, s.d.=1) based
upon the weighted contribution of each sub-test to a particular

factor. This weighing is a function of the measure of associ-

90

ation of a given item (the rotated factor loading). In general,
the higher the factor loading for a particular item the stronger
its association with the factor and the more it contributes to
the factor score. Factor scores allow the researcher to treat
these underlying dimensions as variables and their weighted
scores as variable scores.

Guilford (1954) in discussing experimental controls for

factor analysis observed that, '...It is good practice to con-
trol on the very common variables of age, sex, and educational
level" (p. 528). The analysis of variance was performed to
determine the extent to which experimental controls were present
in this study. In addition, the ITPA and the DTVP are presumed
to show developmental differences and it was expected that
differences would be obtained over the 18-month age range of

the sample.

The sample of 301 85 was divided into three groups by age,
beginning with 60 months. These groups were 60-65 months, 66—
71 months, and 72-77 months. Four 85 who were over 77 months
of age were excluded.

Of the 15 comparisons in the analysis of variance, only
three (Tables 35 and 36) had F—Ratios which were significant
at the .05 level. The second, third, and fourth factors
apparently were unaffected by sex and age effects. This indi-
cated that the WADT test results were not influenced by sex and
age differences in this sample. Also, the ITPA sub-test vari-
ables associated with the serial learning and verbal manual ex-

pression factors were not influenced by sex and age. If these

 

91

ITPA sub-tests were designed to yield differential results at
these age levels, these effects were not present. Consequently,
the usefulness of age norms for the sub-tests associated with
these factors on disadvantaged children was brought into question.

Factor 1 in Table 35 had an F-Ratio which was significant
for age effects. In order to determine which age levels dif-
fered significantly, post hoc comparisons of means were per-
formed using the Scheffe method (Hays, 1963). Each cell I
mean was compared with all other cell means, and three individ—
ual comparisons were performed. Of these three, the comparison
of means between Cell 1 (60-65 months) and Cell 3 (72-77 months)
was significant. These results indicated that differences on
the DTVP sub-test variables occurred only among 55 differing in
age by twelve months.

Factor 5, which had the reception, association, and closure
sub—tests of the ITPA associated with it, had two significant
F-Ratios for age and sex main effects (Table 36).

The F—Ratio for sex showed that the females differed
significantly from the males. It is possible that this dif—
ference can be attributed to either item bias in the sub—tests
or to basic developmental differences. Considering the fact
that language differences have been observed between sexes,
especially at this level, this is the most likely explanation
for the observed difference. If this set of tasks from the
ITPA does differentiate between males and females, the utility
of norms based upon combined scores is questionable.

The second significant F—Ratio of Factor 5 was for age.

It too was submitted to a post hoc comparison of means, and

92

TABLE 35

Two-Way Analysis of Variancea for

Sex/Age for Factor 1.b

 

 

 

 

 

df Mean Squares F-Ratio

A - Sex 1 1.20461444 1.8063
B - Age 2 2.19121325 3.2856c

AB 2 0.61280292 0.9189
Error Term 295 0.66690463
Total 300

aN = 301

b

Alpha of p<.05 required for significance.

CSignificant F-Ratio (.039).

Two-Way Analysis of Variancea

Sex/Age for Factor 5.b

93

TABLE 36

for

 

 

 

 

 

df Mean Squares F-Ratio

A - Sex 1 4.40911723 8.3567C
B — Age 2 8.96763619 16.9965d

AB 2 0.07484508 0.1419
Error Term 295 0.52761732
Total 300

aN = 301

b

cSignificant F-Ratio (.004).

d

Significant F—Ratio (<.005).

Alpha of p<.05 required for significance.

 

 

94

the results showed that the factor score means were significantly
different across each pair of cells. It appeared that as age
increased higher scores on the sub-tests for the older children
could be expected. This result was consistent with expectations
for children of different age levels. For this set of sub—tests,
presumably the ITPA does differentiate between age groups. It
appeared that age norms based upon the tasks associated with

this factor did discriminate among the disadvantaged children

in this sample.

To summarize the results of the analysis of variance for
sex and age effects, 12 F-Ratios out of 15 were not significant.
The ITPA sub—tests for sequential memory and verbal-manual
expression as well as the WADT sub-tests represented by these
non-significant F—Ratios were not affected by sex or age
differences. There were three significant F-Ratios. Factor
1, which loaded the DTVP variables, had a significant age
effect for 55 who were twelve months apart in age. Factor 5

presented significant main effects for both sex and age.

Multiple Regression Analyses: Least Squares Delete and Least
Squares Add

 

The Least Squares Delete and Least Squares Add multiple
regression analysis which follows was aimed at determining
which of several independent variables would serve as the best
predictor of I.Q.

In the Least Squares Delete program, when I.Q. was used
as the criterion measure and the 17 sub—test variables of the

Three—Test Battery were used as independent variables

 

the multiple correlation (R2) for the full group before dele—
tion of any variables was .68. From this set of variables, all
sub-tests except Auditory Association, Auditory Sequential Mem-
ory, Grammatic Closure, and Spatial Relations, were deleted one
at a time without a significant drop in R2. The significance
level was set at .05. With only Auditory Association, Auditory
Sequential Memory, Grammatic Closure, and Spatial Relations
left in the regression equation, the R2 was .63. These four
sub—test variables appeared to be significant contributors to
the explained variance accounted for by this prediction equation.
The Least Squares Add multiple regression analysis yielded
comparable results. For the Three-Test Battery, the first
variable to be added was Auditory Association and the regression
equation R2 was .50. Spatial Relations was added next, increas—
ing the R2 to .58. This increase was significant beyond the
.0005 level. Grammatic Closure was subsequently added with an

R2 increase to .61. The final variable added was Auditory

Sequential Memory which increased the R2 to .63. The computer
program (MSU Agricultural Experiment Station, 1968) identified
the same four sub-test variables as the Least Squares Delete
program above.

These two identical solutions using the multiple regression
formula to determine the best sub-set of predictors of I.Q. in—
dicated that Auditory Association, Auditory Sequential Memory,

Grammatic Closure, and Spatial Relations were the best pre-

dictors of this dependent variable.

CHAPTER IV

DISCUSSION AND CONCLUSIONS

 

This final chapter presents a discussion of the rela-
tionship between the hypothesized factor structure predicted
in Chapter I and the empirical factor structure presented in
Chapter III. In addition, the limitations of this study impli—
cations of this study for future research, and a summary are
presented.

Hypothesis Confirmation: _A Comparison of the Predicted
Factor Structure and the Empirical Factor Structure

For the purpose of this study, the confirmation of an
hypothesis was demonstrated by the degree to which a theore—
tically predicted set of variables belonging to a factor
corresponded to the set of empirically determined variables.
Further, such confirmation depended upon a psychologically
sound explanation which provided a suitable rationale for the
observed association of a set of variables. The confirmation
or disconfirmation of the hypothesized factor structures pre-
sented several difficulties.

First, Guilford's Structure of Intellect model (Figure 3)
upon which much of the predicted factor structure was based,
although the best model available, does have a shortcoming.

The model presents a set of ability dimensions which have been

96

97

obtained with adult 83. However, this does not necessarily
mean that those ability patterns will be matched by a child's
model. Guilford (1966) noted that his SI model presented some
difficulties when applied to the analysis of ability structures
in children. Below the sixth grade level, there has been some
differentiation of his ability factors but it appeared that
their detection depended upon the level of maturity of the S.
When the S possessed the maturity, the appropriate dimen-
sional tests could be administered and Guilford's factors dif-
ferentiated. It appeared that the prediction of ability di-
mensions in kindergarten Ss would be confounded by two things:
the lack of accurate information regarding the structure of
abilities for such 85, and the possibility that the 85 do not
possess sufficient maturity to differentiate the ability factors
when tested with appropriate indices of those factors.

The second difficulty encountered in the confirmation of
predicted factor structures involved the nature of the tasks in
this set of sub-tests. The suitability of these sub-tests to
differentiate the hypothesized factors was based upon a compari-
son of the sub—test tasks with the skills associated with Guil-
ford's SI model. The sub—tests were then grouped according to
the results of that comparison. Additional supporting evidence
was derived from the research review. However, a real possi-
bility exists that the tasks associated with this battery do
not differentiate the dimensions posited by Guilford.

A third difficulty derived from the subjective decisions re-

garding interpretation of the factors. The factor labels were

98

based upon an idiosyncratic decision about how they best described
the character of the underlying dimension.

A fourth difficulty lies in the studies chosen to support
the hypothesized factor structure. Inherent in each of those
studies were the same difficulties presented above. In addi-
tion, the nature of the results offered in those studies may
have been unintentionally misinterpreted.

A comparison in tabular form of the hypothesized factor
structure for this study and its empirical factor structure
is presented in Figure 4. There is some incongruity between
the two structures shown there. Seven hypothesized factors
were not present in the data. Despite the reduced number of
predicted dimensions appearing in the observed results, there
was not a great shift in any of the variables predicted to
associate with a factor. In general, the sub-tests were
associated as predicted. It appeared that the major inconsis—
tency between the two structures resulted from an over predic—
tion of factors rather than from erroneous predictions among
variables. This may have been caused by the aforementioned
difficulties of interpretation. The remainder of the dis-
cussion presents what was presumed to be a logical explanation
of the empirical factor structure in psychological terms so
that the inconsistencies observed regarding this structure and
the predicted factor structure should be mitigated.

The only factor which emerged as predicted was Factor 8
of the hypothetical structure,which was empirical Factor 5.

The WADT sub-tests were predicted to load on an SI dimension

99

Hypothesized Factor Structure

 

 

 

 

 

1 3 ‘ ' '
AR,VA AA.GC VR v
, (cm) (c-NM) _’{_ _

 

 

 

 

 

 

 

 

4 5

ASM VSM \
(MSS) (MFS-v) ’

6 7
PIS,SR EMS,FG,FC \
(CFS) (CFU-v) ’
wADT \
(MSU) 7

 

 

 

 

 

 

 

 

 

9 _ _ _
KW AIS
(TRUNK-STRENGTH) , _ fl;

 

 

10 14
J co >
(LIMB-THRUST) (GROSS BODILY
COORDIwION)
11 13
NB IM IBP ~—-—-9
(STATIC BALANCE) (ARM AIM)
12 15
(ARM STBADINESS) (OCULAR PURSUITS) . _ >
16
RW VAF
(MFU)

 

 

Empirical Factor Structure

1 AR, VR, AA, VA, vc, cc
(cm)

2VE,ME
(NMR)

3 ASM, VSM
(MSS)

4 ms, FG, FC, PIS, SR
(CFS)

5 WADT
(ESU)

6 Kw, AIS
(TRUNK- STRENGTH AND
LIMB FLEXIBILITY)

7 J,OC
(LIMB IMPULSION AND
GROSS COORDINATION)

8 WB,IM,IBP
(LIMB AND GROSS PRECISION)

9 CB, Rw, 01>, VAF
(MFU)

 

Figure 4. A Comparison of the Hypothesized Factor Structure

1

(HFS) and the Empirical Factor Structure (EFS).

1Broken lines Show variables which shifted predicted factor.
Boxes contain predicted factors which merged in empirical

structure.

100

labelled Memory for Symbolic Units (MSU). This dimension is
the ability to remember isolated items of symbolic information,
such as syllables or words. Some tasks associated with this
factor are memory for listed nonsense words or memory for non—
sense words through free recall. The WADT sub-tests did
associate with this factor.

A post hoc review of the SI abilities suggested a more
appropriate classification for the WADT dimension to be
Evaluation of Symbolic Units (ESU). This is the ability to
make rapid decisions regarding the symbolic identity or
accuracy of words, letter sets, and number sets. An example
of the associated tasks which correlated with the latter factor
was symbol identities. In this task, the S judged whether
both members of pairs of words were the same or different.
This task was similar to the task required by the WADT. It
will be recalled that the WADT presented forty word-pairs to
the S. Thirty of these were differentiated by one phoneme
while the remaining ten word-pairs were the same. The S
responded to the reading of these word-pairs by indicating
which were the same and which were different. This test
clearly required the same kind of skill as that required by
the E50 ability, Symbolic Identification.

The inconsistencies between the ITPA hypotheses and the
predicted factor structure appeared to be related to the ITPA
theoretical model. Meyers (1968), whose review of ITPA fac-

torial studies provided the basis for the ITPA predictions,

 

 

101

concluded that most of the studies he summarized had shown the
auditory and visual channels of communication from the ITPA
theoretical model to be the most useful for classifying the
sub-test variables of the ITPA. As a result of his conclusion,
the predicted factor structure of the present study stressed
these two communication modes. However, the results of this
study suggested an alternative solution to account for the fact
that the empirical factors had their ITPA variables associated
as they were.

In the present study, the ITPA's theoretical dimension,
channels of communication was less significant than the psycho-
linguistic process dimension. The latter dimension specified
the acquisition and use of the habits required for normal
language accomplishments, and was comprised of the receptive,
orgafizathxn and expressive psycholinguistic processes.

The first of these, reception, is concerned with how
meaning is obtained from auditory or visual linguistic stimuli.
The second process, organization, refers to the way in which
linguistic symbols are processed internal to the organism.

And the final process, expression, is concerned with how one
expresses oneself in words or gestures.

In the empirical factor structure, the ITPA sub-tests
appeared to form a single dichotomy. Those variables associated
with either reception or organization loaded on empirical Factors
1 or 1 while those related to expression loaded on empirical
Factor 2. In the data, this dichotomous separation by process
suggested that the ITPA emphasized the psycholinguistic pro-

cesses of reception and expression.

 

102

The explanation offered above suggested an altered ITPA
model which obtained empirical support in this study. All
three empirical factors loaded by ITPA variables were readily
interpreted if the model dimension was rotated to an expres-
sion-reception dichotomy.

Empirical Factor 1, labelled Cognition of Semantic Re-
lations (CMR), or semantic relations, is the ability to see
relations between ideas or meanings of words. An example of
a task associated with this dimension is verbal analogies.
This task involves the completion of a meaningful semantic
relationship.

The six variables associated with empirical Factor 1
represented the reception, association or organization, and
closure sub-tests. The first two terms, reception and associa-
tion, were defined above. Closure assessed the 8's ability
to integrate discrete verbal or visual units into a whole.

The first sub-test associated with this factor, Auditory
Reception, required the S to give a "yes" or "no" response
to a series of verbal questions. While not precisely a verbal
analogy, this task did require the S to complete a meaningful
verbal chain in order to be correct. Another sub-test related
to empirical Factor 1, Auditory Association, required the S
to complete a verbal analogy exactly as the SI task required.

A third sub-test, Grammatic Closure, required the S to
respond to incomplete verbal statements after first viewing

pictures which portrayed the content of the verbalizations.

103

This sub-test introduced a visual element, but its basic task
was to assess the ability to see a relationship between ideas
or meanings of words. Grammatic Closure is consistent with the
nature of the semantic relations task described above.

The three visual sub—tests of the ITPA which appeared to
be related to this factor may have loaded on it because the
Ss in this study may have been incapable of differentiating
the visual sub-tests. It will be recalled that this was
one difficulty discussed in interpreting the factor structure.

It seemed that these three sub-tests, Visual Reception,
Visual Association, and Visual Closure, required the 85 to
see relationships of a semantic nature. For example, the
Visual Closure sub-test required the S to identify an object
(e.g. a dog picture» and then from a new picture the S was
required to identify all partially hidden dogs in the picture.
This task has implicit in it the necessity to perceive a rela-
tionship between the idea of a dog and a class of body parts
associated with the concept dog. It seemed reasonable to assume
that these relationships were mediated in semantic terms by
the S. Once the object had been identified, the 5 might
have employed the object's name as a mediator while identify-
ing parts of the object.

The Visual Reception and Visual Association sub-tests pre—
sented highly similar tasks. In the former, the examiner pre-
sented a stimulus picture to the S, then the S was required
to point to one of four pictures which was related (e.g. the

stimulus picture was of a dog and one of the four response

104

pictures was of a different breed). The latter task, Visual
Association, required the S to point out which of four pic—
tures was most closely associated with a central theme (e.g.
the central picture was of a dog and one of the four response
pictures was of a bone). It is probable that a considerable
semantic element operated during the decision-making process
of the S. The ability to perceive relations either auditori-
ally or visually seemed to be involved in all these tasks.

Factor 2 of the empirical factor structure was named
Convergent Production of Semantic Relations (NMR). This
factor involved a semantic dimension which related to the
ability to produce a word or idea that conformed to specific
relational requirements. An example of a task associated with
this dimension was one requiring the S to produce a word
that was similar in meaning to two other given words. This
task, which required the generation of information from given
information to produce a predetermined response, involved a
type of convergent production ability.

The ITPA variables which related to Factor 2 were the
two expression sub—tests. The first, Verbal Expression,
required the S to describe an object which was handed him
by the examiner. Correct responses were defined in terms of
ten descrete categories. Some of these categories involved
shape, color, composition, function, and numerosity. For
example, the S was given an envelope and he would respond
by saying that the object was an envelope, it was white, it

was square, it was made of paper. Each of these responses

105

received credit when it belonged to a category.

The other expression sub-test, Manual Expression, required
the S to look at a picture of an object and indicate with a
gesture the activity involved in manipulating the pictured
object. For example, the S performed a hammering action on
the table after seeing a picture of a hammer. In both sub-tests
it appeared that the S was being asked to produce a gesture
or word that conformed to specified requirements. He was to
generate information from given information (e.g. the sight
of an envelope cued a set of related descriptive terms, or the
hammer picture recalled the use to which a hammer was put).

Empirical Factor 3, Memory for Symbolic Systems (M581 is
the ability to remember the order of symbolic information.
Tasks associated with this dimension included memory for
transposition of digits, consonants, nonsense word span, and
memory for order of listed numbers. These tasks all seemed to
tap memory for symbolic sequences in both a visual and verbal
mode. The two sequential memory sub—tests of the ITPA were
related to this factor. They required either memory for visual
symbolic sequences or verbal symbolic sequences.

Auditory Sequential Memory, it will be recalled, was a
digit span task similar to those associated with this dimension.
The S repeated a series of digits from two to seven in length
in response to an auditory presentation of the digit sequence.

The Visual Sequential Memory sub-test required the S to
replicate the order of a sequence of geometric figures after

having been exposed to it for a short time. The position in

106

space of the figure was not important, only the sequential order
was scored. This task appeared to be similar to the task re-
lated to empirical Factor 3 although it uses figural symbols
rather than digits or consonants. It was possible that the
Visual Sequential Memory sub-test loaded on empirical Factor

3 because it was purely figural.

Presumably, figural perceptions are developed before digit
and consonant recognition, thus the task was within the ability
level of the Ss in this sample. A similar task using digits
or consonant which required the S to read digits would almost
certainly be inappropriate for kindergarten 85. This suggested
that the Visual Sequential Memory sub—test may provide a useful
alternative in testing non—readers for sequential memory.
Further, it appears that if this ability dimension is to be
differentiated in young 85, an appropriate task to use might
be a figural sequential memory task.

The decision to hypothesize two dimensions, Factors 6
and 7, for the DTVP sub—tests was based on apparent similari-
ties between the test tasks and Guilford and Hoepfner's (1966)
description of the SI tasks. However, the research review
indicated that this test could be characterized as unidimensional.
The interpretation of empirical Factor 4 in this study was quite
clear. The DTVP was unidimensional.

Empirical Factor 4 appeared to be related to Guilford's
Cognition of Figural Systems (CFS), a Spatial orientation ability.

CFS is the ability to comprehend arrangements and positions of

107

visual objects in space. Some of the tasks which load on this
factor required the Ss: (a) To select from a group of six
drawings of a card shown rotated and/or turned over, the ones
which show the card not turned over, (b) To indicate from a
stimulus cube which of two drawings of the cube are either of
the same cube,or not the same cube judging from the markings
on the faces of the cubes, and (c) To indicate the position of
a boat with respect to the landscape after a pictured change
in the boat's position. These three tasks tested the spatial
orientation dimension.

The Frostig sub—test, Eye-Motor Coordination, is comprised
of two tasks. First, the S is required to draw lines between
progressively smaller boundaries. Second, the S is required
to draw straight lines between two objects and to connect as
many as three dots with straight lines between dot pairs.
Presumably, this variable tests the hand-eye coordination of
the S. However, it appeared that the required tasks were
related to the spatial orientation tasks because drawing lines,
whether curved or straight between boundaries or objects, did
require the S to perceive accurately the orientation of the
boundary or object with respect to the appropriate placement
of his pencilled lines.

The second DTVP variable, Figure-Ground, required the S
to draw lines around various geometric forms presented in a
distracting background. The discrimination of these figures
and their position in the distracting background appeared to

couple the orientation of the particular form in its space with

 

108

the recognition of that form.

Form Constancy,the third DTVP sub—test, required the S
to outline circles and squares presented in various orientations.
In some cases there were squares within squares with the forms
rotated into a different plane or these forms were presented
within unrelated geometric figures. It seemed that spatial
orientation was an important concomitant of this task.

The Position in Space sub-test, the fourth DTVP variable,
required the S to choose one of four objects which was either
identically oriented in space to a stimulus object or was
oriented in the inverse plane (e.g. the S selected one table
which was up-side down when all other tables shown are right—
side up, or the S selected one of four snowmen which corre—
sponded exactly to a stimulus snowman). Presumably, the re-
lationship of this task to a spatial relations dimension was
established here.

The final DTVP variable, Spatial Relations, required the
S to reproduce on the left half of a page a stimulus form
presented on the right half of that page. This was done by
connecting a series of dots in exactly the same form outline
and spatial orientation relative to the stimulus. Because
this task is labelled spatial relations and seemed to test
this ability, its association with the CFS dimension appeared
to be a logical one.

In summary, this set of Frostig variables purported to
test five unique abilities,but they seemed to be testing the

Spatial relations dimension described here. The discrepancy

 

109

between the predicted factor structure and the empirical factor
structure appeared to have resulted from an unwarranted reliance
upon the task descriptions presented by Frostig. These descrip-
tions are found in Chapter I.

The hypothetical factor structure posited eight factors
to explain the factorial nature of the PPMS. However, the
empirical factor structure resulted in four factors which
accounted for the PPMS factor structure.

Three predicted factors, 12, 15, and 16, merged to form
empirical Factor 9. This seemed to be a cognitive ability
dimension and was labelled Memory for Figural Units (MFU). The
tasks related to this dimension were visual memory abilities.
MFU is the ability to remember given figural objects. An
example of the tasks related to the MFU dimension was reproduc—
tion of designs. In this task, the S reproduced geometric
designs after having had a brief exposure to them.

The tasks related to the three factors which merged to
form this MFU dimension were found in the following PPMS
variables: Chalkboard, Rhythmic Writing, Visual Achievement
Forms, and Ocular Pursuits.

The Chalkboard task required the S to draw a single
circle across the midline of his body with one hand, draw two
circles simultaneously, one with each hand, draw a horizontal
line from right to left across his body midline, and draw ver-

tical parallel lines one with each hand. These tasks presumably
tested directionality and perceptual-motor match. However,
the performance of these tasks required the S to be able to

recall what the figure looked like before he could reproduce it.

 

110

The test instructions to the examiner stipulated that the task
was not to be demonstrated. Also, it seemed that the performance
of this task was conditioned by the maturity of the S. In-
adequate maturity would preclude the completion of these tasks.
It appeared that while these tasks tested perceptual-motor
functioning, an important cognitive ability, MFU, was related
to them.

Rhythmic Writing, another task which loaded on empirical
Factor 9, presented directionality skills. The S copied
written motifs (e.g._jj_rL_, eaaaaae, and pbpbpb ). Although
there may be a motor coordination component associated with
Rhythmic Writing, its successful completion required short
term memory for a figure.

The Visual Achievement Forms variable of the PPMS tested

the S's ability to reproduce,in prOper perspective geometric
forms. This task tested more than one ability, because the
geometric figures had to be reproduced in proportion to their
size as well as being placed on the page so that all the figures
could be drawn there. However, the reproduction of these geo-
metric forms appeared primarily to be a visual memory task.
It seemed that the ability to perform these tasks adequately
required a memory skill to reproduce the figures and to dimen-
sionalize them on the page so that all the figures were in the
same perspective.

The final variable related to this dimension was Ocular
Pursuits. This sub—test included various tasks in which the
eye followed a penlight moved from right to left, up and down,

and diagonally from left to right. These tasks tested both

111

monocular vision and binocular vision. This variable loaded
on the MFU factor because all the variables loading on this
factor have a visual component. It is possible that its
high correlation with this factor resulted from the visual
nature of the related tasks. The Ocular Pursuits variable
might load on a different factor if the PPMS were factor
analyzed with purely visual tests. Furthermore, the other
PPMS variables seemed to demonstrate tasks which were repre-
sented by Guilford's MFU ability. These data suggested the
presence of a cognitive dimension in the PPMS.

The three remaining PPMS empirical factors fit Guilford's
Matrix of Psychomotor Abilities presented in Chapter I (Table
I). The labelling of these factors resulted from the use of
the marginal designations in that table. The designations
which provided suitable classification categories for the psy-
chomotor abilities were: (1) the part of the body involved
and (2) the type of ability involved.

Empirical Factor 6, Trunk-Limb Flexibility and Strength,
was comprised of the PPMS variables, Kraus-Weber and Angels-in-
the-Snow. The factor label was derived from the trunk-strength
and limb-flexibility marginals presented by the Psychomotor
Abilities Index. Examples of the tasks associated with these
marginals are leg raising and kicking-height. The first task,
a trunk-strength ability, required the S to raise his leg
to the height of his head while in a sitting position. In
the kicking-height task, a flexibility skill, the S kick-

ed as high in the air as he could. This demonstrates

 

112

his flexibility: the extent to which that part of his body is
free to bend,or the scope of movement dependent upon a par—
ticular joint.

The Kraus-Weber variable presented two tasks. The first
required the S, in a prone position, to raise his trunk from
the floor for ten seconds while placing his hands behind his
neck. The other Kraus—Weber task required the S, in a prone
position, to raise his legs in the air for ten seconds. There
was a great deal of similarity between these tasks and the leg
raising task related to the Psychomotor Abilities Matrix.

The Angels—in-the-Snow tasks appeared to be limb-flexi-
bility tasks like the kicking-height ability. One example of
an Angels-in—the-Snow task has the S, in a prone position,
separate his legs laterally. move them as far apart as
possible,and then return his legs together. Another task has
the S, while prone, move his left arm and right leg from a
rest position, against the body, to one extended laterally from
his body before finally returning the extremities to rest.

These two PPMS variables, Kraus—Weber and Angels-in-
the-Snow, are related to the Psychomotor Abilities Matrix.
However, they appeared to have little in common except the fact
that they are both done in a prone position. This suggested
the possibility that some abilities here may be differentiated
on the basis of the Spatial position of the body during the
task. Indeed, this was the case when empirical Factor 8 was

analyzed.

 

113

Empirical Factor 8, labelled limb and gross precision,
was comprised of the PPMS sub-tests, Walking Board, Imitation
of Movements, and Identification of Body Parts. The marginals
which appeared to relate to the PPMS sub-tests were gross static
balance and limb dynamic precision. Both of these designations
were precision abilities, one static and one dynamic. Static
precision has to do with the accuracy with which a bodily posi—
tion can be held, while dynamic precision has to do with the
precision of directed movements.

A task descriptive of a static precision ability is the
two-foot rail-balance in which the S walks, heel-to-toe, on
a one inch board. The PPMS walking board sub-test required
the S to walk forwards, backwards, and sideways on a rail.

Dynamic precision is associated with tasks which do not
appear to exemplify the related PPMS sub—test tasks. One
such incongruent task was pursuit-aiming II in which the S
traces through a series of small Openings in a maze pattern.
This lack of a suitable task description explaining the rela-
tionship between dynamic precision and the empirically associat-
ed PPMS variables probably resulted from the tests which Guil-
ford used to postulate the psychomotor abilities. These abili-
ties were derived from tests of physical fitness, apparatus-
tests, and printed tests. Guilford used one kind of test in
each analysis to determine his postulations.

However, the definition of dynamic precision was descrip-
tive of the tasks related to the PPMS sub-tests which associated

here. It will be recalled that dynamic precision had to do with

 

114

the precision of directed movements. The PPMS sub—test, Imita—
tion of Movements, required the S to stand facing the examiner
and to imitate precisely the arm movements made by the examiner
in a manner analogous to semaphore signaling. Identification
of Body Parts required the S to touch the specific body part
named by the examiner.

Walking Board was a static precision task,while Imitation
of Movements and Identification of Body Parts were dynamic
precision tasks. Each of these PPMS variables appeared to be
precision tasks performed in an erect body position. Thus, it
seems possible that the tasks related to empirical Factors 6
and 8 are differentiated by the position the body assumed in
performing the tasks associated with them.

It was evident that at least one variable related to
empirical Factor 6, Angels-in-the—Snow, appeared to be an
analog of the tasks seen in the sub-tests, Imitation of Move—
ments and Identification of Body Parts. The latter sub-tests
were associated with empirical Factor 8. These three PPMS
sub-tests all involved directed movements of the limbs to
certain fairly precise positions. This result supported the
interpretation in this study' of two empirical factors differen-
tiated by the body position in which the related tasks were
performed.

The final factor which emerged from this investigation
was Factor 7 which was comprised of the PPMS sub-test variables,
Jumping and Obstacle Course. This factor appeared to be related

to the marginal designations, limb impulsion and gross coordina-

 

115

tion.

Impulsion pertains to the rate at which movements are
initiated from the stationary position. An example of an im-
pulsion task is a vertical jump. The tasks related to the
Jumping variable involve unilateral and bilateral jumping,
hopping, and skipping activities. They all appeared to be
clearly associated with the limb impulsion designation.

The gross coordination ability is exemplified by the hurdle-
jump and cable-jump tasks. In the latter, the S is required
to jump through a cable that he holds. The Obstacle Course
sub-test of the PPMS required the S to step over a knee-high
barrier which was placed between two chairs, to duck under the
barrier which has been moved to shoulder height, and to slip
between a wall and the tip of a stick that has been positioned
at a distance from the wall barely adequate to perform the
activity. It appeared that the Obstacle Course variable was
related here to the gross coordination ability.

Guilford (1958) noted in his discussion of the formulation
of the Psychomotor matrix that, "This factor apparently involves
coordinated activities of muscles of arms and legs, and perhaps
also the trunk" (page 172). This statement was supported by
the factorial association of the two PPMS sub-tests here,
because both involved coordinated activities of the limbs and
the trunk. However, these tests might be differentiated if
their analysis included tasks which clearly separated the limb
impulsion aspects of the PPMS variables from the gross coordi-

nation dimension.

 

116

To summarize, the hypothetical factor structure accurately
predicted Factor 8. A total of nine factors emerged from the
empirical analysis compared to 16 factors predicted from the
logical analysis. Several reasons were offered to explain
this discrepancy, one of which may have been the nature of the
sub-tests employed in the present battery. These sub-tests
may not have permitted an adequate differentiation of the
abilities derived from Guilford's model. Another factor ac-
counting for the discrepancy may be due to the nature of the
subject population tested and/or the age of the population.
Also, because these children did not come from a middle class
environment, they may not have had the opportunity to acquire
a highly differentiated ability structure. Finally, it is
possible that Guilford's highly differentiated ability model
is only appropriate at the adult level.

In general, the relationship of the sub-tests and the
empirical factors that resulted from the data appeared to have
a logical basis in the theoretical models proposed in Chapter
I. It is suggested that analysis of the sub—test variables
included in this study be performed with indices which are
highly associated with the hypothetical factors. This should
result in a more accurate prediction of the dimensional nature
of some of those variables. This seems to be particularly true
in the case of the visual and auditory sub-tests associated with
the ITPA and the psychomotor tasks related to the PPMS.

However, it does not appear that re-analysis would affect

either the suggested psycholinguistic process dichotomy of

 

117

reception and expression seen in the ITPA or the cognitive
loading of some PPMS variables. The hypothetical interpreta-
tion of the DTVP as a unifactorial test would have resulted if
less stress were placed on the inadequate test descriptions
relative to their factor character, and greater stress were
placed on the results from factorial research with the DTVP.
The Wepman Auditory Discrimination Test appeared to be accu-
rately predicted as a unidimensional test.

After the theoretical Factor structure and the empirical
factor structure of this 28 sub-test battery have been com-
pared, it is possible to suggest a set of sub-tests which
assess each of the ability factors identified in this study.

In factor order, according to the empirical factor struc-
ture presented in Figure 4, these sub-tests are: (a) Visual
Reception; (b) Verbal Expression; (c) Auditory Sequential
Memory; (d) Spatial Relations; (e) the WADT; (f) Angels—in-the—
Snow; (9) Jumping; (h) Identification of Body Parts; and (i)
Chalkboard. In addition to being the nine sub-tests with the
highest factor loadings, two of these tests accounted for a
significant portion of the variance in the multiple regression
analysis in which I.Q. was the criterion variable.

The addition of Auditory Reception and Grammatic Closure
to this set of nine tests constitutes the major predictors of
the nine ability factors and I.Q. A practical result of this
investigation has been the identification of these 11 sub-tests
which permits a reduction in diagnostic assessment time by at

least 50%.

 

118

Limitations of This Study

 

The results and discussion of this investigation which have
been presented are subject to certain limitations. These limi—
tations are:

a. The possibility that kindergarten 85 would not
possess sufficient maturity to differentiate the
ability dimensions posited by Guilford's SI model;

b. The 85 used in this study were all disadvantaged
children, whose characteristics are not representa-
tive of the general‘population of kindergarten 85,
making it difficult to generalize the factorial
results to the latter population;

c. The further development of the factor analytic
technique employed here may lead to a refinement
of hypothesis confirmation as used in this study;

d. The interpretation of the dimensions, presented
here, involved idiosyncratic decisions regarding the
appropriateness of the variable associations and
labelling;

e. The tasks represented by the Sub-tests, in the
present battery of tests, may not have included
tasks which differentiated the ability dimensions
proposed by Guilford; and

The ability dimensions posited by Guilford may
be appropriate only for adults or older school
age 55.

l'h
0

Implications for Future Research

 

Factor studies are usually exploratory. An investigator
has reason to believe that a group of variables are related to
a common underlying ability. Its identification will do a great
deal to explicate the nature of the variable set he is interested
in. The natural solution to his problem is the use of factor
analysis. Once done the investigator should turn his attention
to refining the variable set associated with the factor and

verify the factor under a variety of circumstances. The impli-

 

119

cations for further research below apply the factor variable

refinement and factor verification techniques.

This study identified nine factors presumed to be dimen—

sions of learning disabilities. Using these dimensions as a

model the following research appears fruitful:

1.

2.

A replication of this study using a sample of
300 55 for the Four-Test Battery;

An item analysis of the data to determine which
items are associated most highly to the factors.

A pool of these items and related items generated
by the investigator or selected from other tests
could be administered and factor analyzed to select
the items most highly associated with the factors.
Presumably this refinement would make available a
set of factor indices that have known factor asso—
ciation;

 

The sub-tests suggested as most representative of
the factor structure should be subjected to analysis
using marker variables to test the stability of this
factor structure. Then additional related tests
should be factor analyzed to determine the set of
sub-tests most associated with this factor structure;

Additional tests presumed to be associated with
learning disabilities should be placed into an
analysis with the known factor variables and the
factor character of the new tests determined. A
model of dimensions of learning disabilities would
result;

The factor scores of the 55 should be screened and
samples selected from the lower third, middle third,
and upper third of the 55. These samples should be
followed in school to determine the predictive
effects of this factor structure on school learning.
Presumably the lower third of this 85 pool will have
significantly greater problems in learning;

Multiple regression equations should be generated
and their efficiency tested. A limited indication
of this battery's predictive power for I.Q. was

the topic of one analysis. The need is to deter-
mine the best set of predictors for school achieve—
ment;

120

7. If these factors continue to show stability
they could become the basis for research into
remedial education. Presumably, if a child lacks
ability in a factor, knowledge of the specific
factor structure and character should permit one
to suggest activities associated with those factors
which would help improve the child's deficit;

8. This study suggested a possible deficit in the
theoretical model underlying the ITPA. If the
test is a three dimensional test, as suggested by
this study, then the usefulness of the theoretical
model is questioned. It should be examined to
establish the validity of its constructs or the
operational application of those constructs; and

9. The PPMS should be subjected to more rigorous
analysis to establish if the cognitive/psycho—
motor confusion in the sub—tests continues. If
so, the test might be modified to place it
appropriately as a perceptual motor test or a
cognitive test.

Summary

The major purpose of this study was to establish the
underlying dimensions of a set of tests of learning disability.
The tests chosed for study were the Illinois Test of Psycho-
linguistic Abilities, the Frostig Developmental Test of Visual
Perception, the Wepman Auditory Discrimination Test, and the
Purdue Perceptual Motor Survey.

It is assumed that the most economical application of
theory results in the theoretical dimensions of a particular
test matching the empirical dimensions found by factor analysis.
The test is the operational model of the theory. If this is
true, then a factor analysis of the present battery would
result in 28 factors or dimensions.

It became apparent upon examination of the material in the

tests that there was redundancy. To test the source of this

 

121

redundancy a suitable theoretical model was sought which would
explain the dimensionality of this battery without repetition.
The best theoretical models seemed to be Guilford's Structure
of Intellect Model and his Matrix of Psychomotor Abilities.
These two models provided the theoretical framework for
positing a factor structure for this battery of 16 dimensions.

These hypotheses appeared to be the most economical
explanation of the test battery and they summarized both the
tasks associated with the tests and the existing research to
form the hypothetical factor structure.

This test battery was administered to 305 disadvantaged
kindergarten 85. All the 85 took the ITPA, the DTVP, and
the WADT but time limitations permitted the administration of
the PPMS to only 93 55. All tests were given individually
by examiners who were advanced students in Education or Psychol-
ogy. The battery was given following the procedures of the
test manuals. To standardize the WADT it was recorded on tape
to avoid examiner differences in reading of the items. One
sub—test of the PPMS, Rhythmic Writing, was modified to include
only the first three items. The investigator felt these were
the only items suitable for use with the 85.

All the data analyses were done in the Michigan State
University Computer Center using the CDC 3600 computer. The
data were submitted to Principal Axis Factor Analysis with.
Varimax Rotation. The cut—off for determining the number of

factors to be rotated was an eigenvalue of 1.000. All factors

 

122

that were interpreted had at least one variable loading on them
in excess of .70, and the entire variable set associated with
the factor was loaded at least .50.

In addition to these analyses, a Two-Way Analysis of
Variance for age and sex was done with the factor scores. These
are standardized scores which are derived from the raw scores
multiplied by a weighted value associated with the factor load-
ing. In effect, the factor score transforms the factor into
a variable. The advantage of these scores is that they are
useful for individual comparisons.

The final analyses were multiple regression routines to
determine for this set of variables the best predictors of I.Q.
The Least Squares Delete program begins with the full set of
independent variables and deletesthem one at a time until all
variables which do not contribute significantly to the variance
of the criterion are eliminated. The Least Squares Add program
reverses the process by beginning with the best variable and
adding variables until those variables which contribute signifi-
cantly to the criterion variance are accounted for. The re-
sulting variables are the best set to begin with in predicting
I.Q.

Separate factor analyses for the Four Tests, for Three
Tests (excluding the PPMS), for the PPMS, for the ITPA, and for
the DTVP were consistent in their results. The major conclu—
sions of this study were:

I 1. The Four-Test Battery was essentially one of at

lease nine dimensions. These factors were Cognition

 

123

of Semantic Relations, Convergent Production of

Semantic Relations, Memory for Symbolic Systems,

Cognition of Figural Systems, Evaluation of Symbolic

Units, TrunkuLimb Flexibility and Strength, Limb

Impulsion and Gross Coordination, Limb and Gross

Precision, and Memory for Figural Units;

The succeeding analyses each produced similar

results. The factorial character of the separate

tests in the battery is as follows:

a. The ITPA includes at least three factors.
These are Cognition of Semantic Relations,
‘Convergent Production of Semantic Relations,
and Memory for Symbolic Systems.

b. The DTVP is a unidimensional test. This
factor is described as Cognition of Figural

Systems.

c. The WADT is a unidimensional test involving
the factor, Evaluation of Symbolic Units.

d. The PPMS includes at least four dimensions
and these include one clearly cognitive factor
Memory for Figural Units) and three psychomotor
dimensions. These are Trunk-Limb Flexibility
and Strength, Limb Impulsion and Gross Coordina-
tion, and Limb and Gross Precision.
The theory underlying the ITPA inadequately explains
the dimensional character of the test. It was
suggested that the model be thoroughly reviewed. From
these results it appeared the dimensional character
of the ITPA sub-tests are best explained by the re-
ception/expression dichotomy;

It is suggested that nine sub-tests instead of 28 could

be used to approximate the underlying nature of this

 

124

battery. These are Visual Reception (ITPA),
Verbal Expression (ITPA), Auditory Sequential
Memory (ITPA), Spatial Relations (DTVP), WADT,
Angels-in-the—Snow (PPMS), Jumping (PPMS), Identi—
fication of Body Parts (PPMS), and Chalkboard
(PPMS):

Auditory Association, Auditory Sequential Memory,
Grammatic Closure, and Spatial Relations seem to
be the best set of variables for predicting I.Q.

from this battery.

 

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APPENDIX

 

Means and Standard Deviations of All Variables1

130

Appendix la

for Four Tests.

 

 

 

 

Variables Means S:§§g:§g;
1 AR 18.882 5.586
2 VR 15.548 4.744
3 VSM 15.430 5.564
4 AA 16.839 4.838
5 ASM 22.183 7.885
6 VA 16.850 5.103
7 VC 21.301 6.589
8 VB 17.720 5.569
9 GC 11.333 3.754

10 ME 20.559 6.525

11 EMC 11.914 3.723

12 FG 11.473 3.923

13 FC 5.935 2.828

14 PIS 4.668 1.517

15 SR 3.011 1.787

16 DIFF 18.828 4.865

17 SAME 8.366 2.088

18 WB 10.398 1.532

19 J 3.151 .961

20 IBP 3.054 1.158

21 IM 2.979 .703

22 0C 3.742 .566

23 K-W 3.656 .596

24 AIS 3.441 .740

25 CB 13.161 2.142

26 RW 9.441 2.425

27 OP 13.505 2.754

28 VAF 5.570 1.668

1

131

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132
Appendix 1c

Means and Standard Deviations of All Variables1 for Three Tests

 

 

 

 

Variables Means Standard
Deviation
1 AR 18.925 5.977
2 VR 14.931 5.142
3 VSM 14.823 5.279
4 AA 17.033 5.187
5 ASM 22.885 8.349
6 VA 16.492 5.006
7 VC 20.180 6.637
8 VB 17.764 5.776
9 GC 11.810 4.881
10 ME 21.193 5.710
11 EMC 11.456 4.046
12 F-G 11.738 4.630
13 FC 5.879 3.242
14 PIS 4.849 1.711
15 SR 2.885 1.897
16 DIFF 19.469 5.418
17 SAME 8.108 2.294
1

N = 305

 

 

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Intercorrelation Matrix of Eleven Variablesl

Appendix 1e

134

 

 

 

for the PPMS
1 2 3 4 5 6 7 8 9 10 11

1 WE ---

2 J .22 ---

3 IBP .05 .30 ---

4 IM .06 .20 .24 ---

5 0C .16 .21 .17 .20 ---

6 KW .23 .09 .14 .21 .12 -——

7 AIS .37 .29 .17 .35 .07 .47 ---

8 CB .35 .14 .33 .24 .02 .23 .40 ---

9 Rw .21 .10 .16 .35 .15 .43 .26 .45 —--
10 OP .25 .21 .08 .17 .17 .14 .18 .36 .36 -—-
11 VAF .20 .33 .37 .27 .22 .15 .15 .36 .30 .27 ---

1N 93

 

Appendix 1f

135

Intercorrelation Matrix of Ten Variables1

for the ITPA

 

 

 

1 2 3 4 5 6 7 8 9 10
1 AR —--
2 VR .34 —-—
3 vsm .33 .23 --—
4 AA .47 .36 .38 -—-
5 ASM .25 .17 .28 .32 ———
6 VA .31 .40 .27 .46 .17 -——
7 vc .36 .27 .23 .31 .09 .31 ---
8 VB .31 .19 .28 .32 .07 .21 .05 --—
9 GC .42 .29 .32 .61 .26 .37 .30 .29 ---
10 ME .17 .14 .22 .24 .06 .24 .12 .52 .25 —--
1N 305

 

136

Appendix lg

Intercorrelation Matrix of Five Variablesl for the DTVP

 

 

1 2 3 4 5
EMC _-_

PG .35 ---

FC .14 .35 -_-

PIS .26 .37 .25 -_-

SR .36 .58 .31 .52 ---

 

N = 305

 

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On on is N« on an {N nu Nu HN on 3 3 NH OH «H 31.»..— NH HH 2 o o N o n a n N H
.
I NFC-Hm .HoucanSSnouu-L 2.» «o a: «a ngHuIHotoonoucH
.N 532:4 .N 53.8.:

 

138

Appendix 2b
VARIMAX ROTATED FACTOR MATRIX

 

 

 

Purdue 1-Motor Survey
Tasks Factors
1 II III IV V VI h2
1. Walking Board, Forward .03 .04 .77 -.18 .19 .07 .67
2. Walking Board, Backward .01 .21 .68 -.16 -.01 .33 .64
3. walking Board, sideways .03 .17 .74 -.15 -.18 .03 .63
4. Jumping .13 .21 -.04 -.18 .07 .65 .53
5. Ident. DIM My Pa ”t .20 .17 .14 -.10 .07 .54 .40
6. Imitation of rMovements .26 .27 .10 .11 .07 .63 .57
7. Obstacle Con -.20 .03 .44 -.07 .14 -.07 .26
B. Chalkboard: rCircle .03 .67 .00 -.25 -.04 .26 .58
9. Chalkboard: DBL Circle .06 .66 .15 —.14 -.01 .18 .51
10. Chalkboard: Lines, Lateral .12 .64 .15 —.21 .16 .ll .53
ll. Chalkboard: Lines, Vertical .11 .63 .10 -.ll .21 -.06 .30
12. Kraus-Weber -.15 .09 .12 -.50 .00 -.06 .30
13. Angels—in-the-Snow —.23 .29 .28 .07 -.10 .37 .37
14. Ocular Pursuita, Both eyes,
era .75 .06 .10 .01 .28 .12 .66
15. GP, Both eyes, Vertical .73 .10 .06 -.09 -.16 .30 .66
16. OP, Both eyes, Diagonal .83 .02 .08 -.04 .ll .14 .74
17. OP, Both eyes, Rota ary .82 - .04 .03 -.02 .06 .19 .71
18. Ocular Pursuits, Right eye,
.78 .36 .00 .02 .09 .04 .75
19. OF, Right eye, Vertical .82 .28 .02 -.04 .03 -.06 .76
2 OP, Right eye, Diagonal .83 .24 .04 -.14 .05 .08 .78
21. 09, ight eye, Rotary .81 .21 .05 .04 .14 -.02 .73
22. Ocular Pursuits, Left Eye,
.81 .00 .08 -.23 .07 .22 .77
23. OP, Left eye, Vertical .77 -.07 .ll -.25 .09 .30 .77
24. GP, Left eye, Di iag onal .81 -.05 .12 -.29 -.04 .05 .75
25. 0?, Left eye, Rota ary .76 -.08 .09 -.29 -.01 .24 .74
26. Developmental Drawing: Form .16 .ll .10 ..01 .75 .03 .62
27. Developmental Drawing:
Organization .13 .12 .01 -.29 .69 .18 .62
28. Rhythmic Writing: Rh thm .15 .l . -.
29. Rhythmic Writing: y 5 11 75 '03 '21 ‘66
Reproduction .ll .27 .10 -.
30. Rhythmic Writing: 60 '17 ‘45 '63
Orientation .11 .23 .17 —,75 .12 .,03 _57
v 1 26
i . .08 .07 .08 .05 .07

 

2
V (:Vi) - .61

 

lvi - 0 of variance explained by factor

2 .
V (xvi) - 0 of total varianceexplained by all factors

 

MICIHIIIWHSIMIWIUITHWITIWIIIWI'BTM
3 1293 03046 9930