{DIFFERENTIAL VALIDIT‘IES 0F SELECTED
VARIABLES IN THE PREDICTION OF
COLLEGE SUCCESS FOR BLACKS
AND WHITES

Thesis for the Degree of Ph. D.
MICHIGAN STATE UNIVERSITY
ANTHONY K. KALLINGAL
1970

   
 
  

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ABSTRACT

DIFFERENTIAL VALIDITIES OF SELECTED
VARIABLES IN THE PREDICTION OF
COLLEGE SUCCESS FOR BLACKS
AND WHITES

by Anthony K. Kallingal

This study explored three major research questions:

1. Is the same rule of prediction applicable to
blacks and whites when aptitude test variables and linear
regression are to predict college success? The same rule
of prediction will be applicable to blacks and whites
only if the regression surfaces represented by the equa-
tions for these two groups are homogeneous. Thus the
question becomes: Are the regression surfaces for blacks
and whites homogeneous? The ultimate aim was to discover
whether the use of aptitude test scores with the same re-
gression equation to predict college success for blacks
and whites would be biased against blacks.

2. How much of the criterion variance is ex-

flflainnd by the aptitude variables in each of the two

    

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Anthony 16. MW

3. Can the accuracy of prediction in.the case of
blacks be improved by the use of curvilinear models, by
the use of high school GPA in addition to the aptitude
variables and by the use of moderator variables?

The samples selected for the study were from the
population of freshmen who entered Michigan State Univer-
sity in the fall of 1968 and who completed the 1970 win-
ter term. Sample one consisted of all black students who
had complete data for various comparisons. For one set
of comparisons the black sample was 224 and for another
set of comparisons it was 216. Sample two consisted of
students randomly chosen from the white population. Its
size for one set of comparisons was 511 and for another
268.

The principal instruments in the study were MSU
English, MSU Reading, and the College Qualification Test
(CQT) with three subtests of Verbal, Informational and
Numerical abilities. The scores on these tests were used
in multiple regression to predict college success defined
in terms of the cumulative GPA at the end of the 1970
winter term and a test score GPA which was based on the
grades received in the basic college courses taken during
the name period. The basic college courses included area

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After establishing the fit of the linear model in
regression, the two groups were compared in terms of the
regression functions and the proportion of criterion var—
iance explained by aptitude variables. These comparisons
were made using the cumulative GPA and the test score GPA.
Improved prediction accuracy in the case of blacks was
attempted by exploring the possibility of the use of cur-
vilinear regression, by the use of high school GPA in
addition to the aptitude variables, and by the use of
moderator variables. The moderator variables were not
used in the regression equation but as basis for identi-
fying homogeneous subgroups in terms of increased pre-
diction accuracy.

The major statistical tools employed in the study
were factor analysis, 2 tests, and Variance Ratio Tests.
The decision rule in all tests was to reject the null hy-
pothesis at a = .05 level of type I error.

Results showed that the regression equations for
the two groups were significantly, though not substantially,
different. The regression equation for.blacks predicted
criterion values that were slightly lower than those that‘

would be predicted from the white or common regression ‘

equation.

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Anthony 1:. lallinghl

integrated university like Michigan State would improve,
the academic achievement of blacks; and, hence, predic-
tion from common regression would result in underestimates
of criterion values. Irrelevancy of curriculum and lack
of special intervention techniques to compensate for
earlier disadvantages might account for the lack of ex-
pected improvement in the academic achievement of blacks.

The partitioning procedure in which the overall
preportion of explained variance was partitioned into
parts attributable to individual factors revealed the
differing contributions of Verbal Ability Factor and
Numerical Ability Factor. Verbal Ability Factor was more
important in the prediction of both criteria for blacks
than for whites, and Numerical Ability Factor was more
important in the prediction of the test score GPA for
whites than for blacks.

Both groups were found to be equally predictable
in terms of the cumulative GPA. In the white sample
studied, twenty—eight percent of the criterion variance
was accounted for by the aptitude variables and in the
black sample twenty-eight percent of the criterion var-
iance was explained by the aptitude variables. The test

score GPA of the blacks were better predicted than the:

   

telt score GPA of the whites. In the black sample fiitge:

   
 

‘,g§g 'percent of the criterion variance was as?;_

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Anthony K. Kallingal.

forty-three percent of the criterion variance was ex-
plained by the aptitude variables.
An examination of scatter diagrams showed that
curvilinear models held no promise of improving predic-
tion accuracy over that achieved by linear model. The
addition of high school GPA to the set aptitude variables
resulted in six percent improvement with respect to the
criterion variance explained by the aptitude variables.
The six percent improvement was found to be statistically
significant. Sex and intra-individual variability index
were effective as moderator variables. Females were I
better predicted than males with respect to the cumulative
GPA, but not the test score GPA. Both criteria were bet- '

ter predicted for the low intra-individual variability

group than for high variability group.

 

 

DIFFERENTIAL'VALIDITIES
VARIABLES IN THE PREDI
COLLEGE SUCCESS FOR BLACKS

AND WHITES

or SELECTED
CTION OF
BY

Anthony K. Kallingal

A THESIS

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

DOCTOR OF PHILOSOPHY

College of Education

 

 

ACKNOWLEDGMENTS

My most sincere thanks as? expressed to my major
adviser, Dr. Robert C. Craig?‘;;o has been a source of
constant encouragement and support throughout my doc-
toral program. Sincere thanks are extended also to the
other members of the doctoral committee, Dr. Mary Ellen
McSweeney, Dr. Dale Alam and Dr. James Parker for their
constructive criticism.

Special thanks are due to Dr. Lawrence Lezotte
and Dr. Arvo E. Juola for their help in gathering the
data for this dissertation. Thanks are also due to Dr.
Willard G. Warrington for making the facilities of the
Office of Evaluation Services available for my use during
this project.

Finally I thank my wife, Leela, and my brother,

George, for their help and support during the three years

Of my graduate study.

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TABLE OF CONTENTS

ACKNOWI‘EDGMENTS O I O U C O I I I O C C O . I

LIST OF TABLES o o o o o o o I o I o o o o 0

LIST OF FIGURES . . . . . . . . . . . . . . .

Chapter

I INTRODUCTION . . . . . . . . . . . .

Statement of the Problem .,. . . .
Definition of the Terms . . . . . .
Theoretical Considerations

Need for Separate Rules of Prediction

Improvement of Prediction . . .

Assumption of Linearity in Prediction

Moderator variables in Prediction
Purpose of the Study . . .
Hypothesis in the Study . .
Limitations of the Study .
Summary . . . . . . . . . .

II REVIEW OF THE LITERATURE . . . . . .

III METHODOLOGY - o o I o e o , O O 0

Introduction . . . . . . . . .
Earlier Studies on Prediction:
A Brief Summary . . . . . . . . .
Comparison of Predictive Validities
for Blacks and Whites . ... .
Attempts to Improve Prediction
Use of High School GPA . .
Use of Alternate Models . .
Use of Moderator Variables
Summary . . . . . . . . . . .

Population and Samples f... .
Instrumentation andCr toxin '

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Page

 
 
   

    

stical Analyses
r l I

IV ANALYSES OF DATA:
The Data and its Transformation
Homogeneity of
Variances Expla
Examination of
Influence of Hi

Moderator Varia
V SUMMARY AND CONCLUSIONS

Discussion of Results . .
Suggestions for Further Research

ined by Aptitude Variables
Curvilinear Rel
gh School Schol

ationship
arship

bles in Prediction

 

132
135

an.” ‘6

 

 

 

LIST OF TABLES

Tables

2.1 Multiple Correlations of SAT-V, SAT-M, and
High School Grades with the Freshmen

Grade Point Average for White and Negro
Samples . . .

3.1 Intercorrelation Matrix of Test Variables

4.1 Means, Standard Deviations and Intercor-
relations of Group I

4.2 Means, Standard Deviations and Intercor-
relations of Group II .

4.3 Rotated Factor Loadings

4.4 Correlations of Factors with Criteria .

4.5 Analysis of Regression - Test for Group I

4.6 Analysis of Regression - Test for Group II.
4.7 Analysis of Regression - Test for Group I .
4.8 Analysis of Regression - Test for Group II.

4.9 Regression Coefficients and Standard Errors
with the Cumulative GPA as Criterion . .

4.10 Regression Coefficients and Standard Errors
with the Test Score GPA as Criterion . .

4.11, Analysis of Homogeneity of Regressions on

the Cumulative GPA as Criterion . . . . ..

, Analysis" of Homogeneity of Regressim "
the Test Score GPA as u.1mi¢n.rg_,;é

L

Page

33
57

75

76
77
79
80
80
81
82

85

   
   
    

 

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wa4.14. Correlations, Squares of Correlations,
' Values of Fisher Z' s and of z-statistic
with the Test Score GPA as Criterion . . . 95

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Sunttev Bi.m :;m a“
M.¢wwu1ative GPA en
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LIST OF-FIGURES

Figures

3.1

 

Curves Illustrating a Number of Different

Types of Mathematical Functions .

Scatter Diagram and
Cumulative GPA on
Blacks . . . . .

Scatter Diagram and
Cumulative GPA on
Whites . . . . .

Scatter Diagram and
Cumulative GPA on
Blacks . . . . .

Scatter Diagram and
Cumulative GPA on
mites O i I I I

Scatter Diagram and
Cumulative GPA on
Blacks . . . . .

Scatter Diagram and
Cumulative GPA on
Whites . . . . .

Scatter Diagram and
Cumulative GPA on
for Blacks . . .

Scatter Diagram and
Cumulative GPA on
for Whites . . .

Scatter Diagram and
Cumulative GPA on
Blacks . . . . .

Scatter Diagram and
,1 , Cumulative GPA on
M 2 I h .mite." . o I 0

Regression of the
MSU English for

Regression of the
MSU English for

Regression of the
MSU Reading for

e e o e 0 e o O 0

Regression of the
MSU Reading for

Regression of the
CQT—Verbal for

Regression of the
CQT-Verbal for

e e l I e e O o 0

Regression of the
COT—Informational

Regression of the»

COT-Informational

Regression of the
COT-Numerical for

Regression of the
COT-Numerical tor.'

:-¢ ‘_1

Page

61

97

98

99

100

101

102

103

104

 

 

 

CHAPTER I

INTRODUCTION

Statement of the Problem

 

With the increased demands for intellectual com-

petence in modern society, larger numbers of youth from

all segments of society are entering colleges and univer-

sities. In this context many educators find that the ex-

isting methods of prediction need to be improved so that
no student with the potential for success in college is
barred unjustly from gaining entrance to an institution
of higher learning. As a result, the search for better
predictors of college success has been pursued with in-
creased effort during the past two decades.

This increased effort has produced many predic—
tion studies relating to college success. In spite of
considerable variability of findings in these studies,

certain generalizations appear warranted. Usually high

school scholarship, measured either as high school grade

point average (GPA) or as high school rank, is found he m~¥Ll

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' the best single predictor of college succest”“‘
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also have some validity as predictors of academic success
(Segel, 1934; Crawford and Durham, 1946; Chauncey and
Frederiksen, 1951; and Fishman 1957). The academic suc-
cess of women is more predictable than that of men (Berdie,
1951; Knoell, 1961; and Seashore, 1962). The use of cer-
tain moderator variables has proved to be useful in iden-
tifying homogenous groups in terms of accurate prediction
(Ghiselli, 1960).

The above generalizations about the prediction of
college success generally have come under intensive study
recently to ascertain whether or not they are equally ap-
plicable to certain populations of students, especially
disadvantaged blacks. The applicability of these general-
izations to the population of disadvantaged black students
is of unquestionable importance today because of the in-
creased demand for larger enrollment of minority youth in
colleges and universities.

Some educators have doubted that aptitude test
scores are as valid for predicting the academic success
of the disadvantaged as for the advantaged (Clark and
Plotkin, 1963). Most of the black students in univer—
sities and colleges come from disadvantaged environments

(Fishman et a1., 1964). Hence, there is a need to in-

flestigate the predictive validities of aptitude mo fi“

 

 

are introduced to the relatively richer environment of

integrated colleges because of the possibility that the
change will improve their academic achievement. This
study addresses itself to this problem of differential
prediction of college success in integrated colleges,
using aptitude measures as predictors.

This problem of differing validities of aptitude
tests for predicting college success involves three as-
pects. First of all it must be ascertained whether or not the
same rules of prediction are applicable for both groups.
If not, the appropriate rules of prediction must be deter—
mined. Finally the amount of criterion variance that is
accounted for by aptitude variables individually and col—
lectively in each group should be assessed.

Another generalization accruing from predictive
studies is that high school scholarship is usually the
best single predictor of college success. But a recent
study by Thomas and Stanley (1969) cast serious doubts
on the usefulness of high school grades in predicting
college success of black students. Unreliability of
grade reporting, invalidity of grades in high school,
restriction in range, and intergroup differences in per-
sonality characteristic were advanced to explain this

PhengmenOn. Further research is suggested in View of fiEfi M

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' to this suggestion, this study investigated the relative Bil
improvement in prediction for blacks by combining aptitude
predictors and high school grade point average.

Past studies to improve the accuracy of prediction
by the use of personality and environmental variables as
additional predictors have not, to a large extent, been
very successful. Another approach to the use of these
variables has been suggested by Ghiselli (1956), namely,
as moderator variables. In this study the effective-
ness of the use of moderator variables in the case of
black students was also examined.

The problem to which this study addressed itself
was threefold: the problem of differential predictive
validities of aptitude variables, the problem of relative
contribution in prediction of high school grades when

added to the set of aptitude variables, and the effective—

 

ness of the use of moderator variables in the case of

black students.

Definition of Terms "

    
   
  
     

 

Throughout this manuscript several terms are used.
repeatedly. In the interest of clarity those terms are de-
fined below. «-t
l. Eradictor .

   

  
  

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or antecedent variable that provides information fdf
forecasting an unobserved event. The changes or dif4
ferences in the predictor variable are associated with
changes or differences in the unobserved event. Values
of a predictor variable thus afford a basis for pre-
diction of the unobserved event.

Criterion

The term "criterion" is used to refer to a dependent or
consequent variable which is presumed to be predictable
from the predictor variable or variables. A set of ob-
servable activities of behaviors that are relevant to
the criterion and that potentially can provide measures
may be termed the "criterion performance." The scores
obtained on an instrument or scale representing the
criterion variable are termed "criterion measures."
Regression equation

The term "regression equation" is used to refer to the
functional form of the relationship between the pre-
dictors and the criterion. This is expressed in the
form of a mathematical function in which Y, the crite—
rion, is set equal to some expression which contains

values on XS, predictors, and certain constants or

parameters. The functional form of the relationship

 

 

 

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Need for separate rules "__ ‘ ' H
7 are iction *
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in terms of two variables, which can then be readily

extended to the case of many variables. If we were to
plot the pairs of values of the two variables in a
plane where one is measured among the vertical axis
and the other is measured along the horizontal axis.,
the plotted points will reveal a pattern. The pattehq
may be such that the plotted points will be more or
less either along a straight line or along some curve.
In the case of a straight line pattern, the function-
al relationship is said to be linear and the mathemat- \
ical formula used to express this relationship is {
referred to as linear model.

Moderator variable

The term "moderator variable" is used to refer to a

variable, quantitative or qualitative, which improves

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the usefulness of a predictor or set of predictors by
isolating subgroups of individuals for whom that pre—
dictor or set of predictors are especially appropriate. '
A detailed explanation of this term will be provided

later in this section.

Theoretical Considerations

  
 
 

        

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the many factors that influence predictive validity of a
test in general, some affect predictive validity differene
tially for blacks and whites. Two factors that have dif-
ferential influence on predictive validity seem to be
crucial to the writer. The first one is the strength of
approximation of measured aptitude to the true intellec-
tual potential of the two groups. The second one is the
effect of events on the development of intellectual poten-
tial during the period that intervenes between measurement
of aptitude and measurement of criterion. This may be
referred to as differential developmental effect. Predic-
tion with the same rule will be jeopardized to the extent g
that there is significant discrepancy between the measured
capacity and the true intellectual potential of the groups
concerned, and to the extent that there is a differential 1
rate of development of the true intellectual potential for i
one group. These two factors will now be discussed in some
detail.
Assuming a satisfactory level of measurement accur-
acy for both groups, aptitude tests measure the current
functional capacity of blacks and whites equally well. In
this respect, the aptitude tests cannot be said to be
biased against any group even though they point out the' ‘_‘.J

existence of deficiencies in blacks. Clifford, stages; },5; y"
, 7 -‘ , . 1' ..

     
   

 

 

 

in the social, the economic, the educational, and the cul-
tural domains of American life is as erroneous as it would
be for residents of Bismark, North Dakota, to condemn the
use of thermometers as biased, when, as this is being writ-
ten, the temperature of Bismark is -11 F and in Miami,
Florida it is 83 F." Ausubel (1963) has written: "The
intelligence test...proposes to measure functional capacity
rather than to account for it. If the culturally deprived
child scores low on an intelligence test because of the
inadequacy of his environment, it is not the test which is
unfair but the social order which permits him to develop
under such conditions." Ausubel's statement about intel-
ligence tests is equally applicable in the case of aptitude
tests.

However, the problem of interest here is not what i
the aptitude tests measure, but whether the measured capac-
ity provides a fair picture of the innate potential of the
groups concerned. Léswlong as there is a significant dis-
crepancy between the measured capacity and the innate po-
tential, there is the possibility of a growth spurt due to
changes in the environmentfy’

In the case of most black students, it is safe to

assume that the measured capacity does not truly reflect;

      

fihe innate potential because of prior disadvantaged: »

 

 

Ausubel (1963) have described the characteristics of the.
home environment of Negro children that have a detrimental
effect upon their ego development. Deutsch (1963) while
discussing the learning process of disadvantaged child
makes references to the lack of variety of stimulation in
the home. The school environment does not seem to be any
better for black children than that at home. The majority
of Negro students, educated in both urban and rural com-
munities in North and South, have experienced grossly in-
adequate elementary and high school education (Green, 1969).
The result of a deprived environment both at home
and at school is that most blacks score below national
norms on aptitude tests. Bloom (1964) has documented the
fact that a deprived environment at home and in school will
seriously interfere with an individuals performance on
aptitude tests. According to Pettigrew (1964), the severe-
ly deprived environment of the average Negro child can
lower his measured aptitude in two ways. It can act to
deter his actual intellectual development by presenting
him with such a constricted encounter with the world that
his innate potential is barely tapped, and it can act to

mask his actual functioning intelligence in the test sit-

uation by not preparing him culturally and motivationallye-‘

for such a middle class task. It is fairly obvioussrgjg
”1: iflssfunctional capacity measured by spmdtaflsw*”**w‘

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10

children and consequently there.is the possibility of a-‘~-
growth spurt due to changes in the environment. Predic-
tion will be in error to extent that this growth spurt

has really occurred.

The second crucial factor affecting predictive
validity is related to the nature of intervening events.
This class of events is particularly important when the
criterion measure is obtained considerably later than the
testing of aptitude. If the time interval between the
test administration and the criterial assessment is lengthy,
a host of situational, motivational and maturational changes
may occur in the interim. An illness, an inspiring teacher,
a shift in the aspiration level or in the direction of
interest, remedial training, an emotional crisis, a growth
spurt or retrogression in the abilities sampled by the test
- all of these changes intervening between the testing and
the point of criterion assessment may decrease the predic-
tive power of the test.

One of the more consistent findings in research with
disadvantaged children is the decline in academic aptitude
test scores of such children with time (Fishman §E_al.,
1964). The decline is in relation to the performance of

advantaged groups. It is plausible to assume that-this,de-

cline represents cumulative effects of diminishedugvsck‘

 

 

‘WV...‘.

  

 

11

consideration, the predictive power of the academic aptitude‘
tests is impaired.

Looking in another direction, the normative inter-
pretation of test results cannot reveal how much the status
of underprivileged individuals might be changed if their
environmental opportunities and incentives for learning were
to be improved significantly. Some evidence for this type
of change is apparent in the success of the Boys Club of
New York in its educational program, which is designed to
give promising boys from tenement districts opportunities
to overcome their environmental handicaps through scholar—
ships to outstanding schools and colleges. Although the
majority of boys currently enrolled in this program had
mediocre aptitude and achievement test scores up to the
time they were given scholarships, practically all of the
boys have achieved creditable academic success at challeng-
ing boarding schools and colleges (Fishman gt_al., 1964).

A similar reasoning is applicable in the case of
black students attending integrated universities like Mich-
igan State University. It appears safe to assume that the
University environment is relatively richer and more stim-
ulating than they had previously known. The encounter with

this new environment may provide the needed motivation to

black students and thus possibly trigger an acceles~l:
ling ‘ .

 

 

 

 

If the above two assumptions, namely that of lack w
of congruity between measured aptitude and the innate po-
tential and that of accelerated growth of academic poten-
tial, were to be true in the case of black students attend-
ing Michigan State University, then the use of a common
rule of prediction for blacks and whites will result in
underestimates of achievement for blacks.

An analysis of regression equations computed sep-
arately for blacks and whites based on aptitude tests and
the GPA at the end of sophomore year would, it was believed,
provide empirical evidence for the lack of accuracy in es—
timating the success of black students from a common re—
gression line and possibly provide evidence of an acceler-
ated growth in the academic potential of the blacks at

Michigan State University.

Improvement of prediction

 

A regression equation computed by least square
methods provided a rule to predict achievement with the
minimum of error possible within the constraints of date.
In statistical terms the sum of squares for error, Eng-Y)2

where Y is the observed measure and Y is the predicted

measure on achievement, is minimum in least square pre-

  
 

diction. This error reflects the criteriOn Verfl

1.qu x... . o' ’394-

r ;_ not accounted for by the predictors "
" }I),§§'. put 1L.

 

  
     

 

   
 

the square of the correlation between the criteriomwadd.W &
predictors. Past studies have revealed that aptitude th;:f
have average correlations of .50 with college grade pointW1m ‘1)-
average. Consequently a large part of variance in college

GPA is not explained by aptitude tests. There have been

varied and repeated attempts to reduce the unexplained

variance so as to improve the quality of prediction. These

attempts have included procedures such as the addition of

high school GPA to the set of aptitude measures, the use

of alternate models for prediction, and the use of moder-

ator variables.

 

The assumption of 1
linearity in prediction

 

In almost all studies concerning prediction of
academic performance, the methods assume linear relation-
ships - that is, they assume that a unit increase in pre-
dictor variable will be followed by unit increases (or
decreases in the case of negative relationships) in the
criterion, and this will occur in the entire distribution
of scores. However, when one considers the degree of
relationship between ability and performance, he may find

that ability measures are predictive at some segments of

  
      
     

the range but not at others, and perhaps they are preng_Ij W
h} [NJ-.1. J,

:ve pnly up to a certain point. As McCloli
* h_, and 1.x- J¢.u be rraaeae as ‘ . -

 

  

   
   

Let us admit that morons cannot do good school waif.
But what evidence is there that intelligence is not
a threshold type of variable, that once a person
has a certain minimal level of intelligence his-per-
formance beyond that point is uncorrelated with his
ability? Several studies suggest that if such a
minimal level is set fairly high, ability may no
longer play a crucial role in success. Ann Roe in
her study of eminent scientists has reported in-
telligence test data showing a wide range from the
highest to the lowest person tested. It is true
that the average score was very high, but it is
equally true that there were several scientists ~
whose tested intelligence was only moderately above
average. In other words, given a certain high
level of intelligence, it is possible to be one of
the world's greatest living scientists.

The lack of linear relationship necessitates considerable f

     
  
  
  
   
   
   
  
    
  
 
   

computational work. However it is quite possible through
techniques of curve fitting to find non—linear regression
equations. The simplest of the non-linear regression is
the quadratic for describing the relationship between the
two variables. Curvilinear relationships are likely when
the predictors are intercorrelated.

For the case involving two continuous predictor
variables (x1, X2) and a single predictor criterion score,
Y', such as grade point average, a general mathematical
solution has been known for some time. The prediction
equation as a general polynomial function assumes the form

'1' = Alxl + Azx2 + A3Xi + A4X§ + Afixlx2 + A6,
where the A's are constants. If A3, A4, and A5 are equal

  

to zero, the equation reduces to linear form. The» 3
Mn, , ‘T V . ”iv (17;; ‘r . L , g

 

  
 

assigned weights by customary regression techniques
(Ezekiel and Fox, 1959). It can also be determined wheth—
er the squared and product terms add significantly to the

accuracy of prediction obtained by the linear composite.

Moderator variables

 

Attempts at improving prediction have involved the
use of large number of variables and multiple correlation
procedures. Improvement in these attempts depends upon
the use of predictors that correlate highly with the cri-

terion, but have low intercorrelations with each other. In

 

practice such predictors are hard to find.

Another approach to the improvement of prediction
has been suggested by Ghiselli (1956) who advocates the
use of moderator variables. The basic idea may be ex-

plained as follows. A look at the scatter of points around

 

the regression line in the case of one criterion and one
predictor will reveal that some individuals lie close to
the regression line and others deviate far from the re-
gression line. Ghiselli raised a simple, but long over-

looked question. If those whose scores fall on or near

the regression line constitute a specific subsample, the

 

 

 

16

variable the 'moderator variable.‘ This idea may easily

be extended analytically to the case of multiple predictors,
where the regression cannot be represented as a line. But
as a hyperplane in an non-dimensional space.

The idea of isolating homogenous subgroups in terms
of predictability and developing different regression equa-
tion for these subgroups has been tried prior to Ghiselli.
The terms 'population control variable,‘ ‘modifier variable,‘
and 'referent variable' have been used instead of the term
'moderator variable.'

A moderator variable may be quantitative or quali-
tative. In the case of a qualitative variable, the moder-
ating function consists in partitioning the sample into
homogenous subsamples in terms of predictability. Separate
regression equations may then be computed for each group to
maximise the accuracy of prediction. In the case of con-
tinous variables Saunders (1956) has developed a multiple
regression model which includes an expression for the
moderator variable. This is similar to the ordinary mul-
tiple regression procedure, except that the moderator
variables need not be correlated with the criterion vari-

able. In this study, moderator variables of the Ghiselli

type were used to maximise the accuracy of prediction for
blacks.

 

 

_ I, .....,
u. ;

 

 

 

  
   

17

Purpose of the Study

It was the purpose of this investigation to compare
the parameters of regressions of college grade point aver-
age (GPA) on aptitude test variables as predictors for black
students and white students at Michigan State University and
to determine the effectiveness of the use of high school GPA
as additional predictor and of the use of moderator variables
in prediction of college success. The aims were to discover

“M,___.
whether the same rule of prediction is applicable to both
groups or not, toLassess the amount of criterion variance
accounted for by these variables in each group, to determine E
the differential contribution of each of the aptitude var-
iables in the prediction of success for blacks and whites

Vuegijl "MA-V! m gram»?
explained variance in the criterion. The_hattery of tests

and to explore the possibility of further reducing the un- 54% ‘
3

administered to entering freshmen at Michigan State Univer-

sity by the Office of Evaluation Services was the basis for

the aptitude variables to be included as predictors. Com—

parison was made not only of the parameters of the regres-

sion on the overall GPA at the end of the winter term 1970

but also on GPA based exclusively on objective test scores

in basic college courses. These courses were American

Thought and Language 111,112,113, Humanities 241, 242 ,2§3, ;

 

 

 

18

A test of goodness of fit was made of eachrof the
regression equations to'determine whether the linear model
is an appropriate method of prediction. In order to deter-
mine the possibility of increased prediction accuracy by
choice of an alternate nonlinear model each of the predic-
tor variables was plotted against each of the criteria and
the resulting diagrams were examined. If the f(x,B) is
B-nonlinear, then statistical literature terms the model
nonlinear, whereas if f(x,8) is x-nonlinear, the model is
called curvilinear. Here the term nonlinear is used in its
generic sense which includes the notion of curvilinearity.
Increased prediction accuracy was also attempted by addition
of high school grade point average to the set of aptitude
variables and by use of moderator variables like sex, intra-
individual variability of the test scores in the aptitude
test battery, curricular preference, and urban-suburban-
rural home background.

The study attempted, therefore, to answer the fol-
lowing questions: '

1. Is the same rule of prediction applicable to both black

and white students?

2. If not, what are the appropriate rules of prediction for.

the two groups?
3- Ebw much of the criterion variance is acev:»m.l.

iflidtude variablaem

, ,-‘ ‘ > ,z ,. . " .
rwwmwst¢ewa“¢£*V~-i
, .w- a.

   
 

   
     
   
 
 

“_wri e.
‘. -

1': ‘_.I ‘r ‘

 
 

 

Y0.“

  

19

 
 
 

adding high school GPA as an additional predictor, laprs

introducing moderator variables, or by chasing an alter-

nate regression model?
The answers to these questions will be of benefit

to those who decide admission policies and those who are

responsible for academic advisement.

Hypotheses in the Study

The following hypotheses were tested in this study.

Each of the following hypotheses used two measures of the
criterion variable, namely the cumulative GPA and the test {
1
a

score GPA. Instead of repeating each hypothesis in terms
of each GPA the common term "college success" is used. How-

ever, each hypothesis was tested in terms of the cumulative
i

GPA and the test score GPA.
A linear equation is a good model of the relationship

1.
between aptitude variables and the college success
for both blacks and whites.

2. The parameters of regression equation for predicting

the college success at the end of sophomore year from

a set of factors derived from aptitude measures are

different for blacks from the corresponding parameter!

'—. C: 01»

for whites.
34fifrhenanount of criterion variance which is pr .,;

  

 

.
. m.

nun -
ll! 1 is enhanced:

a. if high school grade point average is added to thsi

set of aptitude measures, and

b. if moderator variables are used to identify homo-

genous groups in terms of predictability, specifi-

cally:
(1). Prediction is more accurate for those with low

intraindividual variability than those with

"IIH

high variability.

(2). Prediction is more accurate for females than

for males.

(3). Prediction is more accurate for students of

suburban origins than those of rural or urban

 

origins.
(4). Prediction accuracy differs according to the

curricular preference.

Limitations of the Study
There are certain limitations which must be taken

into account when generalizing the results of this study.

These limitations have their source in the assumptiona.e£

  

\— '.‘
NIH

1th. methods employed in the study and in the aeleflflhfln

 

 

21

for whom the prediction rules are to be applied shouid‘bo
similar to the environment and the characteristics of the
subjects from whom the prediction rules were drawn. Stated
in another way, the effectiveness of the prediction rule

for a particular group depends on its similarity of environ-
mental and personality characteristics to the norm group.

To the extent this assumption is violated, the prediction
will be in error.

Another general qualification of prediction studies
is the assumption of linearity of relationship between cri-
terion and predictors. The assumption of linearity in the
case of two variables means that the line of best fit which
specifies the relationship between the predictor and the
criterion is a straight line. To the extent that data \.
deviate from linearity, predictions based on a linear model
will be in error. A test of the linearity assumption was
carried out in this study and therefore information is pro-
vided as to whether data violate this assumption or not.

Another important assumption in prediction studies
using regression techniques is that of independent, normally
distributed error variable associated with each observation
or unit of analysis. The consequences of the violation of

this assumption have been discussed by J. Durbin and G. s.

Watson (1950), and D. Cochrane and G. H. Orcutt (Petite f_y

 

 

 

It

22

this study there is no reason to believe that the assump~:“
tion of independent, normally distributed error variable'
is violated. However, it might be a point of concern when
applying the results of the study to any specific group.

The manner in which the samples for this study were
chosen places some restriction on the generalizability of
the results. The two groups whose regression parameters
were compared were drawn from a population of students who
enrolled at Michigan State University in 1968 and who com-
pleted their sophomore year in 1970. Thus the samples are
not representative of the general population of freshmen
entrants. No information is obtained in this study on
those who dropped out for one reason or another from the
University during the first two years. In terms of gen-
eralizability, this study may be characterised as a study
of the persisters. The usefulness of the results to ad-
mission officers is therefore indirect and limited, since
they are more concerned with the problem of discriminating
the successful from the unsuccessful than with the problem
of differentiation between and within the groups of per-
sistent students.

Another source of limitation is inherent in the

factor analytic techniques employed in the study to avoid‘

the problems of multicollinearity. While factor scores.

in disentangle the “independent" effects of w"

l .

V a

 

 

 

  
   

23

in mind. In most cases, there are problems of factor inter-
pretation, because of unclear factor loading patterns. An-
other disadvantage of factor analytic technique is that the
procedure may lead to loss of information in the data. Keith
F. Punch (1969, p. 77) expressed this when he said:
The conceptual and operational elegance of a small
number of orthogonal predictors does not justify
unfair bruising of raw data and the consequent loss
of information.
This bruising and consequent loss of information occurs when
a few of the total number of the principal components are
chosen to stand for the entire set of variables. In this
study, all the principal components derived from data were

used and therefore no bruising and loss of information have

occurred.

W
This study addressed itself to the problem of wheth-
er the generalizations drawn from research studies about the
prediction of college success are equally applicable to a F

subpopulation of students, specifically the disadvantaged

        
  
   

blacks. After defining the terms frequently used in this
report, theoretical reasons that would indicate the likeli-
hood of differential predictive validities of aptitude var—
iables in the case of blacks and whites in integrated

_colleges were discussed.

24

The traditional approach to the improvement of pre-
diction was outlined. Although the use of non-cognitive
variables has not shown promise of improving prediction,
another approach to the use of these variables was sug-
gested, namely as moderator variables.

Finally, specific hypotheses regarding differential
validities and improvement of prediction were formulated

and the limitations inherent in the study were spelled out.

CHAPTER II

REVIEW OF THE LITERATURE

Introduction

 

The present study, while not a replication of any
previous research, has nevertheless evolved from the ex—
periences of earlier researchers concerned with the pre-
diction of academic performance in general, and specifi-
cally from the experiences of those concerned with
differential prediction of college success for blacks and
whites.

This review of past research experiences relating
to the prediction of academic success has three parts. The
first provides a short overview of earlier prediction
studies. The second reviews the literature that deals with
differential prediction. In this section, important stud-
ies comparing blacks and whites on predictive power of
aptitude, achievement, and other non-intellective variables
are summarized. The third part focuses on attempts to im-

prove the quality of prediction.

25

26

Earlierétudies on Prediction:
a Brief Summary

 

 

The earlier literature contains studies of academic
performance at all educational levels, but that pertaining
to undergraduates in colleges is particularly voluminous.
The use of tests in the selection of applicants for admis-
sion and in the prediction of academic success, defined in
terms of college grades, has been the most explored topic
in educational and psychological research. Segel (1934)
had summarized the findings of 23 studies before 1933.
Garrett, in his 1949 review, covering the entire literature
of nearly two decades, referred to approximately 194 stud—
ies. Fishman (1958) reported 580 studies in the years
between 1950 and 1958.

Most studies used aptitude test scores and high
school grades as predictors of future academic performance.
In an earlier review, Cronbach (1949) reported that abil-
ity test scores correlated about .50 to .55 with college
grade-point averages. More recent studies have not sub-
stantially altered this finding. Travers (1959) who cited
more than 200 prediction studies in his review, concluded
that high school grades are the best single predictor of
college success. A summary by Fishman and Pasanella (1960)
revealed that most of the prediction studies were limited
to a global prediction of either a semester grade-point

average or the freshman year grade-point average. A more

27

recent trend has been to compare subgroups of student
pOpulations on predictive validities and to make predic—
tions for different areas of the college curriculum. An-
other observation that can be made of the earlier studies
is that they attempted to predict academic success through
the use of a single variable, usually a standardized test.
Bruce (1953) summarizes the past research thus:
Since the early twenties, well over 1,000 studies have
been made in an attempt to better understand and cepe
with the problems of University admissions and failure.
About 90 percent of these studies used one variable
and calculated zero order coefficients or correlations
to determine evidence of predictive value of these
variables. Approximately 5 percent of the studies
combined two variables and computed multiple coeffi-
cients of correlation...About eight studies attempted
four or more variables with limited success, but
rarely does any one attempt as many as eight indepen-
dent variables.
More recently, the emphasis has been on the use of a com-
bination of variables. There is a distinct superiority in
multivariable prediction over prediction by the use of a
single factor. In 1953, Cosand summarized studies of
multiple predictors which showed a range of .53 to .83 with
a median of .63 in multiple correlations. These correla—

tions point out the advantage of using several predictors

rather than a single one.

Comparison of Predictive Validites
for Blacfis and Whites

 

Clark and Plotkin (1964) have questioned the

applicability of some of the generalizations that have

28

been drawn from earlier studies on prediction of black
students, especially those in integrated colleges. Fishman
et_al., (1964) have doubted whether academic aptitude tests
are as predictive of the college grades of disadvantaged
youths, especially blacks, as they are for advantaged
youths. An examination of recent studies led Thomas and
Stanley (1969) to reappraise the effectiveness of high
school grades in predicting college success for a segment
of the general pOpulation, namely, the black students.

One of the first studies published on the predic-
tion of college grades from aptitude test scores involving
a large number of Blacks and Whites was that of Hills in
1964. He analyzed the data from several colleges of the
University System of Georgia over a five-year period, from
1958 through 1962. Included among the colleges were the
University of Georgia, Georgia Institute of Technology, a
number of four—year colleges, and three four-year colleges
attended solely by Negroes. SAT—Verbal, SAT-Math, and high
school averages were used to predict freshmen average grade.
The multiple correlation coefficient was computed for each
college for five years. The average R (multiple correla—
tion coefficient) for five years in the three predomin-
antly Negro colleges was .57, while the average R for the
predominantly white Georgia Institute of Technology was
.58. Restriction in range of SAT scores and curtailed
distributions for the predominantly Negro colleges did not

appreciably affect the multiple correlations.

29

Biaggio and Stanley (1964) subjected data reported
by Hills and his associates for the four academic years
1959-60 through 1962-63 to analyses of variance after
applying a correction for the restricted range in the
scores of the Negroes. They found that the correlation
of test scores with the freshman grades was significantly
higher for the Negroes for SAT-Math and SAT-Verbal than
for the Whites. However, when such restriction of range
was not considered, it was found that non—Negro females
could be predicted significantly better than Negro females,
and that there were no significant differences among males.

It is the view of Stanley and Porter (1967) that
Biaggio's procedure for correcting r's for restriction of
range caused by truncation of scores explicitly on a pre-
dictor variable probably overcorrects. For this reason,
comparisons that involve adjusted r's are based on greater
anticipated predictability of freshmen grades within the
predominantly Negro colleges than would likely be achieved
with an easier SAT-like test. Stanley and Porter suggest
another procedure for correction based on extrapolation
from a portion of the distribution (central) to the extrem—
ities of the distribution. The basic purpose of correction
procedures is to estimate the variance that would be ob-
tained if an easier test were to be administered. Only
empirical studies, involving easier instruments, can show
how good these estimates are. Further light needs to be

shed on this problem.

30

Mckelpin (1965) studied the significance of the
predictive validities resulting from the combination of
scholastic aptitude test scores and high school average
for predicting freshmen grades for the students at the
North Carolina College, Durham, which is a predominantly
Negro college. Zero order correlations and multiple
correlations between preadmission indices (SAT scores and
HSA) and first semester average grades were obtained for
the freshmen in 1961, 1962, and 1963 (males and females
separately). Multiple correlations averaged about .65.
They are as high as those usually reported in the litera-
ture for college freshmen.

The author draws two conclusions from the results.
Firstly, in terms of first semester freshman grades at
North Carolina College, SAT scores seem to give a fair
appraisal of what to expect of these students. Secondly,
while the abilities measured by the SAT have not been
deve10ped to any extent in the students tested, the extent
to which the abilities have been developed is reliably
measured.

Mckelpin‘s discussion of the results is particu-
larly important and very pertinent to the present study.
His conjectural remarks have provided a basis for the.
theoretical rationale of the present study. Why do the
predictive validities for freshmen in Negro colleges look

so good, even with the low SAT scores and their restricted

31

range? The answer seems to reside in relationships that
obtain among elements indigenous to both separate high
schools and separate colleges. In other words, the answer
seems to lie in the perpetuation of similar environments
in segregated high schools and colleges. But these pre-
dictive validities do not say anything about the likely
performance of those students who operate under conditions
in which the typical college freshmen in the nation
perform.

Munday (1965) studied the American College Testing
Program data for five predominantly Negro colleges to
determine if the validity of the American College Tests
would be adversely affected in colleges whose student
body was predominantly Negro. The accuracy of the pre—
diction of college grades for the five schools was des-
cribed by three types of multiple correlations. The first
one is the multiple R resulting from optimally weighting
the four ACT tests. The second one is the multiple R
derived from optimally weighting four high school grades.
The final one is developed by averaging the GPA predic-
tions made by the Optimal weighting of tests and those
made by optimally weighting high school grades. The
major finding was that the ACT scores in combination with
high school grades operated with about typical efficiency
in these colleges. The conclusion of the study was that

if standardized measures of academic ability are culture

32

bound, as seems likely, this feature does not appear to
detract from their usefulness as predictors of academic
success.

In order to offset the effect of the restricted
range on correlations, a correction was introduced in the
study by arbitrarily giving each college the same variance
on the ACT composite. As mentioned earlier, this correc-
tion is fraught with danger of unduly inflating the pre-
dictability of grades from ACT test scores.

A well designed study by Stanley and Porter (1967),
using the data reported by Hills, supports the position
that academic aptitude tests predict college freshmen GPA
equally well for blacks and whites. They extended the
Biaggio (1965) study to cover six years; instead of the
original four years. In their basic design, there were
three classificatory factors: predominant racial composi-
tion of colleges (Negro versus Non-Negro), colleges nested
within race, and the six years. The analyses of variance
of r's transformed to Fisher z's were done separately for
men and women to test the statistical significance of the
main effects of race and year and the interaction of race
with year. White males did not differ significantly from
Negro males, but white females were significantly better
predicted than Negro females. The year effect was signi-
ficant beyond the .05 level in both, which means the pre-

dictability of males and females varied from year to year.

33

The interaction of race with year was significant at the
.05 level for women, but not for men. This seemed to re—
sult because white females had about the same r's from
year to year, whereas Negro females fluctuated greatly.

Thus comparisons of zero order r's involving SAT-
Verbal or SAT-Mach as the predictor of freshmen grades
reveal that the achievement of white women was pre-
dicted significantly better than that of NW (Negro
Women) by both, whereas the achievement of white men
was not predicted significantly better or worse than
that of Negro men by either; in fact, freshmen grades
of NM (Negro males) were predicted better than those
of WM (White males) by SAT-V scores in five of the

six years. (Stanley & Porter, op. cit., pp. 209-210)

The best weighted linear composite of SAT-V, SAT—M,
and high school grades resulted in average multiple r's

(via mean z's) for the six years as given in Table 2.1.

TABLE 2 . 1

Multiple Correlations of SAT—V, SAT-M,
and High School Grades with the
Freshmen Grade Point Average for

White and Negro Samples

 

 

 

 

Male Female
White .60 .72
Negro .60 .63

 

The range in multiple r's over the six years was between
.55 and .69 for Negro women, but those for white women were
steady across years. The multiple r's for Negro men varied

from .55 to .69.

34

Thus, in view of the detailed analysis of the Georgia
data and several related studies, it seems likely that
SAT-type test scores are about as correlationally valid
for Negroes competing with Negroes and taught chiefly
by Negroes as they are for non-Negroes taught chiefly
by non-Negroes. Prediction may be approximately equal
for the races within integrated colleges, too, as an
investigation in three such institutions suggest.
(Stanley and Porter, 0p. cit., p. 216)

The investigation referred to by Stanley & Porter
is that of Cleary (1968). She was checking the statement
by Clark and Plotkin (1963) that the academic performance
of the college students they studied was far above the
level that would be indicated by predictive indices such
as SAT scores. A test is biased if the criterion score
predicted from the common regression line is consistently
too high or too low for members of a subgroup. The test
is unfair if the use of the test produces a prediction that
is too low. If such a test is used for selection, members
of a subgroup may be rejected when they were capable of
adequate performance. The samples in her study were drawn
from three integrated colleges of which two were from the
east and one from the southwest. From each college the
samples were selected in the following manner: all the
Negro students of one college were selected to form sample
one; sample two consisted of white students matched with
Negro students on curriculum and class; sample three was

randomly selected from the white students of the college.

Thus there were altogether nine samples in the study.

35

The criterion in each school was Grade Point Average
(GPA). The predictors were the Scholastic Aptitude Test
Verbal (SAT-V) and Mathematical (SAT—M) scores and high
school average or rank. Separate regressions were computed
using first SAT scores only as predictors and then adding
high school rank or average to the set of predictors. Accord—
ing to Cleary, if the regression of the criterion on the test
is the same for different groups, then the test cannot be
said to be biased in terms of its predictive validity. The
regression tests of the analysis of covariance were used to
determine the difference in regressions. The calculations
were performed by a method due to Beaton (1964). The method
of analysis makes it possible to test the hypotheses of
equality of slopes and equality of intercepts.

When the SAT scores alone were used as predictors,
there was no significant difference in regressions in the
two eastern schools. But in the southwest college, the
regression lines were significantly different: the Negro
students' scores were overpredicted by the use of the white
or common regression line. When high school grades or rank-
in-class were used in addition to the SAT scores, the degree
of positive bias for the Negro students increased. An ex-
planation for this was that many of the students may have
attended only partially integrated secondary schools and the
grades from predominantly Negro and predominantly white

schools may not be comparable.

36

The last study to be described in this section is
that of David D. Sampel (1969). This study was designed to
determine if the Cooperative School and College Ability
Test (SCAT) can predict future college academic success of
Negro college students with the same degree of accuracy as
it does for white college students and to discover if the
sex factor need be considered in making predictions. The
sample consisted of 180 Negroes matched with the Whites on
sex, college, and year in school from the University of
Missouri, Columbia. A correlation coefficient was com-
puted between SAT total score and cumulative grade point
average, and between the high school rank and GPA. In the
Negro female group, coefficients were generated that are
normally expected with college GPA. No correlation was
evidenced in the Negro male group. It was hypothesized
that sex is an important consideration when making academic
predictions for college students and that it is inappro-
priate to make academic decisions concerning Negro male
students on the basis of his SCAT total score. He con-
cluded the study with an observation on the Clark and
Plotkin suggestion that standardized tests are not appro-
priate for predicting academic success for Negro students
and that motivation was a more important consideration.
This view, he said, cannot be supported or refuted at this
point, but more investigation is needed in view of the

fact that the SCAT total score used in the current study

37

had no correlation with academic success in the case of
Negro males.

In contrast to the above findings, Green and
Farquhar (1965) observed conspicuous lack of similarity
in the correlations of black and white students between
high school grades and scores on the School and College
Ability Test. Their conclusion was that SCAT scores are
not good predictors of high school success for blacks,
especially for males. They also found that a test of
achievement motivation measured by the Self-Concept of
Academic Ability Scale correlated higher with the school
grades than with the verbal section of the SCAT. The
correlation for males was .36 and for females was .65.
These results seem to corroborate the View of Clark and
Plotkin (1964) that the standardized tests are not appro-
priate for predicting academic success for Negro students;
rather, that motivation is a more important consideration.

Boney (1966) employed a large number of aptitude
and mental ability measures and studied their efficiency
in predicting high school grade point average for Negro
students in secondary schools. The predictor variables
in his study were: the Differential Aptitude Tests, the
California Test of Mental Maturity, the Cooperative Abil-
ity Tests, the Sequential Tests of Educational Progress,
and Junior High School Grade Point Average. He obtained

a multiple R of .80 with standard error of estimate of .87

38

for boys and an R of .82 with standard error of estimate

of .89 for girls and concluded that regression equations

could be computed in junior high school which would pre-

dict high school grades with reasonable accuracy for this
population and that Negro students are as predictable as

other groups.

All of the studies so far described, except that
of Cleary have taken correlation coefficients as a unit of
analysis. The similarity of the correlation coefficients
between predictors and criterion for the two groups indi-
cates that the accuracy of prediction for both groups is
similar. But it does not necessarily indicate that the
same rule of prediction can and should be used for these
two groups. In other words while the correlation coeffi-
cient is similar for both groups, the parameters of the
regressions for these two groups may be significantly dif-
ferent. Cleary (1968) noted in her study a difference in
the regression lines for black and white students at a
southwestern college. But it was a case of overprediction
of black students' college grades by use of a common re-
gression line. In order to ascertain whether the same
rule of prediction can be applied to both groups - which
is of prime concern in this study - further investigation
has to be made about the difference in regression para-

meters.

39

Moreover, the effect of restricted range on corre~
1ations is a disturbing factor in studies comparing the
predictive validities for blacks and whites. Biaggio and
Munday attempted to correct this influence of the restricted
range. But the correction is fraught with the danger of
unduly inflating the predictability of the group for which
the correction is made. The regression weights in regres—
sion equations are less influenced than the correlation
coefficient is by restricted range in predictors. Thus a
comparison of regression equations appears a more appro-
priate procedure than the use of the correlation coeffi—
cient.

Also, all the studies, except that of Cleary and
Sampel, compared black students from predominantly black
institutions with white students from predominantly white
institutions. These conclusions therefore cannot be ex-
tended legitimately to integrated colleges. The environ-
ment of the segregated colleges is likely to be a perpetuation
of the environment in segregated secondary schools, whereas
the environment in the integrated colleges presents a
significant contrast to that in segregated colleges. But
in Cleary's study, this change in environment did not make
any change in regressions for the two groups. However, as
she herself admitted, the schools used in the study did
not represent the full spectrum of colleges in the United
States. General conclusions cannot be reached unless

further research is done on other colleges.

40

Improvement of Prediction

 

As was mentioned earlier, aptitude tests explain
only about one-third of the total variance in the criterion
of GPA. Consequently, the use of these tests alone for
purposes of prediction will result in considerable numbers
of "false positives." This means that many who are judged
to be unlikely to succeed would in fact succeed if they
were given a chance. Like the alchemists of olden days
looking for techniques to change base metals into gold,
the psychologists and educators of modern days have been
constantly searching for methods which will increase the
accuracy of their predictions. These attempts to improve
the quality of prediction have included such procedures
as the addition of high school grades to the set of pre-
dictors, the use of alternate models, the use of moderator
variables, and the use of non—cognitive variables. Most
of these studies have not been on any subgroup of college
students, but on college students in general; however, the
study by J. R. Hills and J. C. Stanley (1970) is an ex-
ception. They found that the use of easier tests improves
the prediction of Negroes' college grades. This was sug-
gested by J. C. Stanley and A. C. Porter: "To predict
college grades with an academic test, the paramount con-
sideration is to choose a well-prepared test of appropriate

difficulty for the persons tested." (1967, 4, p. 216)

41

High School GPA

 

Scholarship in high school has generally been found
to be the best single predictor of college success. (Odell,
1927: Travers, 1949; Garrett, 1949; Lutz, 1968) An examin-
ation of recent studies shows evidence suggesting that high
school grades do not consistently contribute the most to
predicting college grades of black students, at least in
the case of the male sex; but they do contribute the most
in the case of the white students. (Thomas and Stanley,
1969). Munday (1965) reported ACT test superiority over
high school average for five southern, primarily black,
colleges. Cleary (1968) found that for blacks in inte-
grated colleges high school rank correlated .26 and .17
respectively with GPA. For whites in the same college,
high school rank correlated .38 and .30 respectively.
Peterson (1968) found that for a primarily black college,
the correlations between scholarship in high school and
freshmen GPA were much lower than that between the other
predictors and college GPA. In two other colleges which
Peterson studied, the usually-found trend of high school
scholarship superiority in predicting college grades held
up. In his study at a predominantly black state college
in Mississippi, Funches (1967), using high school GPA and
ACT scores as predictors, obtained a correlation of .06
between high school GPA and college GPA, while ACT scores

correlated .36 with college GPA.

42

The invalidity and unreliability of grades in black
high schools have been advanced as plausible explanations
for the relative ineffectiveness of high school grades in
predicting freshmen grade point average of black students
(Thomas and Stanley, 1969). Munday speculated: "...the
predominent 'press' in black high schools is less academic
than in white schools. Indices of achievement (grades)
may then reflect less academic emphasis." (1965, p. 117)

One of the sources of the unreliability of grades
arises from the variability in grading systems that are
prevalent in schools. A student with an "A" grade from
one college may be only as able as, or perhaps less able
than, a student with a grade of "B" from another school.
Various techniques have been employed to correct for this
variability while predicting college achievement from
school grades. These were discussed by Bloom and Peters
(1961). Linn (1966) reviewed the results of several em-
pirical studies that have used 'adjusted' grades to pre-
dict academic achievement. His paper considered some of
the possible techniques which could be used to make grade
adjustments for interschool differences. Most researchers,
however, have found that the improvement in predictive
validity due to the use of adjusted grades has been dis-

couragingly small.

43

Alternate Models

 

D. R. Saunders (1956) developed the moderated re-
gression model and showed that its use does improve pre—
diction accuracy. In his model each parameter in the
usual regression equation is expressed as a function of
the moderator variable. Disadvantages associated with
the use of this model have prevented it from coming into
popular use. Other attempts at using alternate models
like pattern analysis and configural scoring have been of
little value in increasing prediction accuracy. Clifford
E. Lunneborg and Patricia W. Lunneborg reported their
conclusion of studies on pattern prediction as follows:
"...there would seem to be small room for continuing the
conjecture that patterns can go above and beyond predic-
tion from simple linear function of original variables."
(1967, 4, p. 953)

The studies with alternate models have not been
specifically on black students, and therefore the possi-
bility remains that for black students, the traditional
linear model of prediction is not suitable.

Moderator Variables

The use of moderator variables hassuccessfully
identified subgroups whose achievement can be predicted
with greater accuracy. Rather than assuming that pre-
diction errors are random, this approach postulates that

there are systematic differences between predictable and

44

unpredictable individuals. If a third variable, called a
moderator variable, can be found which correlates with the
degree of predictability, then a subgroup of predictable
individuals can be identified. The degree of predictability
is usually measured by deviation, in standard score units,
of the predicted criterion scores from the actual criterion
score. Applying the predictors only to individuals who are
predictable, the validity of predictors can be increased.
Variables such as sex, anxiety, adjustment, and compulsive-
ness have been found to identify groups of high prediction
accuracy (Seashore, 1962; Malnig, 1964; Hoyt and Norman,
1954; Frederiksen and Melville, 1960).

The earlier studies, using moderator variables,
have not been on prediction of academic success. In 1956,
Ghiselli investigated the prediction of performance of
taxi-drivers. The predictor test was a Tap and Dot exer-
cise; the criterion was rating of job performance, after
being on the job for six months. The job applicants had
also filled out an Occupational Level Inventory, which he
hoped to use as the moderator variable. Before the use of
the moderator variable, the predictive validity coefficient
was .259. After identifying the group of predictables with
the moderator variable, the predictive validity was .660,
a large increase from .259.

In a second study, Ghiselli (1960) obtained scores

on an intelligence test, rated on a sociability scale and

45

on an initiative scale, for a group of 232 undergraduates.
The validity coefficient of the "intelligence" scores in
predicting sociability was .226. Using some of the items
in the "initiative" scale to identify a subgroup that could
be more accurately predicted with respect to the criterion
of sociability, he obtained a predictive validity coeffi-
cient of .860.

Brown and Scott (1966) attempted to apply the mod—
erator variable model to a typical academic prediction
situation. Study habits, attitudes and personality var-
iables were studied as possible moderators. The results
were far from encouraging. In no case did they find a
moderator variable that resulted in any significant im-
provement in validity. One explanation was that the
validity of the predictors used in the study were already
highly correlated with the criterion. Another explanation
was that in selecting only the most predictable subjects
the range of variability was affected and thereby the
validity coefficient was lowered.

Berdie (1961) investigated intra-individual con-
sistency of group-test performance. His main hypothesis
was that both grades and future test scores could be pre-
dicted more accurately for students whose scores were con-
sistent through a series of equivalent algebra tests than
for students whose scores were inconsistent. Although the

results were ambiguous with regard to improvement in

46

prediction, he demonstrated that intra-individual consist-
ency can be reliably measured.

Reyes and Clark (1968) carried out research to
test whether it is possible to predict future grades from
present grades more accurately for students who were con-
sistent in their grades than for students who were some-
what erratic. In their study a consistency index did not
improve the accuracy of prediction. Their explanation was
that the observed differences in intra-individual consist-
ency were primarily due to chance. This points out the
need for caution in attributing a moderator effect to var-
iability manifested by a student's academic record.

Before closing this summary of the literature on
prediction, a word must be said about the use of non-
cognitive variables as additional predictors. Graff and
Hansen summarized the studies on non-cognitive variables

in relation to academic achievement as follows:

"A thorough review of the literature indicated that
many studies of the non-cognitive aspects of achieve-
ment have been conducted during the last two decades.
Researchers tried to relate social background factors,
interests, Rorschach and TAT responses, study habits,
and different personality traits to academic achieve-
ment. Unfortunately, the results were generally in-
consistent or non-significant. Some of the investiga-
tions produced correlations similar to those found
with conventional predictors of academic success. The
crucial issue, however, comes in determining how much
these non-intellectual components actually added to
the prediction validity based on high school records
and intellective tests. In general, the increase was
not large enough to warrant incluSion of personalifiy
measures with cognitive factors, particularly if t ey
are to be used for selection purposes. (1970, 11, p.

129).

47

Therefore the use of non-cognitive variables as
additional predictors is not likely to improve prediction
and as such they are not used in this study. Investigation
of some of the non-cognitive variables as moderator variables

is a concern in this study.

Summary

This chapter briefly summarized earlier studies on
prediction, reviewed the literature on differential predic-
tion, and examined past attempts to improve prediction.

One of the main characteristics of the earlier
studies was that they related one independent variable at
a time to the criterion of academic success. These studies
have found high school grades and aptitude test scores to
be useful in predicting college success. More recently,
the trend has been to use a number of variables simultan-
eously to predict the criterion. Multivariable prediction
has demonstrated a distinct superiority over univariate
prediction.

Research studies so far, comparing blacks and whites
in colleges and universities with respect to predictive
validities of aptitude tests reported evidence to show that
standardized tests of aptitude predict college success as
well for blacks as for whites. The criterion of college

success in these studies was either first semester grades

or freshmen grades. A need was apparent to relate aptitude

48

variables to college success at a later time in order to
determine the influence on this relationship of the inter~
action with the university environment.

Literature also indicated a dearth of studies com»
paring the regression functions which provide rules of
prediction. Although the use of non—cognitive variables
as predictors has not added to the prediction validity
based on high school scholarship and aptitude tests, their

use as moderator variables holds out some promise.

CHAPTER III

METHODOLOGY

This chapter consists of descriptions of the
population and the samples, instrumentation and criteria,
research design, statistical hypotheses, and statistical

procedures used to analyze data.

Population and Samples

 

The study population consisted of all freshmen
who entered Michigan State University in Fall, 1968.
Registrar's Office records showed there were 7474 new
students registered for credit courses at that time, not
counting transfer students. When special part-time stu-
dents, foreign students, and students with incomplete
test scores were excluded from the population, 6582 stu-
dents remained.

The pOpulation identified for this study was
separated into two strata: black students and white stu-
dents. Identification of black students was provided by
the Center for Urban Affairs, Michigan State University.
All other-students were assumed to be white students.

The~black students numbered 302 while the white students

49

50

numbered 6,281 after the above mentioned exclusions were
made. All black students formed one sample and 609 white
students randomly chosen from the rest of the population
formed the second sample. The random choice was effected
by sorting all data cards according to the last digit of
the student number and chosing at random one digit to
specify the group. In this case the randomly chosen digit
happened to be 4. The predictor variables were derived
using these samples. A further out in the number in each
sample was necessary for regression analysis as all stu-
dents in the selected samples had not completed the winter
term, 1970. One of the criteria used in the study was the
overall (cumulative) GPA at the end of winter term 1970.
The Registrar's Office provided the overall GPA of 226 stu-
dents in the black sample and 511 students in the white

sample.

Instrumentation and Criteria

 

The purpose of this study was to compare the re-
gression functions for predicting college success of
blacks and whites from aptitude variables and to attempt
to improve the accuracy of prediction for blacks. The
orientation tests administered to almost all freshmen in
fall 1968 formed the basis from which the predictor var-
iables were derived. The derivation procedure is in a

later section in this chapter. There were two indices of

51

college success that were used as criteria: the cumula—
tive GPA at the end of the winter term 1970 and a GPA
based on standardized tests in the four basic college
courses, namely, American Thought and Language (111, 112,
113), Humanities (241, 242, 243), Social Science (231, 232,
233), and Natural Science (191, 192, 193).

Instruments administered to all or most freshmen

were Form C of the College Qualification Tests, MSU Reading

 

Test, and MSU English Test. Each student in the samples

 

completed one of the six forms of the Academic Inventory.

 

The College
ggalifICation Test

 

 

The College Qualification Test (CQT) (Bennet, et_al.,
1957) consists of three ability tests: Verbal containing
75 items, Numerical containing 50 items and Informational
containing 75 items. The informational part contains two
sections: science and social studies. Separate scores were
obtained for each half but not used in this study. Scores
for each test were recorded separately.

In the COT manual (Bennet, et_al., 1957, p. 27)
total score reliability coefficients of .97 for freshmen
males and .96 for freshmen females were found for two state
universities. Those coefficients were obtained by using
the split-half method, in which scores of odd and even
items were compared. Individual test score reliability

coefficients for the group ranged from .81 to .75 for men

52

and .78 to .94 for women. Science and Social Science
scores had the lowest coefficients of reliability. Lehmann
and Dressel (1963, p. 30) reported a split-half reliabil-
ity of .93 for the 1958 freshmen at Michigan State Univer—
sity.

The CQT total score seems to have better predic-
tive power for early college achievement than do individual
test scores when used separately. Hartnett (1963) indi-
cated that correlations from .50 to .70 seem to be the
usual findings when relating total score to early college
performance. In one study, Juola (1963) determined that
CQT total score was Specially useful for predicting a stu-

dent's first quarter grade point average (GPA).

Michigan State University
Reading Test

 

 

The MSU Reading Test was developed by the office

 

of Evaluation Services. The test was designed to measure
students' ability to comprehend ideas expressed in para-
graphs representative of those found in textual materials
of various academic areas at Michigan State University.
The test consists of 50 items and is used on a
supplementary basis for selecting students for the Prep-
aratory English Program as well as selection into the
honors program. The reliability of the test has been es-

timated on several occasions by the Office of Evaluation

53

Services to be approximately .80. Lehmann and Dressel
(1963, p. 30) obtained a reliability coefficient of .79
on their study population.

Hartnett (1963, p. 62) reports validity coeffi-
cients of .35 to .65 for males using academic performance

(grades) as the criterion.

Michigan_§tate Universit
English Test ‘

 

 

The MSU English Test was developed by the Office

 

of Evaluation Services. The test was designed to measure
students' proficiency in grammar and expression. It con-
sists of 38 objective items representing several aspects
of English usage and is primarily used to select students
requiring assistance in the Preparatory English Program.
Reliability of the test has been estimated on
several occasions by the Office of Evaluation Services to

be approximately .80.

Academic Inventory

The Academic Inventory was developed by the Office
of Evaluation Services to assess high school background,
preparation and academic skills of incoming students. It
was expected that the University College faculty could
determine if the college was adequately and appropriately
meeting the needs of entering students by evaluating stu-

dent reSponses to items in the inventory.

54

There were six forms of the inventory. Each con-
sisted of two sections: one with items of non-intellective
nature and the other with items of cognitive nature. Items
1 to 23 were identical on all forms. These items related
to such things as size of the student's graduating class in
high school, size and nature of the community in which his
high school was located, and information about courses he
took in grades 9 through 12. Some of these common item

responses were utilized in this study to develop moderator

variables.

Criteria

There were two criteria employed in this study. One
was the cumulative grade point average (GPA) at the end of
the winter term 1970, and the other was the grade point av-
erage on tests in basic college courses, namely American
Thought and Language 111, 112, 113, Humanities 241, 242,
243, Social Science 231, 232, 233, and Natural Science 191,
192, 193. Although test scores were available on all
courses, the track system introduced in the fall term 1969
made the raw scores non-comparable. Each track in the same
course had a different examination from the other tracks
and the highest possible scores in these examinations also
varied.

Each student received a grade based on his perform-

ance on examinations in each course. This examination grade

55

was combined with instructor's grade in a 40-60 composite
form and this composite became the final grade of the
student. In this study, only the examination grade was
used.

All Humanities and Social Science tests consisted
of multiple choice items, but the number of items varied
from test to test. The tests in American Thought and
Language and Natural Science Courses contained multiple
choice items and essay items. The reliabilities of these
tests have been estimated every term by the Office of
Evaluation Services and KR#20 coefficients ranged from .78
to .92. In estimating the reliabilities of tests contain-
ing essay items, computation was based only on objective
items.

The basic college course examinations were devel-
oped by the Office of Evaluation Services in c00peration
with the departmental Examination Committees. The tests
were designed to measure students' retention and integra—
tion of knowledge accumulated during the term in each of

the courses.

Research Design

 

The problem of comparing blacks and whites on the
predictive validities of aptitude variables was broken
down into three parts: (1) comparing the linear regres-

sion functions for the two groups, (2) comparing the amount

56

of variance accounted for in the criteria by aptitude
variables individually and collectively, and (3) testing
the linearity assumption of the regression function.

In any study of comparison of regression functions
of different groups, multicollinearity is a potential dan-
ger (Blalock, Jr., 1963, Gordon, 1967, and Darlington,
1968). The problem of multicollinearity is associated
with the use of correlated independent variables in regres-
Sion equations. When the independent variables are highly
correlated, it is extremely difficult to evaluate their
relative importance without running the risk of making
faulty inferences. First of all, the numerical value of
regression coefficients for a particular sample will
fluctuate depending upon which variable is taken first in
the regression equation. As the order of independent var-
iables changes, the regression weights will also change.
Further, the sampling error of the partial slopes will be
quite large. In statistical and mathematical terms, this
means that the variance-covariance matrix associated with
the regression coefficients is not diagonal when the in-
dependent variables are correlated. Since the off-diagonal
elements are non-zero, these have to be added to estimate
the error associated with each regression coefficient. Thus
the estimate of the sampling error will be very large when

the variables are intercorrelated.

57

In this study the independent variables were inter-

correlated as shown in Table 3.1.

Table 3.1. Intercorrelation Matrix of Test Variables*

 

 

 

Variable 1 1.0000

Variable 2 .6714 1.0000

Variable 3 .7088 .7615 1.0000

Variable 4 .5916 .7016 .7093 1.0000
Variable 5 .5320 .5180 .4411 .6386 1.0000

 

*Variable l CQT-Verbal, Variable 2 = CQT-Informational,
Variable 3 CQT-Numerical, Variable 4 = English Effi-
ciency, Variable 5 = Reading

II II

In order to avoid the problems of multicollinear-
ity due to the intercorrelations of.the independent var-
iables, the original variables, namely the five tests,
were transformed into orthogonal variables by factor
analysis. Then scores were computed for each individual
in the two samples on the derived orthogonal variables.
The computer program, Factor AA, used to generate ortho-
gonal variables and to compute factor-scores for each
individual, was originally prepared by Anthony V. Williams,
Department of Geography, Pennsylvania State University, and
adapted for use on 6500 computer at Michigan State Univer-
sity by James Peterson, Computer Institute for Social Sci-

ence Research, and Robert Paul, East Moline, Ill. (CISSR,1969).

58

The transformation of original variables and
scores into orthogonal factors and factor scores did not
affect the accuracy of prediction. If the number of
factors extracted equals the original number of predictor
variables, then it can be shown that the multiple regres-
sion equation constructed to predict the criterion var-
iable from the factors is equivalent to the comparable
equation constructed from the original variables. The
two equations will make identical predictions for any
individual (Darlington, 1969, p. 178). In this study the
number of orthogonal factors derived from the original
variables was equal to the number of original variables.
Moreover, the multiple R's between the predicted and ob-
served scores were found to be identical in either case,
.5292 for white sample and .5119 for black sample.

In order to compare the regression functions for
blacks and whites, the test of homogenity of regression
suggested by Wilson and Carry (1969) was employed. The
purpose of comparison was to discover whether the same
rule of prediction was applicable to black students and
white students. The same rule would not be applicable to
both groups if the separate regression equations were not
homogeneous.

After determining the need for separate regression
equations by which the values of the criterion variable

may be estimated from the predictor variables for the two

59

groups, it is desirable to compare the meaSures of how
closely such estimates agree with the actual values for
the two groups. This was done by a comparison of the co-
efficients of multiple determination, R2, for the two
groups, where R is the coefficient of multiple correlation
which is simply the ratio of the standard deviation of the
estimated values to the standard deviation of the actual
values (Ezekiel, 1963, p. 188). The R2 represents the
proportion of criterion variance accounted for by predic-
tors. A test of no difference in the multiple correlations
will'demonstrate whether the proportions of variances ac-
counted for by predictors are the same in the two groups.
The same objective can be achieved by a comparison of the
conditional variances for the two groups under the assump-
tion of equal criterion variances, but this method was not
used in this study.

The coefficient of multiple determination provides
a means of determining the overall variance contribution
that is attributable to all predictor variables simultane-
ously. The relative importance of each predictor variable h’vvi~
was determined by a partitioning procedure made possibleé‘r’ }f

M

only because the intercorrelated original variables were

 

transformed into orthogonal variables by Principal Com-
ponents Solution. The sum of squares due to regression is
divisible into as many additive parts as there are factors

in the case of orthogonal variables. Each additive part

60

represents the variance accounted for by each factor.
Thus transformation of the original variables into
orthogonal ones made it possible to compare the relative
importance of each factor in the two groups without run-

ning the risk of multicollinearity.

Goodness of fit of the
linear model

 

 

To determine the goodness of the model, the tradi-
tional method of testing the null hypothesis that the
vector of betas are all zero was used:

HO: 8 = O

Rejection of null hypothesis means that the linear model
does provide 32 appropriate method of prediction. It does
not mean that no other model will fit the data either as
well or better. Failure to reject the null hypothesis
implies that the model does not provide a useful rule of
prediction. Therefore in either case of rejection or non-
rejection it is reasonable to explore the possibilities of
using alternate models.

It is possible to represent relations by curves of
various types. There is practically no limit to the dif-
ferent kinds of curves which can be described by mathemati-
cal equations. Ezekiel and Fox (1963, p. 70) list the
equations of a number of curves which are useful in statis-

tical analysis between two variables:

61

1. Y = a + b X + b2 X2
2. Log Y = a + b X
3. Log Y = a + b log X
4. Y = a + b log X
5. Y = 1
a—Tb—Y
6. Y = a + b x + bzx2 + b3x3
7. Y = a + bx + b2 ( 1/X )

Curves corresponding to these equations are shown

in figure 3.1, adapted from Ezekiel and Fox (1963, p. 71).

 

rzai- 1%:st

A Y=a+bx ax3

IgY=rq+ wax}

‘ .

nor-«wmeem

 

 

 

 

 

HY=¢+M§n+m101+4MW

 

 

 

Figure 3.1. Curves illustrating a number
of different types of mathematical functions.

62

Extension to the case of more than one independent
variable is easy. The relationship may be expressed in
the following general mathematical formula:

Y = A + fl (x1) + f2 (x2) + .... + fn (Xn)

Where fl (X1) is a general term expressing the re-
lationship, linear or curvilinear, between the criterion
and any particular variable, and A is a constant.

In all these mathematical formulations, there is
an implicit assumption that the effect of one independent
variable on the criterion is not affected by effect of any
other independent variable. In other words, the model is
additive. When interaction of independent variables on
the criterion is suspected, the equation should consist of,
beyond the additive function, an interaction or joint func-
tion. For example where two independent variables are in—
volved, it would be:

Y = A + fl (x1) + £2 (X2) + f3 (xlxz)

where f3 (X1x2) is read as "joint function of X1 and

X2.
Although the use of any specific curvilinear model
was not attempted in this study, the relationship between
the criteria and each of the predictive variables was

plotted on a scatter diagram and graphically examined for

possible departures from linearity.

63

High School GPA

In order to assess the contribution of high school
scholarship to the prediction of college grade point aver-
age and the test score GPA, a new regression equation was
computed for blacks with high school grade point average
added to the set of aptitude variables as predictors and
the multiple R2 was computed in the case of each. The
increment in multiple R2 over the original R2 reflects the

contribution of high school scholarship in prediction of

college achievement in terms of both criteria.

Moderator Variables

Increased prediction accuracy was attempted also
by the use of moderator variables such as sex, intended
area of college major, home background in terms of urban,
suburban and rural origin, and intraindividual variability
of sub-test scores in the aptitude test battery.

The entire sample of black students in the study
was separated into two subgroups on the basis of each
moderator variable. Separate multiple correlations were
computed for each subgroup. A significant difference in
the correlations indicated the effectiveness of the mod-
erator variable in identifying an homogeneous subgroup in
terms of higher predictability.

Sex identification was available on every student

in the black sample.

64

The data on home background were gathered from
the responses to an item in the Academic Inventory. The
item read as follows:

Which of the following best describes the com-

munity in which your high school was located?

1. Within the city limits of a large city

(200,000 population or over)

2. Within a suburb of a large city

(within 25 miles)
3. Within the city limits of a medium sized city

(50,000 to 199,000)
4. Within a suburb of a medium sized city

(within 10 miles)

5. Within a small city or town or rural area.

For purposes of this study, this variable was dichotomized.
Those who chose alternatives 2 and 3 formed one group and
the rest formed another group. Separate multiple R's were
computed for each group and examined for significant dif-
ference.

Information on the students' major college prefer-
ence was available from the Office of Evaluation Services
in the following specification: 0 for no preference, 1
for Agriculture, 2 for Business, 3 for Engineering, 4 for
Home Economics, 5 for Natural Science, 6 for Veterinary
Medicine, 7 for Education, 9 for Communication Arts, E
for Arts and Letters, N for Social Science, M for Justin
Morrill College, L for Lyman Briggs College, and J for
James Madison College. This variable of college prefer-

ence was dichotomized into a preference for physical and

natural sciences on the one hand and a preference for

65

social and behavioral sciences on the other. The follow-
ing colleges were assigned to the first category: Agricul-
ture, Engineering, Natural Science, Veterinary Medicine
and Lyman Briggs College. The rest of the colleges were
considered as belonging to the social and behavior science
category. The students with no preference were excluded
for this comparison.

The index of intraindividual variability employed
in this study was computed from the individual test scores
in the battery. Scores on individual tests were trans-
formed into standard scores before computing the variance
for an individual so as to avoid the danger that the re-
sulting index might be a function of measurement, rather
than a reflection of the variability of the individual
concerned. On the basis of this individual variability in
aptitude test scores, the group was separated into high
variability group and low variability group and their cor-

relations were compared.

Statistical Hypotheses

For purposes of statistical tests of significance,
the following null hypotheses were formulated from previ-

ously stated purposes and substantive hypotheses.

M .__.,......_1.. _ u
M an... ,2..-
~' lev>o ““““ m ..... W

The reader will recall that 5611 hypotheses are not
statements of expected outcome of research, but they are

statements used in making a decision about rejection or

66

acceptance of the substantive hypotheses which are state-

ments of expected outcome. Hypothesis Testing asks the

question: Under the assumption that the null hypothesis

is true, what is the probability of obtaining the statis-

tics on the observed data?

1.

The use of linear equation to predict the cumula-
tive GPA does not explain any variance in the
criterion.

The use of linear regression equation to predict
the test score GPA does not explain any variance
in the criterion.

The parameters of the regression equation for
predicting the cumulative GPA at the end of the
SOphomore year from a set of factors derived

from aptitude measures are the same for blacks
and whites.

The parameters of the regression equation for
predicting the test score GPA from a set of
factors derived from aptitude measures are same
for blacks and whites.

The prOportion of variance in cumulative GPA that
is predictable from the correlation with aptitude
measures is the same for blacks and whites.

The prOportion of variance in the test score GPA
that is predictable from the correlation with the

aptitude variables is the same for blacks and whites.

10.

11.

12.

13.

67

The accuracy of prediction of the cumulative GPA
for blacks is not enhanced .by adding

the high school GPA to the set of aptitude pre-
dictors.

The accuracy of prediction of the test score GPA
is not enhanced by adding the high

school GPA to the set of aptitude predictors.

When the cumulative GPA is the criterion, the pre-
diction is equally accurate for males and females
in the black population.

When the test score GPA is the criterion the pre-
diction is equally accurate for males and females
in the black population.

When the cumulative GPA is the criterion, the pre-
diction is equally accurate for students of subur-
ban origins as those of urban or rural origins in
the black population.

When the test score GPA is the criterion, the pre-
diction is equally accurate for students of subur-
ban origins as those of urban or rural origins in
the black population.

When the cumulative GPA is the criterion, the pre-
diction is equally accurate for those in the black
population who chose to major in physical and/or
natural sciences as those who chose to major in

social and/or behavioral sciences.

68

14. When the test score GPA is the criterion, the pre-
diction is equally accurate for those in the black
population who chose to major in physical and/or
natural sciences than those who chose to major in
social and/or behavioral sciences.

15. When the cumulative GPA in the criterion, the-pre-
diction is equally accurate for those in the black
population with low intraindividual variability in
the subtests of the aptitude test battery as those
with high variability.

16. When the test score GPA is the criterion, the pre-
diction is equally accurate for those in the black
population with low intra-individual variability
in the subtests of the aptitude test battery as

those with high variability.

Statistical Analysis

Factor analysis with varimax rotation transformed
the original test variables into orthogonal variables or
factors. The computer program, FACTOR AA, (CISSR, 1969)
was used to carry out the computations involved. This
program provided not only the orthogonal factors, but
also factor scores for each individual in the samples.
These factors and factor scores were used to develop re-

gression equations for predicting academic success of

blacks and whites.

69

The test of linearity of the regression equation,
which is really a test to see whether all betas are zero,
was accomplished by analysis of variance (Hays, 1963, p.
520-21).

The parameters of regression equations to predict
the cumulative GPA and the average score on college basic
courses for blacks and whites were analyzed by tests for
homogeneity of regression (Wilson and Carry, 1969).

The prOportions of criterion variances that were
predicted from aptitude variables in the two groups were
analyzed by a two sample Z test on multiple correlations
transformed into Fisher Z's (Hays, 1963, p. 532).

The increment in the criterion variance that was
accounted for by the predictor variables when the high
school GPA was added to the set of aptitude measures was
tested for significance by a "Variance—Ratio Test" sug—
gested by Baggaley (1962). The ratio is given by

2

2
F = (R+ - R ) (N - m — 2)

 

1-Ri
where R is the multiple correlation involving m predictor
and R+ is the multiple correlation involving m + 1 pre-
dictor. The quotient should be referred to an F table
with d.f. = l for the "greater mean square" and d.f. = N

- m — 2 for the "lesser mean square."

70

Finally, the effectiveness of moderator variables
was analyzed by two sample Z tests on Fisher Z transfor—

mations on multiple R's (Hays 1963, p. 532).

Summary

The population identified for the study consisted
of all freshmen who entered Michigan State University in
fall 1968 and completed the winter term 1970. However, a
few exclusions were made for one or more of the following
reasons: lack of complete data, foreign student status,
and part-time status. From the remaining population two
samples were drawn. Sample one consisted of all black stu-
dents, 226 in all, who were identified as such by the Cen-
ter for Urban Affairs at Michigan State University. Sample
two consisted of 511 white students randomly selected from
the pOpulation.

MSU English, MSU Reading, and the College Qualifi-
cation Test (CQT) were the principal instruments employed
in the study. CQT consists of three ability tests: Verbal,
Informational, and Numerical.

Two indices of college success were used as criteria:
the cumulative grade point average (GPA) at the end of the
winter term 1970 and the grade point average on tests in
basic college courses. The basic college courses included
Humanities, American Thought and Language, Social Science,

and Natural Science.

71

i

The designof the study involved the'transforma—
tion of the original predictor variables into orthogonal
factors and comparison of the regression functions of
these factors on the criteria for blacks and whites in
terms of the regression coefficients and the amount of
explained variance. The use of high school scholarship
and of moderator variables was also a part of the study.

Testable statistical hypotheses were formulated
and analyses Specified. Normal variates and Variance
Ratios provided the test statistics needed for the

analyses. The following chapter will deal with the re-

sults of the analyses.

CHAPTER IV

ANALYSES OF DATA: RESULTS

Introduction

 

The major purposes of this study as described in
chapter I were: 1. to compare the regression functions
for predicting college success of blacks and whites from
aptitude measures, 2. to determine the effectiveness of
adding high school GPA to the set of aptitude variables,
3. to assess the effectiveness of sex, curricular prefer-
ence, home background and intra-individual variability as
moderator variables. Specific hypotheses were generated
from these purposes regarding the relationship between
the predictors and the different criteria: the cumulative
GPA at the end of the winter term 1970 and the grade point
average on basic college course examinations. The data
were analysed by a variety of statistical tests. This
chapter is concerned with the results of these tests.

The samples for analyses that used cumulative GPA
as the criterion consisted of 224 blacks and 511 whites,
whereas the samples for analyses using the test score GPA

consisted of 216 blacks and 268 whites. In this chapter,

72

73

for the sake of convenience of presentation, the black
sample will be referred to as Group I and the white sample
as Group II.

In this chapter a brief description of the raw
data and its transformation is provided at first. The
purpose of the transformation was to make the predictors
orthogonal. The advantages of orthogonality were explained
at length in chapter III. Next the results of the tests of
linearity are presented. A brief discussion of the test of
homogeneity of regression is offered before presenting the
results of tests performed on the hypotheses regarding
homogeneity of regression and variance explained by predic-
tors. This is followed by the partitioning procedure in-
tended to ascertain the contribution of the individual pre-
dictor factors and by examination of scatter diagrams in-
tended to detect any curvi-linear relationship in the
data. Finally the results of the tests on hypotheses re-
garding the improvement of prediction by adding high school

GPA and by using moderator variables are presented.

The Data and its Transformation

 

§gmmary Statistics on Raw Data

The five aptitude tests used in this study to pre-
dict college success, defined in terms of the two criteria
used, were MSU English, MSU Reading, CQT-Verbal, CQT-Infor-

mational, and CQT-Numerical. Tables 4.1 and 4.2 provide

74

the means, the standard deviations and the intercorrela-
tions of the variables in the study, the aptitude tests,
high school GPA, the cumulative GPA, and the test score
GPA. The reader should bear in mind that correlations
are affected by the range and, therefore, the variance
and the standard deviation. In the case of a low stand-
ard deviation the obtained correlation coefficient would
be an underestimate of the true correlation (Garrett,
1937, p. 323).

The means in tables 4.1 and 4.2 show that none of
the groups had scores close to the floor of the tests.
The observed variance would not therefore be attributed
to chance alone. Although the means for group I were
generally lower than for group II on all variables, the
standard deviations of MSU English, MSU Reading, CQT-
Verbal, CQT-Informational, high school GPA, and test
score GPA were higher for group I than for group II.

In both groups MSU Reading scores correlated high-
est with the cumulative GPA (.47 for both groups) and with
the test score GPA (.69 for group I and .57 for group II).
CQT-Numerical had the lowest correlations with the cumula-
tive GPA in both groups (.20 for group I and .31 for group
II) and with the test score GPA (.46 for group I and .34
for group II). All aptitude tests had higher correlations
with the test score GPA in both groups than with the cumu-

lative GPA. But the correlation between high school GPA

75

and the test score GPA was lower than the correlations
between high school GPA and the cumulative GPA in group
II whereas the converse was true in group I.

The intercorrelations among MSU English, MSU
Reading, CQT-Verbal, and CQT-Informational were generally

higher than the intercorrelations among other predictor

variables.

Table 4.1. Means, Standard Deviations and Intercorrela-
tions of Group I

 

 

Standard "- -- .
Devia— Intercorrelations
Variable Mean tions 1 2 3 4 5 6 7 8

 

1 19.05 6.56 1.00

2 25.31 8.02 .64 1.00

3 38.52 15.62 .65 .71 1.00

4 37.53 9.93 .56 .65 .72 1.00

5 23.99 8.25 .48 .45 .38 .55 1.00

6 2.82 0.54 .28 .25 .25 .18 .19 1.00

7 2.27 0.47 .42 .47 .43 .38 .20 .37 1.00

8 1.73 0.79 .593 .69 .68 .67 .46 .44 .71 1.00

 

1 = MSU English, 2 MSU Reading, 3 = CQT-Verbal, 4 = CQT-
Informational, 5 = CQT-Numerical, 6 High School GPA, 7 =
the Cumulative GPA, 8 = the Test Score GPA.

Table 4.2. Means, Standard Deviat
tions of Group II

76

ions and Intercorrela-

 

 

 

 

Standard Intercorrelations
Devia-
Variable Mean tions 1 2 3 4 5 6 7 8
l 25.40 5.62 1.00
2 32.94 6.78 .54 .00
3 54.96 11.39 .57 .66 1.00
4 48.15 9.06 .45 .59 .54 1.00
5 33.28 9.46 .39 .36 .21 .54 1.00
6 3 l9 0 50 .36 .34 .25 .36 .39 1.00
7 2.72 0 52 .43 .47 .37 .38 .31 .46 1.00
8 2.65 0 69 .50 .57 55 .54 .34 .38 .76 1.00
1 = MSU English, 2 = MSU Reading, 3 = CQT-Verbal, 4 = CQT
Informational, 5 = CQT-Numerical, 6 = High School GPA, 7 =

Cumulative GPA, 8 = Test Score GPA.

Transformation of Data

Since the predictor variables

were intercorrelated a transformation

into orthogonal variables was carried

analytic techniques in order to avoid

used in this study
of these variables
out through factor

the problem of multi-

collinearity. This transformation resulted in five new

variables with zero intercorrelations.

This section des-

cribes summary statistics on the new variables and their

relationship to the original variables and to the criteria.

77

Factor analysis with principal axis solution and
varimax rotation extracted five orthogonal variables from
the original intercorrelated variables. Table 4.3 pro-
vides the final factor loadings on each of the original

variables.

Table 4.3. Rotated Factor Loadings

 

 

 

Factors
Variable 1 2 3 4 5
1 .2859 -.2380 .8681* .2594 .2018
2 .3237 -.2191 .2933 .8227* .2903
3 .8100* -.1482 .3366 .3395 .3056
4 .2970 -.3339 .2176 .2796 .8214*
5 .1236 -.9225* .2106 .1746 .2425

 

*Signifies the highest factor loading.
Variable 1 = MSU English, Variable 2 = MSU
Reading, Variable 3 = CQT-Verbal, Variable 4
= CQT-Informational, and Variable 5 = CQT-

Numerical.

Factor loading signifies the extent of correlation
between the factor concerned and the original variables.
Each of the original variables had the highest factor load-
ing on one of the orthogonal factors. MSU English correla-
ted .8681 with factor 3; MSU Reading correlated .8227 with
factor 4; CQT-Verbal correlated .8100 with factor 1; COT-
Informational correlated .8214 with factor 5; and CQT-

Numerical correlated -.9225 with factor 2. Each of the

78

factors had a moderate relationship with each of the
other four variables ranging from -.1482 to .3366.

The relationship between a particular factor and
all the variables together may be described in mathemati-
cal terms as follows:

Yi= Ale + AZX2 + Aan

where Yirefers to a factor

A's are constants

X's refer to the original variables

In matrix notation, the above expression reduces to:

l

The computer program that transformed the original

I
Y.=A X

variables into orthogonal factors also computed scores on
each of the factors for each individual in the study.
These scores were used to compute regression equations for
the two groups. These scores were in standard form with
mean 0 and variance 1 for the overall sample. But these
statistics differed slightly for the two samples due to
sampling error. Table 4.4 gives the correlations between

the two criteria and the factors. Sample size for each

correlation is given in parentheSis.

79

Table 4.4. Correlations of Factors with Criteria.

 

 

 

 

 

 

Group I Group II
Factor EEHT‘EFXTNT‘TEEE‘EFKTNT' Cum. GPA(N)‘TE§E—§PATNT_
l .21(224) .40(216) .05(511) .17(268)
2 .05(224) -.14(216) -.18(511) -.15(268)
3 .27(224) .30(216) .28(511) .32(268)
4 .30(224) .4l(216) .31(511) .34(268)
5 .19(224) .36(216) .19(511) .35(268)

 

Assumption of Linearity

The problem of comparing blacks and whites on the
predictive validities involved comparison of regression
equations for the two groups in terms of the coefficients
and the amount of variance explained when using the equa-
tions. The regression equation computed for each group
assumed that the relationship between the criteria and
the predictors could be adequately represented by a linear
model. The usual test of linearity, namely, that the
vector of regression coefficients is a zero vector would
show whether the linear model could explain any variance
at all in the criterion. In this study, this usual test
of linearity was performed on both groups using the two
criteria, the cumulative GPA and the test score GPA.

In order to test the assumption of linearity the

two null hypotheses were formulated and tested for signi-

ficance.

80

Hypothesis 1

 

The hypothesis for the cumulative GPA was:

The use of linear regression equation to predict
the cumulative GPA does not explain any variance

in the criterion.

In statistical terms this hypothesis states that

the vector of regression coefficients (8) is a zero vector

(0). This hypothesis was tested for group I and group II

separately.

Table 4.5. Analysis of Regression - Test for Group I.

 

 

 

Source Sum of Squares d.f. F
Due to Regression 12.688 5 15.486*
Error 35.722 218

Total 3 . 48.410 223

 

*Significant at less than .005 level of type I

 

 

 

error
Table 4.6. Analysis of Regression - Test for Group II.
Source Sum of Squares d.f. F
*
Due to Regression 38.486 5 39.291
Error 98.930 505
Total 137.416 510

 

*Significant at less than .005 level of type I

error.

81

The F ratio was significant in each case. Conse-
quently the null hypothesis was rejected and it was con-
cluded that the regression coefficients were not all zero
and, therefore, a linear model did explain some of the
criterion variance.

Hypothesis 2
The hypothesis for the test score GPA criterion was:

The use of linear regression equation to predict

the test score GPA does not explain any variance

in the criterion.

This hypothesis states that the regression coeffi-

cients are all zero. This was also tested for group I and

group II separately.

Table 4.7. Analysis of Regression - Test for Group I.

 

 

 

 

Source Sum of Squares d.f. F
Due to Regression 12.420 f 15.788*
Error 33.061 210

Total 45.481 215

 

*Significant at less than .005 level of type I
error.

82

Table 4.8. Analysis of Regression — Test for Group II

 

 

Source Sum of Squares d.f. . F
Due to Regression 13.718 5 13.485*
Error 53.304 262

Total 67.022 267

 

*Significant at less than .005 level of type I

error.

The F ratio was significant in each group. Conse-
quently, the null hypothesis was rejected and it was con-
cluded that the regression coefficients associated with
the aptitude variables did explain a significant amount of
the variance in the test score GPA.

The tests involving both criteria showed that a
linear model can be satisfactorily used to estimate values
of the cumulative GPA and the test score GPA for blacks
and whites from the scores on the aptitude tests that were

employed in the study.

Homogeneity of Regression Functions

 

In order to discover whether the same rule of pre-
diction was applicable to black students and white students,
the separate regression equations for the two groups were
compared for homogeneity. Since the test for homogeneity
of regressions, especially in the case of p predictor var—

iables, p>1, is not very common, a brief explanation of

83

the principles and procedures involved seems appropriate.
In geometric terms,%homogeneity of regression is
synonymous with parallelism of regression surfaces. The
simplest case involves a dependent variable Y, an inde-
pendent variable X, and the regression line of Y on X
determined for each group. Homogeneity question is the
same as: Are the two lines parallel? This intuitive
idea can be extended to the general case of p predictor
variable, regresses on two independent variables, X1 and
X2, then the resulting regression is a plane. In the case
of p predictor variables, p>2, the resulting regression is
a p-dimensional surface. Here the analytic question of

homogeneity of regression becomes: Is there significant
variation in thawtwoyyggtgr§_cf_p_regressionlweight§~__“‘\~“\kj
associated with the independent variables? (Wilson and 6
Carry, 1969, p. 81).

The test of homogeneity of means in analysis of
variance is accomplished by comparing the variation a-
mong the sample means with that among the observations.
The test of homogeneity of regression coefficients is
based on the same principle, except that the comparison
is between the variation among the sample regression

coefficients and that among the observations (Li, 1964,

Vol. 1, p. 393).

84

Procedures

 

The test of homogeneity of regressions estimates
the residual sum of squares in two ways. First, the sum
of squares is estimated by using the pooled regression
weights; then the same sum of squares is estimated by
using regression weight§determined for each group separa-

tely.,,Let the former be SS and the latter be SS . The

1 2

difference between the two sums of squares (SS1 - 852) is
obtained and used to test the significance of difference
in regression by a likelihood ratio (Wilson and Carry,

1969). The ratio is given by:

(851 - ssz)(n -g - 9-p>

where n = the number of cases in all groups combined
9 = the number of groups being compared
p = the number of predictor variables
SSl = the residual sum of squares for the pooled
regression weights
882 = the sum of the residual sums of squares

determined for each group

When the null hypothesis that the regression
weights in the populations are the same is true, this
ratio has a sampling distribution which can be approxi-
mated by an F distribution with (g -l).p and (n - g — g.p)
degrees of freedom (Wilson and Carry, 1969, p. 84). It
was this ratio that was employed to test the homogeneity
of regressions of the two groups in this study.

The regression equation for group I with the cumu-

lative GPA as the criterion was found to be:

85

Y = 2.42 + .10Xlr.O2X2 + .13X3 + .15X4 + .09X5.

The regression equation for group II with the
cumulative GPA as the criterion was found to be:

Y = 2.58 + .12Xl - .13X2 + .19X3 + .20X4 + .13X5.

The regression equation for group I with the test

score GPA as the criterion was found to be:

Y = 2.20 + .30Xl - .23X2 + .26X3 + .33x4 + .30x5.
The regression equation for group II with the test

score GPA as the criterion was found to be:

Y = 2.43 + .31X1 - .18X2 + .28X3 + .30X4 + .28X5.

Tables 4.9 and 4.10 give the regression coeffi-

cients and their standard errors.

 

 

 

 

Table 4.9. Regression Coefficients and Standard Errors
with the Cumulative GPA as criterion.
W
Group I Group II
Factors Coefficients Std. Errors Coeffibients Std. Errors
7——.
Constant 2.42 0.035 2.58 0.023
1 0.10 0.025 0.12 0.024
2 -0.02 0.033 -0.13 0.020
3 0.13 0.027 0.19 0.022
4 0.15 0.026 0.20 0.021
5 0.09 0.028 0.13 0.021

 

86

Table 4.10. Regression Coefficients and Standard Errors
with the Test Score GPA as Criterion.

 

 

Groupr Group II Qty
Factors Coefficients Std. Errors Coefficients Std. Errors

 

Constant 2.20 0.045 2.43 0.037
1 0.30 0.032 0.31 0.041
2 -0.23 0.042 -O.18 0.034
3 0.26 0.035 0.28 0.036
4 0.33 0.033 0.30 0.035
5 0.30 0.036 0.28 0.034

 

In order to test for homogeneity of regressions,
the hypotheses were formulated and tested for significance.
Hypothesis 3

The third hypothesis, the first of two relating to
homogeneity of regression, was:

The parameters of the regression equations for

predicting the cumulative GPA at the end of the

SOphomore year from a set of factors derived from

aptitude variables are the same for blacks and

whites.

The test statistic employed was the likelihood

ratio given by

and table 4.11 provides the quantities needed for this

ratio.

87

Table 4.11. Analysis of Homogeneity of Regressions on
The Cumulative GPA

 

 

 

Source ‘ Sum of Squares d.f. F
Pooled Regression 79.314

Total for two groups 51.173 723%)
Difference in Regressions 28.1415’ 5 79.517*

 

*Significant at less than .001 level of type I
error.

The likelihood ratio was significant when the
analysis was completed. Consequently the null hypothesis
was rejected and the alternate hypothesis was acdepted.
It was concluded that the parameters of regressions for
predicting the cumulative GPA from derived factors were
different for blacks and whites.

Hypothesis 4
Hypothesis 4 was stated as follows:

The parameters of the regression equation for pre-

dicting the test score GPA from a set of factors

derived from aptitude measures are the same for

blacks and whites.

The test statistic was the likelihood ratio given by:

(551 - ssz)(n-g-9.P>

 

$52 . (g-l).p

Table 4.12 provides the quantities needed for this ratio.

88

Table 4.12. Analysis of Homogeneity of Regressions on
the Test Score GPA.

 

 

 

Source Sum of Squares d.f. F
Pooled Regressions 130.844 - -
Total for two groups 125.988 475 -
Difference in Regressions 4.856 5 3.677*

 

*Significant at the .01 level of type I error.

The likelihood ratio was significant when the
analysis was completed. Consequently the null hypothesis
was rejected and the alternate hypothesis was accepted.

It was concluded that the parameters of regressions for
predicting the test score GPA from derived factors were
different for blacks and whites.

The reader will recall that one of the purposes
of this study was to compare the regression functions for
predicting college success of blacks and whites from ap-
titude variables. Two criteria were used as indicators
of college success: the cumulative GPA at the end of the
winter term 1970 and the test score GPA based on examina-
tions alone in college basic courses. Results of the
statistical tests revealed a significant difference be-
tween the regression functions of the two groups under
both criteria. Further interpretation of these results

will be provided in next chapter.

T ”5:

89

Variances Explained by
Aptitude Variables

 

The test of homogeneity of regressions revealed a
significant difference in the regression equations for
predicting the cumulative GPA and the test score GPA for
the two groups. This implies that the estimated (pre-
dicted) criterion values will be different for those in
one group from those in the other group, even if the sub-
jects in the two samples had equal scores on predictors.
The goodness of the regression equations is determined by
the proportion of variances accounted for while using the
equations for prediction. The square of the multiple cor-
relation coefficient, R2, otherwise known as the coeffi-
cient of multiple determination represents the proportion
of variance accounted for by the predictors using a linear
regression. In order to investigate whether the propor-
tion of variance explained by the aptitude variables is
the same in both groups, the two additional null hypoth-
eses were generated and tested:

Hypothesis 5
Hypothesis five was as follows:

The proportion of variance in cumulative GPA that

is predictable from the correlation with aptitude

measures is the same for blacks and whites.
Overall Test — The test of this hypothesis involved the

transformation of multiple R into Fisher Z. The reason for

90

this transformation was that the population p's were not
known. When the population 0 = 0, the sampling distribu-
tion of R may be regarded as approximately normal. How-
ever, when population is not zero, the distribution of the
multiple R tends to be very skewed either to the left or
to the right depending on population 0 being greater than
or less than zero. R. A. Fisher (1942) has'shown that the
sampling distribution of a particular function of R is
approximately normal for samples of moderate size, no
matter what the population 0 is.
The function is given by:

Z = 1/2 loge (l + R)/(1 - R))

Since the transformation is 'one to one,‘ infer-
ences about Z are applicable to R.

A test of the hypothesis that the two populations

show equal correlations is provided by the ratio:

 

where Zl'is the transformed value of the correlation co-
efficient for the first sample
22 is the transformed value of the correlation co-
efficient for the second sample
s(Z1-Zz)

 

J1/(N1-3) + 1/N2-3)
For reasonably large samples, this ratio can be referred

to the normal distribution.

91

In this study the multiple correlation for group
I was .5119 and for group II it was .5292 when the cumu-
lative GPA was used as the criterion. The Z values cor-
reSponding to those correlations were .5654 and .5901
reSpectively. The number of students in group I, N1, was

224 and the number in group II, N2, was 511. Thus

 

Z

(.5654 - .5901)/ Ji/221 + 1/503
= -1.547

The value of the test statistic Z was not significant at
a = .05. Consequently, the null hypothesis was not re-
jected. The data, it was concluded, did not provide evi-
dence for a significant difference in the proportion of
variance accounted for by the predictors in both groups.

Partitioning Procedure. The multiple R2 measured
the proportion of variance in the criterion explained by
the five predictor factors simultaneously. The contribu-
tion of each factor was determined by partitioning R2 into
ri , r: , r; , r2 and r: , where ri is the simple corre-
lation of ith factor with the criterion. In the case of
«ngnrintercorrelated factors the sum of the squares of the
individual correlations add up to the multiple R2. Each
r reflects the contribution attributable to each factor.

Table 4.13 provides the simple correlations of
the factors with the cumulative GPA, the squares of the

correlations, the values of the corresponding Fisher 2's

and the values of Z-statistic for the two groups.

92

Table 4.13. Correlations, Squares of Correlations, Values
of Fisher Z's and of Z-statistic.

 

 

 

 

Factor Correlation(r) r2 Fisher Z Z-statistic
Gp.I Gp.II Gp.I Gp.II Gp.I Gp.II Gp.I Gp.II
1 .21 .05 .0441 .0025 .2132 .0500 3.168* 1.127
2 .05 .18 .0025 .0324 .0500 .1820 .743 4.102*
~13 .27 .28 .0729 .0784 .2769 .2877 4.115* 6.485*
4 .31 .31 .0961 .0961 .3205 .3205 4.763* 7.224*
5 .19 .19 .0361 .0361 .1923 .1923 2.858* 4.334*

 

*Significant at or less than .01 level of type I
error.

The statistical tests showed that in group I the
correlations of factors 1,3,4 and 5 with the cumulative GPA
were significantly different from zero, whereas the corre-
lation of factor 2 was not significant. Factor 4 explained
approximately ten percent, factor 3 approximately seven
percent, factor 1 approximately one percent and factor 5
approximately four percent of the criterion variance.

In group II the correlations of factors 2,3,4 and
5 with the cumulative GPA were significant, whereas the
correlation of factor 1 was not significant. Just as in
group I factor 4 explained approximately ten percent of
the criterion variance. Factors 3,5 and 2 explained eight

percent, four percent and three percent of the variance

respectively.

93

The fact that factor 2 in group I and factbr 1 in
group II were not significant suggested the differential
contribution of these two factors in predicting the cumu-
lative GPA. The reader will recall that factor 1 had the
highest loading on CQT-Verbal and factor 2 had the highest
loading on CQT-Numerical. This would suggest that CQT-
Verbal and CQT—Numerical had differential contribution in
prediction for blacks and whites. CQT-Verbal appears
more important in the case of blacks and CQT-Numerical
appears more important in the case of whites.

A test of significance performed on the difference
in correlations for the two groups on factors 1 and 2 us-
ing the ratio suggested by Hays (1963, p. 532) showed a
significance level of a=.05 on factor 1 and a significance
level of a=.10 on factor 2.

Hypothesis 6

The sixth hypothesis was like the fifth except the

test score GPA was the criterion instead of the cumulative

GPA:

The proportion of variance in the test score GPA
that is predictable from the correlation with the
aptitude variables is the same for blacks and
whites.

Overall Test. The test statistic employed was the

 

ratio:
Zl‘zz
s(Z1 -22)

94

is the Fisher Z for the multiple correlation in

the first group
is the Fisher Z for the multiple correlation in

2 the second group
s(Zl -Zz) is the standard error of estimate of the

difference in correlations.

where Z1

Z

The multiple correlation for group I was .7688 and
for group II it was .6551, when the test score GPA was used
as the criterion. The Z values correSponding to those cor-
relations were 1.015 and .7823 respectively.

Nl was 216 and N2 was 268. Thus
(1.015 - .7823)/ Ji/213 + 1/265

2.562

 

Z

The value of the test statistic Z was significant at a —
.01. Consequently, the null hypothesis was rejected and
it was concluded that the proportion of variance accounted
for by aptitude variables is not the same for blacks and
whites when the test score GPA is used as the criterion.
The linear regression predicted the test score GPA with

greater accuracy in the case of blacks than in the case

of Whites.

Partitioning Procedure. In order to determine the

contribution of each factor the multiple R2 was partitioned

. 2 2 2 2 2 . .
into rl , r2 , r3 , r4 and r5 , where ri is the Simple cor-

relation of ith factor with the test score GPA. Table 4.14
provides the simple correlations of the factors with the
test score GPA, the squares of those correlations, the val-

ues of the corresponding Fisher Z's and of Z-statistic.

95

Table 4.14. Correlations, Squares of Correlations, Values
of Fisher 2'3 and of Z-statistic.

 

Correlation(r) r2 Fisher Z Z-statistic

Factor __ 1 _ . ______ —__——.————
Gp.I Gp.II Gp.I Gp.II Gp.I Gp.II Gp.I Gp.II

 

 

 

1 .40 .17 .1600 .0289 .4236 .1717 6.168* 2.800*
2 -.14 -.15 .0196 .0225-.1409-.1511 2.052**2.464**
3 .30 .32 .0900 .1024 .3095 .3316 4.506* 5.408*
4 .41 .34 .1681 .1156 .4356 .3541 6.342* 5.775*
5 .36 .35 .1296 .1225 .3769 .3654 5.488* 5.960*

 

**Significant at .05 level of type I error
*Significant at .01 level of type I error

The statistical tests showed that in both groups
the correlations of all factors were significantly differ-
ent from zero. In group I factors 1 to 5 explained approx-
imately sixteen percent, three percent, nine percent, seven-
teen percent and thirteen percent respectively. In group II
factors 1 to 5 explained approximately three percent, two

percent, ten percent, twelve percent and twelve percent

respectively.

Just as in the case of the cumulative GPA, the

difference in the correlations of factor 1 for the two

groups was marked. In group I the correlation was .47,

whereas in group II the correlation was only .17. Factor
1, the reader will recall, had the highest loading on CQT-
Verbal. CQT-Verbal appears more important in predicting

the test score GPA in the case of blacks than in the case

of whites.

96

A test of significance performed on the difference
in the correlations for the two groups on factor 1 showed

a significance level of less than a = .01.

Examination of Curvilinear
RelatiOnship

The test of linearity performed on the regression
of predictor variables on the cumulative GPA and the test
score GPA in both groups showed that the use of linear

model on prediction explained a significant amount of the

criterion variances. In order to explore the possibility

of improving the accuracy of prediction by addition of
non-linear terms in regression (polynomial in higher de—

gree), each of the criterion variables was plotted against

each of the predictors for each group. The following

figures present the scatter diagrams associated with each

of the predictor variables and each of the criteria.
Examination of figures 3.1 to 3.11 depicting the

scatter diagrams to represent the relationship between

the predictor variables and the cumulative GPA showed

that a linear regression appeared the best fit for the

data. The use of higher degree polynomials for.regression

equations would hardly increase the amount of explained

variance in the criterion of cumulative GPA. The same

trend was noticed in the scatter diagrams, not reported

here, representing the relationship between the predictor

variables and the test score GPA.

 

97

i.
.‘ A
i
‘L— . .
I
L
I
4 4 .
:- J J0 I
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L

+
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i l I J I l 1 l I A I 1 I 1 J . A . l A i
,. . .
b 1‘ l 11 ' ' l . £1 .' " ,‘4 u 1, v', ’4 f) x. l
L ii 4k 1 f 1
['31 " ' 'r ‘ ' ‘1 “ \
( ‘ i. ‘ ) x I j
|>L_.' '7- P I “\ ‘I ’ \‘ ’ i "x J

Scatter Diagram and Regression of the
Cumulative GPA on MSU English for

Blacks

Figure 4.1.

98

7 GPA
m I
”I +
J
’1)!
6;» +4
1:;
' 4
r n
n +$+
n‘ + t + +
+ +
.. ++ +

 

 

 

c. \
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+
4.4.4141
+
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4.

 

 

_ +
+ 3 4
+ + + +
» + + +
4 + + +-
+ I i
1 + +
+ + +
U
A Jr +
-‘ -—_+...._1._..__l_.._.l .. 1.. -L.._._l---_-l_. .L.--._1__._L_.--_.L__J_..___L_.1 _-1 n__ 1 1 1 (fig
10 O 1?. a 15 e [I5 s 21 .3 3.. O as {a 2—« 1 ‘4) L. a"; 2 5H '1

1 KPH—1L- It'll-1

LOH J. T L: 5:? 997: lfihP"/’“= " LI'

Figure 4.2. Scatter Diagram and Regression of the
Cumulative GPA on MSU English for

Whites

99

7 EPA

2.72 2635 323 as
r._
4,.

H7

 

 

"4 Lt..-1___L.___.1_-._i--__i 1 1 4 11 ._ .1 ___i,.-__1 -- _.L_._-J- 1-1 _-_ 1-...1..- _1_._.._1__.___+..

BID .ll.b 15 2 18.8 2‘? L. 2b0 2‘31: 33.2 51.?! «Qt Lu.0

2 READING

BLACKS P? CPA "READ

1‘
I

Figure 4.3. Scatter Diagram and Regression of the
Cumulative GPA on MSU Reading for

Blacks

1-3

3}]

d:

 

100

7 CPA

" "“‘T’““T' “ +—

f
.1.
.1.
+

L- + 1+

 

 

3}'1 all: «5.3

12.0 is 3' m). as 1 De . 1
’7 QEJUUUVC

wH T. TE 5 P? GPA READ

Figure 4.4. Scatter Diagram and Regression of the
Cumulative GPA on MSU Reading for

Whites

7 cm

.1
mf

r—
10
3 ..
m
m
m

 

Figure 4.5.

101

H

 

I’:‘,‘1 (3t, us

Scatter Diagram and Regression of the
Cumulative GPA on CQT-Verbal for

Blacks

102

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-‘ -
5L
_.

{a
.__r_ __ _ _T_.‘_
4

+ . .
T l ‘ i j 1 1 t
a j 4 4
m ‘ T ' o t «b/
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+ i i. 1 4 . , .u
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+ 4 1 , }
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‘3‘ 0 "1'1 1,1 1 l I ’ ’ )"~ 1 ' T ‘ ' T
:3 ‘ J l
i I (V "k _ / T] I
[1*"j ' I ‘* , J

Figure 4.6. Scatter Diagram and Regression of the
Cumulative GPA on CQT-Verbal for

Whites

 

31.

.L
_‘L.
I...
.—
T
t-

Figure 4.7.

103

\
\

l/fl

’ 1

:F‘

, r
i
k a

Scatter Diagram and Regression of the
Cumulative GPA on CQT-Informational
for Blacks

 

104

"7 C3F>Xx

--L%

~r_T-k~

36:5

 

 

 

 

[AH J' ’l 1 H {’1‘}! J‘A (if). T- L

Figure 4.8. Scatter Diagram and Regression of the
Cumulative GPA on CQT-Informational
for Whites

El.

105

 

 

L
+.
+
.+
+—-—_i-_._1--,-ot--.i _. l .1- 1 L 1.. l 1 1 - 4----1 l- x -4- ri _l
5.00 =00 I: r) 1" r“ .111; : J W ' 1m o 2,) J a1 1
“w r 0?»

E3 L... A C K S P? C P A ,_ 11: {j ' F N

Figure 4.9. Scatter Diagram and Regression of the
Cumulative GPA on CQT-Numerical for

Blacks

7C

i

 

 

 

 

Figure 4.10.

106

-f +{ 4
1
l 1 I I J 1 l I I I l 1 I I l
.4. 21;» 1': 5 M ”II ..... m. ,
'1 {‘JH.
' f< ['1 '/5'-\ l 1' 1H J

Scatter Diagram and Regression of the
Cumulative GPA on CQT-Numerical for

Whites

w 3.0 MW sum - ‘ .
,_L;smtumh-1us JL' A'ia sviznlum

‘- 31 1 117?.

 

 

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Figure 4.11.

 

107

+
4 +
1
+ + + -+ +
+ 1 ++
+ +
.1.
. +
+7 4
1 .1-
+ ' pk +
1? +

a
.1
1 1 1 1 1 1 1 1 1 1 1 .1 1 .1. ._L_ .-1 .
‘ 1 1 11 C10 1 ‘1" 3 .‘W =5 1:13 101
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C1

,1 ‘~ 1* \ "v "\ , {,_ "““ *

\ «_ _ _g, , - _J
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Scatter Diagram and Regression of the
Cumulative GPA on High School GPA
for Blacks

 

  
 
 

 
 
 

    

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108

Influence of Hi h School
5mm
In order to assess the contribution of high school
scholarship to the prediction of college success in terms
of the cumulative GPA and the test score GPA in the case
of black students attending an integrated college, two
null hypotheses were tested using a Variance Ratio Test
(Baggley, 1962, p. 21).
Hypothesis 7
Hypothesis 7, the first tested for present purposes,

was :

The accuracy of prediction of the cumulative GPA
for blacks is not enhanced by adding the high
school GPA to the set of aptitude predictors.

The test statistic was:

(Rf - R2)(N-m-2)
F = --——————§ ———————
l - R+

where R = the multiple correlation involving only the

aptitude predictors, .
the multiple correlation involving the aptitude

R:

+ predictors and the high school GPA,
N = the number of subjects,
m = the number of predictors.

The multiple correlation involving only the apti-

tude predictors was .5226 and that involving the aptitude

predictors and high school GPA was .5749, when the cumu-

lative GPA was used as the criterion. The number of

aptitude predictors was 5, and the N was 216. Thus

“1%!
1““
.

 

1 4 1‘.‘
, -_ -, -—
' - V. ':
_ A 1A1 k
r > a

    

71361.1”! ‘
{3111 1186

V11
.1

113583“

 

 

109

.4

2

(.5749 - .52262)(216 -5-2)

= .0514 x 209
.6695

17.918

The value of the test statistic F was significant

 

at a =.Ol level. Consequently the null hypothesis was

rejected and it was concluded that the accuracy of predic-

 

tion of the cumulative GPA for blacks was enhanced by
adding the high school GPA to the set of aptitude predic- '
tors. The aptitude variables alone explained approximate-

ly twenty seven percent of the criterion variance, whereas

the aptitude variables with the high school GPA explained
approximately thirty four percent. The estimated im-

provement in terms of explained variance is six percent.

Hypothesis 8

Hypothesis 8 was:

The accuracy of prediction of the test score GPA
for blacks is not enhanced by adding the high
school GPA to the set of aptitude predictors.

The test statistic was the Variance Ratio:

The multiple correlation involving only the apti-

tude predictors was .7688 and that involving the aptitude

predictors and high school GPA was .8068. The number of

aptitude predictors was 5, and N was 216. Thus

vino

 

      

enlv;avui -4

 

 

  

 

110

.0598 x 209

The value of the test statistic F was significant
at a=.01 level. Consequently the null hypothesis was re-
jected and it was concluded that the accuracy of predic-
tion of the test score GPA for blacks was enhanced by
adding the high school GPA to the set of aptitude pre-
dictors.

The aptitude variables alone explained fifty
nine percent of the variance in the test score GPA,
whereas sixty five percent was explained when the high
school GPA was added. Thus the estimated improvement
brought about by the addition of high school GPA was six
percent. The same point estimate of the improvement was
observed in the case of the cumulative GPA.

Thus the college achievement, measured in terms
of the cumulative GPA or the test score GPA, was better
predicted by adding the high school GPA to aptitude var-

iables in the case of black students.

Moderator Variables in Prediction

The moderator variables employed in the study were
sex, home background, curricular preference, and intra-
individual variability in scores on the tests in the apti-

tude test battery. In order to determine the effectiveness

 

 

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111

of these moderator variables in predicting college success
defined in terms of the cumulative GPA and the test score
GPA, several additional hypotheses were formulated and

tested for significance by the ratio (Hays, 1963, p. 532):

where Zl represents the value of the Fisher Z transforma-
tion of the multiple correlation coefficient for
the first sample,

represents the transformed value for the second
sample, and

0121-22) = fi/(Nl-s) + l/(N2-3).

This section describes the results of these tests.

22

 

Sex and Predictability

 

Hypothesis 9

 

The hypothesis of the effect of using sex as a moder-

ator variable with cumulative GPA as the criterion was:
When the cumulative GPA is the criterion, the
prediction is equally accurate for males and
females in the black population.

The multiple correlations for males and females were .4490

and .6614 respectively. The corresponding Z values were

.4833 and .7592. There were 87 males and 129 females in

the group. Thus the test statistic ratio was:

Z = .2759 x 102.86 = 1.959
14.49

 

The value of the test statistic was significant at
a=.05 level. Consequently the null hypothesis of equality

of correlations for males and females was rejected. It

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112

was concluded that females are better predicted than males
when the cumulative GPA is the criterion.

The percentage of criterion variance that was ex-
plained by the predictors for male group was twenty,
whereas for females it was approximately forty four. Thus
there was a twenty four percent improvement in the accuracy
of prediction for females over that for males.

Hypothesis.10

 

The hypothesis of the effect of using sex as a moder-
ator variable with test score GPA as the criterion was:
When the test score GPA is the criterion, the
prediction is equally accurate for males and
females in the black population.
The multiple correlation coefficients for males
and females were .77l3 and .8345 respectively. The corres-
ponding Z values were 1.021 and 1.238. There were 87 males
and 129 females in the group. Thus the test statistic

ratio was:

.217 x 102.86

The value of the test statistic was not significant
at a=.05 level. Consequently the null hypothesis of equal-
ity of correlations for males and females was not rejected.
The data, it was concluded, did not provide evidence for
the effectiveness of sex as moderator variable when the
test score GPA was the criterion. This sex was effective
as a moderator variable only when cumulative GPA was the

criterion.

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113

Home Background
and Predictability

Hypothesis 11
Again two hypotheses were tested with the first using
cumulative GPA:
When the cumulative GPA is the criterion, the pre-
diction is equally accurate for students of subur-
ban origins as those of urban or rural origins in
the black population.
The multiple correlation coefficients for students
of suburban origins and those of urban origins were .6493
and .5696 respectively. The corresponding Z values were
.7751 and .6472. There were 153 in the urban and rural
group, and 41 in the suburban group. Thus the test sta-
tistic was:

.1279 x 75.50

The value of the test statistic was not signifi-
cant at a=.05 level. Consequently the null hypothesis of
equality of correlations for these two groups was not re-
jected. The data, it was concluded, did not provide evi-
dence for the effectiveness of home background as moderator
variable when the cumulative GPA was the criterion.
Hypothesis 12

The second hypothesis concerning home background was:

When the test score GPA is the criterion, the pre-

diction is equally accurate for students of subur-
ban origins as those of urban or rural origins in

the black population.

 

      

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114

The multiple correlation coefficients for students
of suburban origins and those of urban or rural origins
were .8855 and .7972 respectively. The corresponding Z
values were 1.399 and 1.089. There were 41 in the suburban
group and 153 in the urban or rural group. Thus the test

statistic was:

The value of the test statistic was not signifi-
cant at a=.05 level. Consequently for test score GPA as
for cumulative GPA, the null hypothesis of equality of
correlations for these two groups was not rejected. Again
it was concluded that the data did not provide evidence
for the effectiveness of home background as moderator var-
iable when the test score GPA was the criterion.

Curricular Preference
and Predictability

There were only 18 students who preferred Social
Science Curriculum. 121 Students preferred Physical or
Natural Science Curriculum. The rest did not have any
preference at all. Since the number in Social Science
Category was too small, the intended analysis for the
effectiveness of curricular preference as the moderator

variable was not performed.

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115
Intra-individual variability-
and Predictability
Hypothesis 13
The hypothesis relating intra-individual variability
to the prediction of cumulative GPA was:

When the cumulative GPA is the criterion, the pre-

diction is equally accurate for those in the black

pOpulation with low intra—individual variability
in the sub-tests of the aptitude test battery as
those with high variability.

The multiple correlation coefficients for the low
variability and high variability groups were .5734 and
.3517 respectively. The corresponding Z values were .6530
and .3270. There were 101 students in the low variability
group and 115 in the high variability group. Thus, the

test statistic was:

Z = .3260 x 104.57 = 2.353
14.49

The value of the test statistic was significant

at a=.05 level. Consequently the null hypothesis of

equal prediction accuracy for these two groups was rejected.

It was concluded that students with low intra-individual

variability in the sub-test scores of aptitude test battery

were better predicted than those with high variability when

the cumulative GPA is the criterion.

The variance that was explained by the predictors
in the low variability group was thirty three percent,
whereas the variance explained in high variability group

was twelve percent. The estimate of increase in accuracy

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116

of prediction is twenty one percent in terms of the ex-
plained criterion variance.

Hypothesis 14.

The coresponding hypothesis for test score GPA was:

When the test score GPA is the criterion, the pre-
diction is equally accurate for those in the black
population with low intra-individual variability

in the sub-test scores of the aptitude test battery
as those with high variability.

in
‘M

The multiple correlation coefficients for the low

variability and high variability groups were .7635 and

1;... -‘*.-...—_
I
.

.5760 respectively. The corresponding Z values were 1.005
and .6565. There were 101 students in the low variability
group and 115 in the high variability group. Thus the

test statistic was:

.3485 x 104.57

The value of the test statistic was significant
at a=.05 level. Consequently the null hypothesis was
again rejected and it was concluded that test score GPA
like cumulative GPA was better predicted for students with
low intra-individual variability than for students with
high variability in sub-test scores.

The percentage of variance explained in the low
variability group was fifty eight and the percentage in
the high variability group was only thirty three. The
estimate of increase in accuracy of prediction for the
low variability group was twenty in terms of explained

variance.

117

The analyses on the effectiveness of moderator var-
iables revealed that sex and intra-individual variability
successfully identified a subgroup of the population for
whom prediction was more accurate than the other in the
pOpulation. Whereas the variable of home background was
not effective as a moderator variable. Sex was effective
only when the cumulative GPA was the criterion. The esti-
mate of improvement in prediction was twenty percent approx-
imately. A ten percent improvement that was observed when
the test score GPA was the criterion happened to be statis-
tically non-significant. Intra-individual variability in-
dex was effective in the case of both criteria. When the
cumulative GPA was the criterion, there was a twenty one
percent improvement of prediction in the low variability
group. When the test score GPA was the criterion, the im-

provement was twenty percent.

W

This chapter has presented the results of the
statistical analyses performed on the data collected for
the study. Results indicated that the use of linear regres-
sion equations based on aptitude variables was helpful in
explaining a significant amount of variance in the cumula-
tive GPA and in the test score GPA. This was true for
both groups. The regression equations for the two groups

were found to be significantly different in the case of

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118

both criteria. The partitioning procedure revealed the
differing contribution of factors 1 and 2 when the cumu—
lative GPA was the criterion and of factor 1 when the
test score GPA was the criterion. Factor 1 eXplained a
significantly higher percentage of variance in group I
than in group II. Factor 2, however, explained a signi—
ficantly higher percentage of variance in group II than
in group I. The overall variance that was accounted for
by all the factors together was the same when the cumula-
tive GPA was the criterion. There was a significant dif—
ference when the test score GPA was the criterion. A
significantly larger proportion of criterion variance was
explained in group I than in group II when the test score
GPA was the criterion.

An examination of the scatter diagrams led to the
conclusion that a linear regression model would be the,
best fit for the data. Curvilinear regressions would not
in any way augment the accuracy of prediction. The use
of high school grade point average in addition to the apti-
tude variables as predictors resulted in significant imr
provement in predicting both criteria in the case of blacks.
The estimated improvement was six percent in both criteria.
The variables of sex and intra-individual variability index
were found to be effective as moderator variables. There
was a twenty percent improvement in the prediction of the

cumulative GPA for females over males. Approximately

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twenty percent improvement was achieved in the low varia-
bility group in predicting both the cumulative GPA and the

test score GPA.

Chapter V will deal with the interpretation of the

results.

 

 

 

 

CHAPTER V
SUMMARY AND CONCLUSIONS

This chapter presents an overview of the research
reported. The results of the research are discussed and

suggestions for further research are made.

Overview

This study explored three major research questions:

1. Is the same rule of prediction applicable to
blacks and whites while using aptitude test variables to
predict college success? The rule of prediction is a
linear regression equation. The same rule of prediction
is applicable to blacks and whites only if the regression
surfaces represented by the equations for these two groups
are homogeneous. Thus the question becomes: Are the re-
gression surfaces for blacks and whites homogeneous? The
ultimate aim was to discover whether the use of aptitude
test scores with the same regression equation to predict
college success for blacks and whites would be biased
against blacks.

2. How much of the criterion variance is explain-

ed by the aptitude variables in the two groups?

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Is there a significant difference in the multiple
correlation coefficients between the criterion and the
aptitude variables for the two groups.

3. Can the accuracy of prediction in the case of
blacks be improved by the use of curvilinear models, by
the use of high school GPA in addition to the aptitude F
variables and by the use of moderator variables?

The samples selected for the study were from the

population of freshmen who entered Michigan State Univer-

'.:m:—-—-———._._. _

sity in fall, 1968 and who completed the winter term 1970.
SamEYeL8fi%}consisted of all black students who had com-
plete data for various comparisons. For one set of com-
parisons the black sample was 224 and for another set of
comparisons it was 216. Sample two consisted of students
randomly chosen from the white population. Its size for
one set of comparisons was 511 and for another 268.

The principal instruments in the study were MSU
English, MSU Reading, and the College Qualification Test
(CQT) with three subtests of Verbal, Informational, and
Numerical abilities. The scores on these tests were used
in multiple regression to predict college success defined
in terms of the cumulative GPA at the end of winter term
1970 and a test score GPA which was based on the grades
received in the basic college courses taken during the same
period. The basic college courses included courses in American
Thought and'Language, Humanities, Natural Science, and Social

Science.

  

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After establishing the fit of the linear model in
regression, the two groups were compared in terms of the
regression functions and the proportion of criterion var-
iance explained by aptitude variables. These comparisons
were made using the cumulative GPA and the test score GPA.
Improved prediction accuracy in the case of blacks was
attempted by exploring the possibility of the use of our-
vilinear regression, by the use of high school GPA in
addition to the aptitude variables, and by the use of
moderator variables. The moderator variables were not
used in the regression equation but as basis for identify-
ing homogeneous subgroups in terms of increased prediction
accuracy.

The major statistical tools employed in the study
were factor analysis, Z tests, and Variance Ratio Tests.
The decision rule in all tests was to reject the null
hypothesis at a = .05 level of type I error.

Results showed that the regression equations for
the two groups were significantly, though not substantially
different. The regression equation for blacks predicted
criterion values that were slightly lower than those that
would be predicted from the white or common regression
equation.

The partitioning procedure revealed the differing
contributions of factors 1 and 2 in predicting the criteria.

Factor 1 might be described as Verbal Ability Factor since

 

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it has the highest factor loading (.8100) on the CQT-Ver—
bal subtest. Factor 2 might be described as Numerical
Ability Factor since it has the highest factor loading
(-.9225) on the CAT-Numerical subtest.

Both groups were found to be equally predictable
in terms of the cumulative GPA. The test score GPA of
the blacks were better predicted than the test score GPA
of the whites.

An examination of scatter diagrams showed that cur-
vilinear models held no promise of improving prediction
accuracy over that achieved by linear model. The addition
of high school GPA to the set of aptitude variables resulted
in six percent improvement with respect to the criterion
variance explained by the aptitude variables. The six per-
cent improvement was found to be statistically significant.
Sex and intra-individual variability index were effective
as moderator variables. Females were better predicted than
males with respect to the cumulative GPA, but not the test
score GPA. Both criteria were better predicted for the low
intra-individual variability group than for the high varia-
bility group.

The implications of these results are taken up in

the next section.

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Discussion of Results

 

The first research question the study attempted to
answer was the homogeneity of regressions for blacks and
whites. The regressions in question were linear in form.
Before the regressions were compared for homogeneity, the
apprOpriateness of linearity was examined in terms of its
ability to explain a substantial proportion of the criter—
ion variance.

In both groups the use of linear regression equa-
tions predicted a significant amount of the criterion var-
iance. This was true in the case of the cumulative GPA
and the test score GPA. Therefore it was concluded that
the linear model fit the data satisfactorily. A linear
fit in this context was defined to be the ability of the
model to predict a significant amount of the variance in
the criterion. Given this definition, it is possible that
a linear model fits a given set of data and at the same
time a curvilinear model fits the same set of data equally
well or better. Hence at this point no decision was made
about the possibility of improved prediction accuracy by
the use of curvilinear models.

Regression equations for predicting the cumulative
GPA and the test score GPA were found to be significantly
different for the two groups. In both cases the regression
coefficients were generally lower for blacks than for whites.
This is indication that the use of white or common regres-

sion equation would result in overestimates of the criterion

 

 

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125

values for blacks.5 This finding is opposed to what has

_been anticipated. It was anticipated that the relatively

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richer environment of an integrated University like Michi-
gan State would provide the needed stimulation for the.
blacks to achieve higher than what would be predicted on
the basis of common regression and consequently the cri-
terion estimates from a separate regression would generally
be higher than those from common regression estimates.

The reason why the environment at Michigan State
did not have the expected influence on the academic achieve-
ment of blacks would be a matter of conjecture and specula-
tion. Itmmight be that the content ofrmajority of the
courses offered at Michigan State was perceived to be
irrelevant to the blacks as a group and as a result they
were not motivated to learn them. ”It;mightflbe_that more
supportive programs would be needed before they would be
able to take full advantage of the new environment. Further
research would be needed before one can make definitive
statements about the apparent ineffectiveness of the rela-
tively richer environment of an integrated University like
Michigan State on the academic achievement of blacks.

The difference obtained in the regression coeffici-
ents for the two groups in the study, though statistically
significant, does not appear to begmeaningful or substan-

tial. Firstly, the numerical difference between the re-

gression coefficients in the two groups is very small.

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Secondly, the difference in the predicted Y.Smue;gg the 3R1:
different equationzwon the same set of data is also very
small. In other words the use of either equation will not
show a large difference in the estimated criterion values;
For example, the use of black regre531on on one set of data
resulted in a value of 2.582, and the use of white regres-
sion on the same set of data resulted in a value of 2.742,
the difference being only .16. A statistically signifi-

cant difference need not always be a meaningful or substan-
tial difference. A statistical test will show a small ' _31
difference as significant if the sample size of the groups
involved is large. Such appears to be the case in this
study.

The fact that the criterion values predicted from
the black regression equation were lower than the criterion
values that would be predicted from a common or white re-
gression equation leads to the conclusion that the use of
the same regression equation for blacks and whites would
not be biased against the blacks. These results and con-1221
clusions agree with those of Cleary (1968) who studied the
bias of Scholastic Aptitude Test as predictor of college
grades. She concluded her findings as follows (Cleary,
1968, p. 123):

The schools used in this study do not represent

the spectrum of colleges in the United States, so

general conclusions cannot be reached. In the

three colleges studied, however, there was little
evidence that the Scholastic Aptitude Test is

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biased as a predictor of college grades. In the

two eastern schools, there were not significant

differences in the regression lines for Negro

and white students. In the one college in the

southwest, the regression lines for Negro and

white students were significantly different:

the Negro students' scores were overpredicted

by the use of the white or common regression

lines.

The final conclusion arising from the comparison
of the regression equations must be tempered by the con-
sideration that in regression theory the independent var-
iables are assumed to be measured without error, i.e., they
are perfectly reliable. Clearly MSU Reading, MSU English,
and CQT are not perfectly reliable. If departures from
perfect reliability were to be the same for the two groups,
the results of the comparison of regression equations
would not be altered. However, if the errors of measure—
ment in the independent variables were to be different in
the two groups, this would affect the results of the
comparison.

The second question to which this study addressed
was the amount of variance explained by the aptitude var-
iables for each group. The proportion of variance ex-
plained by the predictors is an index of how good the
regression is. If a significantly lesser proportion of
variance is explained by the predictors in the case of

blacks than in the case of whites, the prediction might be

considered unfair for blacks.

    
 

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An analysis of the multiple correlations between
the aptitude variables and the cumulative GPA for blacks
and whites did not show any significant difference. The
aptitude variables predicted the cumulative GPA equally
well for blacks and whites. In the white sample studied,
twenty eight percent of the criterion variance was account-
ed for by the aptitude variables and in the black sample
twenty six percent of the criterion variance was explained
by the aptitude variables.

In predicting the test score GPA, the accuracy
level was found to be higher for blacks than for whites.
Analysis of the multiple correlations revealed that the
difference in the accuracy level was significant. In the
black sample fifty-nine percent of the criterion variance
was explained by aptitude variables, whereas in the
white sample only forty-three percent of the criterion
variance was explained by the aptitude variables.

The overall conclusion is that prediction of
college success from MSU English, MSU Reading, and the
College Qualification Test is equally valid and reliable
for blacks and whites at Michigan State University.

However, the differing contributions for the two
groups of factors 1 and 2 (Verbal Ability Factor and Numer—
ical Ability Factor) in predicting the cumulative GPA and
of factor 1 in predicting the test score GPA.was brought

to light in the partitioning procedures. Factor 1 explained

129

a significantly higher percentage of criterion variance

in the blacks (four percent) than in the whites (.25 per-
cent) when the cumulative GPA was the criterion. Factor

2 explained .25 percent in the blacks and three percent in
the whites. When the test score GPA was the criterion,
factor 1 still differed in the proportion of contribution
in the two groups. Factor I explained sixteen percent in
the blacks and three percent of the criterion variance in
the whites.

The low correlations and consequent proportion of
explained variance might be due to either lack of range or
due to lack of true relationship in the data. The correla-
tion between factor 1 and the cumulative GPA in the whites
was only .05, but in the case of the test score GPA the
correlation was .17. This increase in correlation leads
one to believe that the low correlations cannot be attri-
buted to lack of range, but is a reflection of the true
relationship. The same reasoning is applicable to factor
2, the correlation of which with the cumulative GPA in
the blacks was only .05, but with the test score GPA it
was .14. Thus the low correlation may be said to reflect
the true state of affairs, namely the Numerical Ability
Factor is almost uncorrelated with the cumulative GPA in
thewblacks.

Finally this study sought to improve prediction

accuracy in the case of black students by exploring the

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possibility of using curvilinear regression, by the use

of high school GPA in addition to the aptitude variables
and by the use of moderator variables to identify individ-
uals of high predictability. ‘

Visual inspection of scatter-diagrams associated
with each of the independent variables and each of the
criteria showed that the use of curvilinear models would
not reduce the errors of prediction any more than the
linear model. However, visual inspection is not as ac-
curate as analytical procedures. Higher degree polynomials
might be hypothesized to be good fit of the data and the
regression coefficients associated with the higher terms of
the polynomial could be tested for significance. This pro-
cedure would provide more accurate results than the visual
inspection undertaken in this study.

When high school GPA was added to the regression
equation, the increment in the explained criterion var-
iance in the case of blacks was significantly different
from zero both in the cumulative GPA and in the test score
GPA. The prOportion of variance in the cumulative GPA
eXplained by aptitude variables alone was .2731 whereas
after the high school GPA was added it was .3305. The pro-
portion of variance in the test score GPA explained by the
aptitude variables alone was .5911 and after high school
GPA it was .6509. Thus it was concluded that college

achievement, measured in terms of the cumulative GPA or

 

 

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131

the test score GPA, was better predicted by adding the high
school GPA to the aptitude variables in the.case of black
students.

The conclusion of this study with respect to the
contribution of high school GPA might be compared with the
conclusion arrived at by Thomas and Stanley (1969) after ;
reviewing a number of studies on the effectiveness of high t
school grades for predicting college grades of black stu-
dents. They stated that “evidence seems to suggest that
high school grades_do not consistently contribute the most
to predicting the college grades of black students, per-
haps particularly of men, whereas they do for whites."

(1969, p. 204). The concern in this study was not com-
parison of blacks and whites with respect to the contribu-
tion of high school grades in prediction of college success,
but the absolute improvement effected in the black popula-
tion alone. It is possible and likely that the contribu-
tion in whites is greater than in blacks. This study has
shown that the absolute improvement in prediction is sig-
nificant and worthwhile in blacks, when high school GPA is
added to the aptitude variables.

I Analyses on the effectiveness of moderator varia-
bles revealed that sex and intra-individual variability
index could be used to identify subgroups of blacks for
whom better prediction would be possible. One of the

psychometric implications of this result is the possibility

 

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of discovering subgroups of individuals for whom a parti-
cular test or set of tests will be specially effective for

predictive purposes. The result has also implication in

counselling. Counselors are concerned from time to time 5/

with pgoviding information to students regarding academic
prognoses. The results of this study have shown that
the accuracy with which this can be done is a function of
characteristics like sex and intra-individual variability
index. Females were better predicted than males, and
similarly individuals of low intra-individual variability
were better predicted than those with high variability.
Still another implication of the results regarding the
effectiveness of moderator variables is that it can pro-
vide hints about the dynamics of personality character-
istics in college achievement. This study was not planned
to investigate what personality dynamics are operating to
produce academic achievement. However, by demonstrating
that differentially accurate predictions can be made for
students classified on moderator variables, the study has
provided support for the position that personality charac-
teristics may play an important role in academic achieve-

ment.

Suggestions for Further Research

In regression theory it is assumed that the inde-

pendent variables are measured without error. This means

    

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133

that they are perfectly reliable. Clearly this is an
assumption that can be hardly met in social and behavior-
al sciences. Hence methods of correcting the influence

of unreliability resulting from errors of measurement have
been proposed by Cochran (1968). Investigations are needed
that incorporate these methods of correction for unrelia-
bility in the independent variables.

Irrelevancy of curriculum for blacks and lack of
special intervention techniques to compensate for earlier
disadvantages were suggested as possible explanations for
the apparent ineffectiveness of the environment of an
integrated university like Michigan State to improve the
academic achievement of the black students. These con-
jectures require further research and experimentation.

This research demonstrated the usefulness of high
school GPA as additional predictor in multiple prediction
of college success in the case of blacks at Michigan State
University. A possibility for future research would be to
compare blacks and whites with respect to the improvement
in prediction from adding high school scholarship to the
aptitude variables.

The moderator variables used in this research were
treated as dichotomies for the purpose of identifying the
individuals of higher predictability. Better methOds of
accomplishing this purpose might be developed. It should

be possible to employ a continuous measure of each variable

 

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rather than a dichotomy. Methods might be developed to
facilitate the discovery of variables which relate to the
predictive value of a test.

Another possibility for future research is an ex-
tension of the study to include criteria at different
intervals to find out whether the same relationships found

in this study hold across time.

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140

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141

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