Prognosis of Freshman Academic Achievement at the Pennsylvania State College

Citation preview

The Pennsylvania State College The Graduate School Department of Education and Psychology

PROGNOSIS OF FRESHMAN ACADEMIC ACHIEVEMENT AT THE PENNSYLVANIA STATE COLLEGE

\i ■'k

A Thesis by IRVING COBLENTZ

i-1

Submitted in partial fulfillment of the requirements for the degree of

| '■S'

H

DOCTOR OF PHILOSOPHY August, 1942

Approved: Professor of Psychology ?

Q

' (r>. s$L-_

/^Head of Department/

r i’ll

£ :4 R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

ACKNOWLEDGMENT

Sincere appreciation is offered to Dr. R. G. Bernreuter who suggested this research and who gave generous help and guid­ ance until the work was completed. Grateful acknowledgment is accorded to Dr. J . E. DeCamp and to Dr. R. G. Bernreuter, who interested the writer in the sci­ v

K;

ence of psychology and under whom it was always a real opportunity to study.

To Dr. B. V. Moore and Dr. E. B. Van Ormer thanks are

given for much helpful advice and friendly interest. The author is indebted also to Mr. Henry Borov; and to Miss Betty VJhittaker for invaluable assistance.

I

250176

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

I

TABLE OF CONTENTS

Chapter

Page

I . INTRODUCTION A. Introduction to Problem ................. B. Statement of Problem ....................

1 6

II. THE DATA AND THEIR TREATMENT A. The Subjects........................... B. The Prediction Instruments .............. C. Criteria of Academic Success ............ D. Statistical Methods .....................

7 9 16 19

III. RESULTS A.. Organizationof Results................... B. The School of Chemistry and Physics ........ C. The School of Engineering......... 64. D. The School of Mineral Industries. 91 E. The School of Lower D ivision..... 120 F. The School of Agriculture - Non-Technical . . G. The School of Agriculture - Scientific . . . H. The School of Agriculture - Two-Year . . . . , I. Summary Section.........................

I38 151 162 172

IV. BIBLIOGRAPHY......... ........................ SUMMARY AND CONCLUSIONS ....................... APPENDIX.....................................

206 20S 215

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

20 23

'M

LIST OF TABLES

Table I. Descriptive Outline of Moore-Nell Examination . . . . II. Median Freshman Averages and Freshman Ranks of 1720 Freshmen of the Class of 19-43 Distributed According to High School Ranks.........................

Page 10

15

School of Chemistry and Physics III. Interrelationship Between Predictive Items and FirstSemester Average for School of Chemistry and Physics........................ IV. Partial Regression Coefficients of Prediction Batteries for Chemistry and Physics Students ............. V. Means and Standard Deviations for First-Semester Average, High School Rank and the Five Parts of the Moore-Nell for the School of Chemistry and P h y s i c s ....... VI. Standard Deviation Ratios for Regression Equations used in Prediction of First-Semester Average for Chemistry and Physics Students.........................

26

29

32

34

VII. Regression Equations for Prediction of First-Semester Average for Chemistry and Physics Students . . . .

3^

VIII. Correlations Between Predictive Measures and Individual Course Grades for School of Chemistry and Physics

43

IX. Correlations and Standard Error Ratios of Moore-Nell Four Parts and. Moore-Nell Five Parts to First-Semes­ ter Average and Grade in Chemistry and Mathematics

46

X. Partial Regression Coefficients, Multiple Correlations, Probable Errors of Estimate and Percents of Fore­ casting Efficiency for Moore-Nell Parts and Trans­ muted High School Rank Using Chemistry I Grade as the Criterion.............................. XI. Standard Deviation Ratios for Regression Equations used in Prediction of Chemistry I Grade ............. XII. Prediction Equations using Chemistry I Grade as the Criterion...................

.1 R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.

49

50

52

LIST OF TABLES (Continued)

Table XIII.

XIV.

XV.

XVI,

XVII,

Pape Partial Regression Coefficients, Multiple Correlations, Probable Errors of Estimate and Percentages of Fore­ casting Efficiency for Prediction Items using Mathe­ matics Grade as Criterion.....................

56

Standard Deviation Ratios for Prediction Equations using Mathematics Grade as Criterion ...........

57

Prediction Equations using Grade in Mathematics as Criterion......................... ■.........

59

Partial Regression Coefficients and Multiple Correlations using English Composition I as Criterion .......

61

Correlations of Personality and Interest Measures with First-Semester Average for the School of Chemistry and Physics................................ ..

63

School of Engineering XVIII,

XIX.

XX.

XXI,

XXII.

XXIII.

XXIV.

Interrelationship between Predictive Indices and FirstSemester Average for the School of Engineering . .

67

Partial Regression Coefficients of Prediction Variables for School of Engineering.................. 71 Means and Standard Deviations for Prediction Variables and First-Semester Average for School of Engineering

73

Standard Deviation Ratios for Regression Equations for Prediction of First-Semester Average ...........

74-

Score-Forra Regression Equations, Multiple Correlations, Probable Errors of Estimate and Percents of Fore­ casting Efficiency for Prediction of First-Semester Average for Engineering Students ...............

79

Correlations betr/een Predictive Measures and Grade in Mathematics and First-Semester Average .........

81

Correlations of Moore-Nell Four Parts -and Moore-Nell Five Parts with Semester Average and Mathematics

i •: ■ / £

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.

■({

,

iii.

: t;

LIST OF TABLES (Continued)

Table XXV.

XXVI.

XXVII.

XXVIII.

XXIX,

Pag;e Partial Regression Coefficients and Multiple Corre­ lations for the Predictive Items using Mathematics Grade as Criterion...........................

85

Means and Standard Deviations for Predictive Items and Grade in Mathematics............

86

Standard Deviation Ratios for Regression Equations for Prediction of Mathematics Gra.de........

37

Score-Form Regression Equation for the Prediction of Grade in Mathematics..............

38

Correlations betvreen Personality and Interest Measures and Semester Average .........................

90

School of Mineral Industries XXX.

XXXI.

XXXII,

XXXIII.

XXXIV.

XXXV.

Partial Regression Coefficients for Predictive Items using First-Semester Averageas Criterion . . . .

96

Means "'.nd Standard Deviations for Predictive Items and Semester Average .............................

97

Means and Standard Deviations for Predictive Items and Semester Average (N -w 1 0 0 ) ............. 98 Standard Deviation Ratios for Regression Equations Shorn in Table X X X V .............. .*........

98

Regression Equations, Multiple Correlations, Probable Errors of Estimate and Percents of Forecasting Efficiency for the Prediction of First-Semester Average for Mineral Industries Students . . . . .

102

Intercorrelations betv/een Predictive Measures and In­ dividual Course Grades...................

105

.

XXXVI.

Interrelationship betv/een Eight Predictive Items and First-Semester Average for the School of Mineral Industries........................... 94-

A; 'M ■>;

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

LIST OF TABLES (Continued) Page

Table XXXVII.

XXXVIII.

XXXIX.

XL.

XLI. ,

U

XLII.

Partial Regression Coefficients and Multiple Correla­ tions for Predictive Measures when Chemistry Grade is the Criterion..................... .

107

Standard Deviation Ratios for Regression Equations used in the Prediction of Chemistry I Grade . •

107

•

Regression Equation, Multiple Correlation, Probable Error of Estimate and Percent of Forecasting Effi­ ciency for the Prediction of Chemistry I Grade for the School of Mineral Industries ..............

108

Partial Regression Coefficients and Multiple Correla­ tions for Predictive Measures when Mathematics Grade is the Criterion.......................... .

110

Standard Deviation Ratios for Regression Equations used in Prediction of Mathematics Grade ....... .

110

Regression Equation, Multiple Correlation, Probable Error of Estimate and Percent of Forecasting Effi­ ciency for the Prediction of Grade in Mathematics for the School of Mineral Industries . . .

111

XLIII. Partial Regression Coefficients and Multiple Correla. tions for Predictive Measures when English Grade is Criterion . . . ..............................

113

Li IM

XLIV. Correlations of Personality and Interest Measures with First-Semester Average ........................

116

:1

XLV. Interrelationship between Six Predictive Measures and First-Semester Average......... .............

117

if ii

-i

XLVI.

p

3

XLVII.

XLVIII.

Partial Regression Coefficients for Prediction Batteries for the School of Mineral Industries ...........

118

Standard Deviation Ratios used in Regression Equations Shown in Table XLVIII .......................

118

Regression Equations for Prediction of First-Semester Average for Mineral Industries Students . . . . .

119

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

V.

LIST OF TABLES (Continued) Page

Table School of Lower Division XLIX.

L.

LI.

Interrelationship between Predictive Items and FirstSemester Average for the School of Lower Division

122

Partial Regression Coefficients for Predictive Measures using Semester Average as Criterion . ._.........

123

Means and Standard Deviations for Predictive Items and Semester Average .............................

124.

Standard Deviation Ratios used in Regression Equations • • • Shown in Tables LIII and LVIII .........

126

Regression Equations, Multiple Correlations, Probable Errors of Estimate and Percents of Forecasting Effi­ ciency for Prediction of First-Semester Average of Lower Division Students .......................

127

Comparison of a Selected Battery for Lower Division with a Selected Battery for Each of the Foregoing Schools

129

Interrelationship between Moore-Nell (Four Parts), High School Ran]-:, the Studi msness Index and Semester Average ......................................

131

Partial Regression Coefficients for Predictive Measures when Semester Average is the Criterion .

132

Means and Standard Deviations for Three Predictive Items and First-Semester Average ..............

133

Regression Equations for Prediction of First-Semester Average for Lower Division Students .............

135

Correlations between Personality and Interest Measures and First-Semester Average .....................

137

a

LII.

LIII.

LIV.

LV.

:.L ;

i-A

LVI.

*

ill

LVII.

LVIII.

LIX.

«

School of Agriculture - Non-Technical LX.

Interrelationship between Predictive Items and FirstSemester Average for the School of Agriculture Non-Technical ............................. • •

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

HO

,

vi.

LIST OF TABLES (Continued) Page

Table LXI.

LXII. ;:S

LXIII. :v'i

$ :v"

LXIV.

LXV,

LXVI.

Partial Regression Coefficients for Predictive Indices used in Regression Equations for the School of Agriculture - Non-Technical ....................

141

Means and Standard Deviations for Predictive Items and First-Semester Average for School of Agricul­ ture - Non-Technical ..........................

142

Standard Deviation Ratios used in Score-Form Regression Equations for Prediction of Semester Average for the School of Agriculture - Non-Technical .......

143

Regression Equations, Multiple Correlations, Probable Errors of Estimate and Percents of Forecasting Effi­ ciency for the School of Agriculture - Non-Technical

146

Interrelationship between First-Semester Average and High School Rank, Moore-Nell Total Score (Four Parts), Life Insurance Salesman Scale and the Dominance Scale of the Bernreuter Personality Inventory ......... 148 Relation of Personality and Interest Measures to FirstSemester Average for the School of Agriculture Non-Technical................ ......... .

150

p,v

Agriculture - Scientific LXVII. u

LXVIII.

LXIX.

I,XX.

Interrelationship between Predictive Indices 'and FirstSemester Average for the School of Agriculture Scientific . ................ .................

152

Partial Regression Coefficients used in Prediction Batteries for the School of Agriculture - Scientific

154

Means and Standard Deviations for Prediction Indices and First-Semester Average for the School of Agri­ culture - Scientific .........................

155

Standard Deviation Ratios used in Score-Form Regression Equations for Prediction of First-Semester Average for School of Agriculture - Scientific .........

156

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

vii.

LIST OF TABLES (Continued) Page

Table LXXI.

LXXII,

'Ob

Relationship of Personality and Interest Measures to First-Semester Average for the School of Agricul­ ture - Scientific ...........................

159

•

161

Agriculture - Two-Year LXXIII.

a

Score-Form Regression Equations, Multiple Correlations, Probable Errors of Estimate and Percents of Fore­ casting Efficiency for the School of Agriculture Scientific ....................................

LXXIV.

Interrelationship between Predictive Indices and FirstSemester Average for the School of Agriculture Two-Year '• •

163

Partial Regression Coefficients of the Items in the Pre­ diction Batteries for the Two-Year Curriculum in the School of Agriculture .....................

165

LXXV. Means and Standard Deviations for Prediction Indices and First-Semester -Average for the School of Agri­ ..................... culture - Two-Year L)D(VI.

166

Standard Deviation Ratios used in Score-Form Regression Equations for Prediction of First-Semester Average for School of Agriculture - Two-Year ............

167

Regression Equations, Multiple Correlations, Probable Errors of Estimate and Percents of Forecasting Effi­ ciency for the Two-Year Curriculum in the School of Agriculture ................................

169

LXXVIII. Relation of Personality and Interest Measures to FirstSemester Average for the Two-Year Curriculum in the School of Agriculture .........................

171

LXXVII.

LXXIX.

Correlations of the Moore-Nell Test Parts, the Total Test Score (Parts Unweighted) and the Total Test Score (Parts Weighted) with.the Semester Average for the Seven Populations .....................

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.

m

V I 11 .

LIST OF TABLES (Continued)

Table LXXX.

Correlations of High School Rank with First-Semester Average for the Seven Groups Employed in this Study.......... . , . . . ....................

175

Means and Standard Deviations of Semester-Average, High School Rank and the Moore-Nell Test Parts for the Seven G r o u p s ................................

177

Reliability of Differences between Means for Seven Var­ iables Obtained for the Several Schools .........

178

Most Practical Forecasting Batteries for the Seven Groups Employed in this Study .....

187

Relationshipof Moore-Nell Test Parts with Chemistry I Grade for the Schools of Chemistry and Physics and Mineral Industries ............................

188

Relationshipof Moore-Nell Test Parts with Mathematics Grade for the Schools of Chemistry and Physics, En­ gineering and Mineral Industries

190

Relationship of Moore-Nell Test Parts with English Composition I Grade for the Schools of Chemistry and Physics and Mineral Industries ................

197

Multiple Correlations, Probable Errors of Estimate and Percents of Forecasting Efficiency for the Selected Most Practical. Regression Equations for the Predic­ tion of Chemistry I Grade for the Schools of Chemis­ try and Physics and Engineering ..............

194-

LXXXVIII. Multiple Correlations, Probable Errors of Estimate and Percents of Forecasting Efficiency for the Most Practical Regression Equations for the Prediction of Mathematics Grade .for the Schools of Chemistry and Physics, Engineering and Mineral Industries . . . .

196

LXXXI.

3

LXXXII.

, :■!

4

.: .

LXXXIII.

LXXXIV.

LXXXV.

LXXXVI, u ;:y b;-3 i

LXXXVII,

1 •Si I P

Page

LXXXIX.

Percentage Distribution of Letter Grades on Occupational Scales for the Strong Vocational Interest Blank (Men) Obtained for the Schools of Chemistry and Physics, Engineering, Mineral Industries, Lower Division and Agriculture ..................................

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

201-205

CHAPTER I

l|

INTRODUCTION TO THE PROBLEM

The problem of vocational counseling for college students has become one of the most urgent and necessary steps in the successful administration of a college program.

At one time it was a function of

%

the interested associates of the student to offer a priori advice as to

|

the preferred course of study, but the proferring of successful vocational guidance is now a recognized part of academic service. An important development in counseling service has come through the increasing requests of college students for guidance into programs

1 of study in which they are most likely to be successful.

At the Psycho-

Educational Clinic of The Pennsylvania State College, the students who seek aid are functionally, divided into three major types.

They are,

I first, the vocational adjustment problems, who are poorly located in their present curricula, and who frequently have been sent to the Clin­ ic by their adviser or the dean of their school because of poor scholf

arship.

There are, secondly, the personality problems who have come

because of serious personality difficulties affecting general college adjustment.

\4

The third class is made up of those interested and often

well-adjusted students who wish to have their choice of vocation corro­ borated.

There is, frequently, a curiosity manifested by the latter

group as to whether some unrecognized and latent ability can be un­ covered by the clinical instruments.

All of these types of counseling

1 R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .

!|

problems can be and often are related Intimately to one another. For example, the personality case may be very seriously maladjusted vocationally.

Often, the student who has been successful enough aca­

demically because of superior ability may be affected emotionally by

■f his choice of career. All of these problems demand that careful professional procedures alone be used in determining the psychological equipment of an individual, and the utilization of that equipment for most effective functioning.

Currently, the seriousness of this problem cannot be

;7'1 doubted.

With the entire program of the country engaged in expediting

the processes of production, it is the responsibility of all colleges to turn away less potential failures and graduate more well-trained, capable and adjusted people in a shorter period of time.

Peace-time

standards of very high scholarship as a requirement for college en­ 1

trance have changed to a wartime policy which demands that the student quota be maintained in spite of appreciably fewer applications.

Under

if

such conditions, many applicants who would have been rejected formerly will now gain admittance.

This points the way toward a very careful

program of guidance which will strive to maintain the academic standards ■j

•

of the college by training its students along the lines for which they are best fitted. Another ever-current aspect of this problem is the number of students who are dropped each year from college because of low grades. At one time, a popular philosophy of many professors was that the number

'll R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

of students who failed a course served as a criterion of the high stan­ dards of that course.

It is now believed that student mortality is not

so much a matter of high standards as it is a matter of poor selection ' A #

'A

of students.

If the selection process is not discriminative, the per­

. :■■■:

centage of failures will continue to be extremely high in spite of

%

standards.

It is true that the first semester of a college student*s

career is often the crucial one.

%

More vocational difficulties prob-

ably occur during this period than at any other one period of the col­ lege course.

I

Acknowledgment of this is evidenced by the increasing de­

■ mands for vocational counseling by incoming freshmen. During the fall semester of 1940, the number of prospective

s freshmen asking for vocational advice at the Psycho-Educational Clinic was so great that it was decided to administer a battery of tests to all

i :S'i

incoming freshmen for guidance purposes.

we

e;;

The Thurstone Tests of Primary Mental Ability, which were given during freshman week as a part of the guidance program, became the ba­ sis for the prediction of the first-semester average of the entering

;®

freshman student.

In 1941 > the Thurstone Tests of Primary Mental Abil-

|

ity were no longer available, and a test prepared by B. V. Moore and

;!/

R. B. Nell (ll) of The Pennsylvania State College was used in its place.

I (It was impossible to predict the student1s probable success from this measure as no research on it had been completed.

Borow (2), in 1941#

made a study using the Moore-Nell, but his populations were not strict­ ly representative of those of any of the schools of the college.

J

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

It

was felt that there was a serious need for a Study to determine the validity of the Moore-Well examination for the prediction of achieve­ ment within the different schools of The Pennsylvania State College. In the literature of college prediction, the different measure­ ments used for the forecasting of success or failure of students are mainly of two kinds: the high school record and psychological tests of aptitude and achievement.

Harris (7) notes a number of investigations

of prediction from different measures of high school attainment.

He

points out that it seems evident from a number of studies that "rank in high school graduating class" seems to be slightly superior to any other single predictive measure taken from the high school record.

Segel and

Proffitt (17) report a great many correlations with high school grades and contend that success or failure in a specific high school subject shows enough of a positive relationship with college achievement in the same subject to be of some advantage in differential prediction. The use of psychological tests for prediction seems to be most effective when carefully selected predictive batteries are developed. Segel (14-) gives the results of a number of studies which plainly indi­ cate that a more precise prediction is possible when several measures are used in combination.

He lists eighteen correlations between various

combinations of predictive items and college achievement. from .56 to .81 with a median of approximately .65.

These range

It seems clear that

well-chosen prediction batteries are potentially of great value in the hands of the vocational counselor.

However, it is not the purpose here

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission .

to give a review of the literature on the prediction of college suc­ cess.

Extensive surveys of the findings in this field of research

are presented in Segel (14) > Harris (7 and 8) and Borow (2).

Borow

also reviews the prediction research which has been conducted at The Pennsylvania State College. Reemphasizing the need for vocational counseling measures which i.

:'4 have scientific integrity, and acknowledging the real progress of other ■'V.

investigators in this field, the writer decided to adopt the objectives ..

which appear in the following section of this chapter for the direction of this study.

8 S.

I

i m

8 ■W

!

1 § § R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

i

STATEMENT OF TEE PROBLEM

The purposes of this study were the followings 1. To determine the relationships of the Moore-Nell test parts, high school rank, personality traits, interest measures and a studiousness index scale with first-semester average for each of seven college groups, namely; The School of Chemis­ try and Physics, the School of Engineering, the School of Mineral Industries, the School of Lower Division and the non-technical, scientific and two-year groups of the School of Agriculture. 2. To find the differential importance of each test part for prediction in the various schools. 3. To develop equations for the prediction of first-semester average within each school.

A* To find the relationship of the Moore-Nell test parts and high school rank with freshman chemistry, mathematics and English composition grades for certain schools. 5. To construct regression equations for the prediction of grades in freshman chemistry and mathematics for certain schools.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

'

CHAPTER II THE DATA AND THEIR TREATMENT

THE SUBJECTS

This study used the male members of the freshmen class of 1941-42 of The Pennsylvania State College as subjects.

These students

were enrolled in the Schools of Agriculture, Chemistry and Physics, Engineering, Lower Division, and Mineral Industries, and separate stu­ dies were made for each group* In the case of the School of Agriculture, a division of the students into three smaller groups was made for the purpose of more in­ tensive research.

This school offers a two-year curriculum to students

interested in a briefer, less professional course in agriculture.

The

requirements for admission to this curriculum are lower than elsewhere and the students are as a whole of relatively inferior academic ability.

* In recognition of this deficiency, the standards of satisfactory per-

I

formance are correspondingly lower, and many of the credits obtained

lit from the Two-Xear course in Agriculture are not acceptable for use toward a degree in a four-year curriculum at The Pennsylvania State College.

It

was decided, therefore, to study the Two-Xear Agricultural curriculum as a separate group. A further dichotomy was made of the four-year curriculum in agri-

1

culture.

Since part of the students are engaged in studying material of

an essentially research nature, this unit was called the scientific group.

it ft sit

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

The other division included students whose work is of a practical or applied type, and may be designated as non-technical. The School of Mineral Industries was used in a special phase of the study which concerned the influence of studiousness upon college grades.

Only seventy-eight students out of the one hundred subjects in

the Mineral Industries School composed the group for whom a studious­ ness index score was obtained.

Therefore, the Mineral Industries School

had two divisions, one which included all of the members of the school, and a special group of seventy-eight for the investigation of studious­ ness. Only those students for whom complete records were available could be used.

In the case of each school, some students were lost be­

cause of withdrawal from college during the first semester.

vi$

3$

ri$

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

THE PREDICTION INSTRUMENTS

All of the tests used in this study were administered to the freshmen in September, 19>41» under the direction of Dr. R. G. Bernreuter.

As explained in the introductory chapter, the testing program

is a part of the vocational guidance service offered by the PsychoEducational Clinic and is held each, year during freshman week at The Pennsylvania State College.

A. The Moore-Nell Examination ( U ) * One instrument employed in this study was an examination con­ structed in 1939 by B. V. Moore and R. B. Nell of The Department of Education and Psychology of The Pennsylvania State College.

It is com­

posed of five sub-tests on specific subject matter which are intended to disclose the eligibility of the applicants for admission to the col­ lege.

Multiple-choice items are used, with the number of choices being

five throughout the test. sponses.

The total score is the number of correct re­

Directions and two sample problems precede each test part.

Examinees are told when to begin each part, and are not permitted to work on any other section of the test if they finish before the time limit is called. A descriptive outline of the test is presented in Table I.

m sH

* Copy available at the Department of Education and Psychology of The Pennsylvania State College.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

TABLE I DESCRIPTIVE OUTLINE OF MOORE-NELL EXAMINATION

Test

Identification Symbol

Number of Questions

Time Limit (Minutes)

120

20

Vocabulary

Voc.

Paragraph Reading*

P.R.

Arithmetic Processes

A.P.

35

25

English Usage

E.U.

35

15

Algebraic Processes

Alg. 273

100

25

B. The Strong Vocational Interest Blank This scale was prepared by E. K. Strong for the purpose of ascertaining how closely an individual’s likes and dislikes agree with those of successful men in specific occupations.

A detailed descrip­

tion of the test can be found in the “Manual for Vocational Interest Blank for Men” prepared by Strong.

In the present study, the tests

were scored for forty occupations. Raw scores on the V.I.B. were converted in order to facilitate

ft

computations. Appendix.

The method by which this was done is explained in the

Strong (18) indicates that there is no advantage in using

raw scores in place of letter grades.

However, such scores were used

* This test originally contained 36 questions,

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

for some occupational scales in this study in order to determine whether the raw scores would give higher correlations with the criteria than would the letter grades.

One reason for this decision is that let­

ter grades do not represent equi-distant intervals.

The following, taken

from Strong's manual,will make this clear.

Letter Grade

Present Value

Percentage of Normal Distribution

A

-0.56 and above

69.2

B+

-0.56 to -16

15.0

B

-l.Otf to -1.56

9.2

B-

-1.56 to -2.0(7

■4*4

c+

-2.00-to -2.56

1.7

C

-2.56 and below

0.6

C. Vocational Interest Blank Studiousness Index (23) A number of the Vocational Interest Blanks were scored with the Young-Estabrooks Scale for Measuring Studiousness.

This is a set of

weights for the items of the Vocational Interest Blank, prepared by C. W. Young and G. H. Estabrooks, to measure certain non-intellectual fac­ tors which, may contribute to academic success. . In reporting findings of their studies using the Studiousness Index, Young and Estabrooks say, "The term 'studiousness' applies to the sum total of factors of personality and attitude which make for

with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

high college grades and which are not correlated with intelligence." They maintain that one cannot speak of the validity of the scale but of the usefulness in improving the prediction made by in­ telligence tests.

In this way, the usefulness of the scale bears an

inverse relationship to the correlation between grades and intelli­ gence. In using the Studiousness Index, loung and Estabrooks report correlations of .35 with semester average for a group of Colgate stu­ dents.

Mosier (12), who used the same scale in studying a group of

University of Florida students, found correlations around .30 with hon­ or point average for the different curricula of the school. In order to facilitate use of the punched-card method of scor­ ing, the item weights for the present study were reduced to a range from plus to minus four.

All weights falling above or below this range

automatically received a weight of plus or minus four respectively. All intermediate weights retained their original values.

A constant

of five was then added to all scores to eliminate minus values. Since the Studiousness Index was prepared for the original Strong Vocational Interest Blank, it was necessary to make some adap­ tions for use vdth the revised blank.

The change necessitated the

omission of certain items which were not common to both the original and the revised blanks.

Items included on either blank which were

omitted on the other, were eliminated from the study. The final result was a method of scoring the items of the Strong

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

Vocational Interest Blank which yielded a measure of the studiousness manifested by the student.

Since the success of Young and Estabrooks

warranted the investigation of this scale as a measurement of predic­ tion, it was used experimentally for several of the schools in this study.

It was hoped that such a measure could be successfully employ­

ed to supplement other items in a prediction battery and not as an in­ dependent forecaster of college success.

D. The Bernreuter Personality Inventory (l) This is an instrument of the questionnaire type which serves as a measure of certain personality traits. factors.

It can be scored for six

These are stability, self-sufficiency, introversion-extro-

version, dominance-submission, self-confidence, and sociability. The inventories used in this study were scored for the follow­ ing factors: stability (Bl-N, reversed), self-sufficiency (B2-S), and dominance (B4--D).

E. High School Rank An individual’s rank in his high school graduating class, as well as serving as an index of academic aptitude, often gives an indi­ cation of the extent to which he has made use of his scholastic abil­ ities, and can be suggestive of his application to study in future aca­ demic pursuit.

Since one of the purposes of this study was to construct

prediction equations, a measure was sought which would give an estimate

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

of an individual’s application tb previous formal instruction.

The

high school rank offers such an estimate. In previous studies at The Pennsylvania State College, the high school rank was recorded in quintiles or as a transmuted number vjhich attempted to equate the disparate standards of grading among Pennsylvania high schools.

The registrar of the college developed a

conversion technique for equalizing the rankings of the various high school rankings.

Borow (2) describes the system in detail and then

demonstrates that the method is not superior to the quintile-rank system because of the relatively low reliability of this transmuted . rank. Borow1s (2) procedure of psychologically grading the high school rank was used in this study.

This method consists of converting the

high school quintile ranks into the median college decile ranks earned by students in the corresponding quintiles of high school standing.

Ta­

ble II, taken ftorn Borow*s thesis, (page 64), shows the median college freshman decile rank earned by the students in each quintile of high school rank based on a population of 1720 freshmen of the class of 1943*

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.

TABLE II

MEDIAN FRESHMAN AVERAGES AND FRESHMAN RANKS OF 1720 FRESHMEN OF THE CLASS OF 194-3 DISTRIBUTED ACCORDING TO HIGH SCHOOL RANKS

High School Rank (quintiles)

Median College Median College Freshman Average Freshman Rank (deciles)

Median College Freshman Rank (constant of 2 subtracted)

1

1.65

3

1

2

1.21

6

4

3

.33

8

6

4

.67

8

6

5

.50

9

7

In this study a constant of 2 was subtracted from the third column in order that smaller numbers might be worked with.

These re­

duced college decile ranks are indicated in the fourth column. It is seen in the fourth column of this table that a low num­ ber indicates high secondary school achievement.

For the Moore-Nell

test parts and for semester average, high numbers signify high achieve­ ment; for the occupational interest and studiousness index scales high values mean greater similarity of interests.

Hence any positive corre­

lations between high school rank and the Moore-Nell test parts and se-

i mester average and between high school rank and the interest and stu-

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.

diousness index scales would appear as negative correlations.

Since

these negative correlations are artifacts, they are reported in this .study as positive correlations.

In the computations of the regression

equations, these seemingly negative correlations are used as positive correlations.

As a result, if the high numbers of the secondary school

rank are multiplied by the appropriate weight in the regression equation the predictions would be erroneous.

In order to make the regression

equations practicable, the high school ranks are reoriented.

These re­

oriented ranks are shown in Table B in the Appendix. Similarly, conversions are required where the total unweighted Moore-Nell scores are employed since the high numbers signify poor achievement.

Also, for the dominance scale changes are necessary be­

cause high scores in dominance are punched in the Hollerith cards as low values, whereas low dominance scores are punched as high values. The numbers punched in the Hollerith cards and their corresponding val­ ues obtained from the prediction instruments, and tables showing the reoriented values are given in the Appendix.

In the equations which

involve the total unweighted Moore-Nell test score and the dominance scale, the appropriate score-form regression weights are multiplied by these reoriented values.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission

CRITERIA OP ACADEMIC SUCCESS

In the selection of the criteria to be used for the study of prediction, it was again necessary to consider some of the specific situations out of which the need for a predictive battery arises. Many of the students who come to the Psycho-Educational Clinic for vocational counselling ask about the probabilities of success or fail­ ure in specific courses.

This is especially true of students who are

interested in transferring from a non-technical curriculum to a tech­ nical one.

In this connection, the question of success in mathematics

or chemistry is frequently encountered.

Again, a number of prospec­

tive enrollees, prior to college entrance, come to the clinic seeking information about the likelihood of success in curricula requiring a great amount of chemistry or mathematics.

There is, furthermore, the

problem of advising freshmen who are experiencing serious difficulty with their work during the first weeks of their college careers.

All

of these situations suggest the desirability of establishing regression equations for the prediction of success in specific courses and in spe­ cific curricula. Since information concerning the relationship of the parts of the Moore-Nell test to the student's performance in English courses was desired, grade in English Composition 1 was used as a criterion for two of the schools.

It was believed that any correlations with English

grades would be lowered somewhat because of the initial exclusion of

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

many students from English credit courses.

By means of an English

placement examination administered during Freshmen Week, those students exhibiting a lack of fundamental English comprehension are re­ quired to take special training iD a course for which no credit was given.

It is likely that, in this study, this condition resulted

in a restriction of the distribution of English Composition grades and, consequently, reduced the magnitude of the correlations wherever these grades were used. The following criteria were used in the present study: First Semester Average First-semester average represents the weighted average of the grades earned by a student for the first semester that he is in col­ lege.

Grades used at The Pennsylvania State College are as follows:

3 (90-100), 2 (80-89), 1 (70-79), 0 (60-69), -1 (45-59), -2 (0-44). A grade of minus one or minus two is a failure. along a scale from -2 to a

+3, with a

Grades run, therefore,

+3 representing the highest

achievement. Chemistry Chemistry I, the course in chemistry, which is used for the Schools of Chemistry and Physics and Mineral Industries, is described by the college catalogue (20) as a "course in inorganic chemistry in which the fundamental principles of the science are studied in connec­ tion with the descriptive chemistry of non-metallic elements and their compounds

".

This is a basic course for all curricula which include

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

an intensive program of chemistry. Mathematics Both Mathematics 4 and Mathematics 20 are offered to enroUees in the School of Chemistry and Physics.

Both are courses in plane

trigonometry and algebra designed for the specific needs of the curri­ cula in which they are taught.

For the School of Mineral Industries,

Mathematics 4 is used as the criterion.

In the School of Engineering,

Mathematics 54 and 55 are included, since certain curricula within this school require these as basic courses.

They are courses in the study

of algebra and trigonometry. All mathematics courses in this study are represented as one criterion under the heading of mathematics. English English Composition 1 is a course in "composition and rhetoric," and is used for the Schools of Chemistry and Physics and Mineral Indus­ tries.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

STATISTICAL METHODS

The Pearson product-moment method was used in this study to calculate all correlations.

In developing multiple correlations and

partial regression coefficients, the Doolittle technique was employed. Standard error ratios were computed to determine the reliability of differences between variables.

The makings for all correlations were

obtained by the use of punched-card methods and equipment. A complete description of the statistical procedures used in this study can be found in Peters and Van Voorhis (13)•

i

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

CHAPTER I I I

RESULTS

A.

ORGANIZATION OF RESULTS

In reporting the results obtained from the study of the seven populations which were used, the following procedures will be observed: 1. Each population will be presented in a separate sec­ tion of the chapterj the final section will be devoted to a summary of the results for all populations. 2. Tables of data will accompany each population and will be brought together for all groups in the summary section. 3. General organization of the data for each section will be as follows: a. Interrelationships of prediction variables to cri­ teria. b. Partial regression coefficients and multiple corre­ lations of prediction batteries. c. Means and standard deviations for predictive items and criteria. d. Standard deviation ratios for regression equations. e. Regression equations. f . Relationship of personality and interest measures to criteria.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

4-. Throughout the chapter, it will be remembered that observations apply to the group which is being presented, unless stated otherwise. 5.

The populations will be presented in the following

order: a. School of Chemistry and Physics. b. School of Engineering. c. School of Mineral Industries. d. School of Lower Division. e. School of Agriculture - Non-Technical f. School of Agriculture - Scientific. g- School of Agriculture - Two-Tear.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.

B.

1.

THE SCHOOL OF CHEMISTRY AND PHYSICS

Interrelationship between Seven Predictive Items and Semester Average

In order to determine the interrelationship between the pre­ dictive items and the criterion, intercorrelations were computed for first-semester average, transmuted high school rank, Vocabulary, Para­ graph Reading, Arithmetic Processes, English Usage and Algebra test parts of the Moore-41ell examination, and the Chemist scale for the Vo­ cational Interest Blank. A horizontal examination of Table III reveals that high school rank gave the highest correlation with the criterion, semester aver­ age.

The correlation is .510.

The next highest correlations were ob­

tained with the Arithmetic Processes, Algebra and English Usage test parts, which show correlations of .4$7, .4^5 and .435, respectively. Somewhat smaller correlations exist between Paragraph Reading and Vo­ cabulary and freshman academic achievement.

A brief survey of the

courses taken by freshmen in the School of Chemistry and Physics may suggest a possible explanation of these relationships.

Of the eigh­

teen and one-half credits which comprise the first-semester schedule, only six, or less than one-third, are of a highly verbal nature; at least ten credits are devoted to technical material such as chemistry and mathematics.

It would seem reasonable, then, that the technical

sections of the college aptitude examination such as Arithmetic Pro-

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.

cesses and Algebra possess higher relationships than the verbal sections to the semester average.

It is interesting to note that

English Usage, a non-mathematical test part, is related to semester average to almost the same extent as the Arithmetic Processes and Algebra sections of the Moore-Nell examination. The occupational scale for Chemist on the Strong Vocational Interest Blank gave a negligible correlation with semester average. It is possible that the skewness of the distribution of the Chemist interest scores is partly responsible for the seemingly low relation­ ship.

As will be shown later, fifty-five percent of the Ghemistry

and Physics students receive letter grades of A or B-f on the Chemist scale.

It might be well to point out again that the Strong Vocation­

al Interest Blank is a measure of the degree of interest in common with successful workers, but does not give a direct indication of ability. Further inspection of Table III reveals that, among the in­ terrelationships of predictive items, high school rank correlates relatively low with the test parts of the Moore-Nell and with the Chemist scale of the Vocational Interest Blank.

Arithmetic Processes,

English Usage and Algebra give correlations of .180, .181 and .183 with high school rank.

Paragraph Reading and the Chemist scale show

practically no relationship with correlations of .050 and .051.

It

may be noted here that the magnitude of all correlations for high school rank is.limited by the skewed distribution of the high school

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

ranks.

This is essentially the same situation which exists with

regard to the Chemist scale, mentioned above.

Table IV shows the

mean of high school rank for the School of Chemistry-and Physics to be 2.55.

This means that in terms of transmuted rank, the mean

falls somewhere between the first and second fifths, again demon­ strating the skewness of the distribution of high school rank. The correlations of Vocabulary with Paragraph Reading and English Usage, being

.485 and .416, respectively, show a contrast

to the correlations with Arithmetic Processes and Algebra, which are .308 and .260.

This finding is in keeping with the expectation that

higher correlations will exist between Vocabulary and other verbal test parts than between Vocabulary and mathematical sections.

How­

ever, Paragraph Reading is related to Arithmetic Processes and English Usage to almost the same degree, with correlations of .327 and .324-. A vertical examination of the last column of Table III reveals the absence of any significant degree of correspondence of the Chemist scale of the Vocational Interest Blank to high school rank and to most parts of the Moore-Nell examination.

The exception is the correla­

tion of .343 obtained with Algebra, indicating that students with high interest scores on the Chemist scale of the Vocational Interest Blank tend to make high scores on the Algebra test.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

TABLE I I I

INTERRELATIONSHIP BETWEEN PREDICTIVE ITEMS AND FIRST-SEMESTER AVERAGE FOR THE SCHOOL OF CHEMISTRY AND PHYSICS

N = 228

Sem.

H.S.R.

Voc.

P.R.

A.P.

E.U.

Alg.

Chem V.I.B,

.510

.283

.220

.487

.435

.485

.085

.118

.050

.180

.181

.183

.051

.4*5

.308

.416

.260

.150

.327

.324

.248

.075

.433

.486

.166

•445

.100

Av. Sern. Av. H.S.R. Voc. P.R. A.P. E.U.

Alg.

.343

Chem. V.I.B.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

2.

Examination of the Partial Regression Coefficients Used for Re­ gression Equations for Prediction of First-Semester Average

A horizontal examination of Table IV reveals the contribu­ tions made by each of the variables to the prognosis of freshman academic success when these items are combined into prediction teams. A vertical inspection shows the different weights obtained for the same factor when it is used in different batteries. It can be seen from the first column that high school rank was weighted relatively high in all of the teams of which it was a member.

The weights vary between .3950 and .3971.

The second and

third columns show the negligible contributions of the Vocabulary and Paragraph Reading test parts to the multiple correlations.

On

the other hand, English Usage, with partial regression coefficients distributed from .13S0 to .1997, makes some contribution to the pre­ diction formula. The Arithmetic Processes test part, which is given in the fourth column of Table IV, makes an appreciable contribution to the prediction team.

It is seen that this test part possesses beta

weights which are all within a range of .2296 and .2723 •

This sug­

gests that the degree of arithmetic skill possessed by a student in the School of Chemistry and Physics is related to his success in that school.

The Algebra test part, with beta weights progressing from

.2244 to .2940, makes a considerable contribution to the prediction of success.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

The Chemist scale of the Vocational Interest Blank adds virtually nothing to the effectiveness of the prediction battery# By examining all of the weights for the first team shown across the first row of Table IV, it is noted that high school rank, and the Algebra and Arithmetic Processes test parts have the highest partial regression coefficients. are .3950, .2330 and .2300.

Their respective weights

In the second battery the partial re­

gression coefficients of the predictive measures, in order of mag­ nitude, are shown to be Algebra, Arithmetic Processes, English Us­ age, Vocabulary, Paragraph Reading and the Chemist scale of the Vo­ cational Interest Blank.

The third team reveals Arithmetic Processes

and Algebra to be of about the same magnitude, with English Usage possessing a somewhat smaller beta weight. Reading make negligible contributions.

Vocabulary and Paragraph

High school rank, Arithmetic

Processes and Algebra possess the highest beta weights in the fourth battery. It was decided to omit the test parts of Vocabulary and Para­ graph Reading from the fifth and sixth teams because of their pre­ viously demonstrated ineffectiveness.

By using the remaining fore­

casting variables, beta weights for the remaining three test parts maintain the same relative order as in the foregoing regression equations. This is observed by reference to the last row of Table IV.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

TABLE IV

SCHOOL OF CHEMISTRY AND PHYSICS

PARTIAL REGRESSION COEFFICIENTS OF PREDICTION BATTERIES FOR CHEMISTRY AND PHYSICS STUDENTS

Egi

H.S.R.

Voc.

P.R.

A.P.

E.U.

Alg.

Chem. S.

1.

.3950

.0570

-.0040

.2300

.1380

.2330

-.0830

2.

.0787

-.0286

.2688

.1732

.2940

-.0875

3.

.0690

-.0250

.2690

.1810

.2610

.0473

-.0004

.2296

.1444

.2244

.2362

.1601

.2263

.2723

.1997

.2638

•4*

.3959

5.

.3971

6.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.

2,.

Comparison of Means and Standard Deviations for First-Semester Average. High School Rank, and the Parts of the Moore-Nell

In Table V the means and standard deviations of the firstsemester average, the transmuted high school rank and the parts of the college aptitude examination are presented.

A survey of this

table, in relation to the tables of means and standard deviations for the other schools used in this study, will be given in the sum­ mary section. It will be noted that the mean semester average for the School of Chemistry and Physics is 1.24- and the standard deviation is .911.

This average, which is .24 above +1.00, the minimal stan­

dard for satisfactory college achievement, corresponds very closely to past estimates of the all-college average for an entire freshman class. The mean of the high school rank is located at 2.55* must be remembered that this represents a transmuted rank.

It By re-

,\

ferring to Table II, it becomes evident that 2.55 would fall some­ where between the first and second fifths. in terms of transmuted rank is 1.96.

The standard deviation

Since this figure is somewhat

larger than the standard deviation of the original scale of ranks, no meaningful deduction can be drawn concerning the variability of the population in high school performance. For the Vocabulary part of the Moore-Nell, the mean was 64.23 and the standard deviation 16.10.

Reference to Table I shows that the

Reproduced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.

total number of questions of the Vocabulary test is 120.

Thus,

the mean number of words answered correctly by the Chemistry and Physics students was slightly over 50 percent of the items on this test part. The mean score earned for Paragraph Reading was 33.27.

Since

the total score possible is forty-eight, the mean score for this school on the Paragraph Reading test part is 66 percent of the total score.

The standard deviation was A.41. For Arithmetic Processes the mean score attained was 25.62

and the standard deviation was 4-.64. Further inspection of Table V shows that English Usage and Algebra possess means of 29.24- and 26,02, respectively.

The stan­

dard deviations, in the same order of naming,were 2.99 and 4-53*

The

maximum number of points on both these tests is 35.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

TABLE V

MEANS AND STANDARD DEVIATIONS FOR FIRST-SEMESTER AVERAGE, HIGH SCHOOL RANK AND THE FIVE PARTS OF THE MOORE-NELL FOR SCHOOL OF CHEMISTRY AND PHYSICS

N - 228

Mean S.D.

Sem. Av.

H.S.R.

Voc.

P.R.

A.P.

E.U.

Alg.

1.24

2.55

64.23

33.27

25.82

29.24

28.02

1.96

16.10

4.41

4-64

2.99

4.53

.911

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .

4-.

In order to deyelop the score-form regression equations listed

in Table VII, standard deviation ratios were computed for each of the prediction items.

By this technique, the unequal variabilities

of the several distributions were equated. for each variable is listed.

In Table VI the ratio

To calculate the standard deviation

ratios, the standard deviation of the criterion, semester average, was divided by the standard deviation of each prediction part.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .

TABLE V I

SCHOOL OF CHEMISTRY AND PHYSICS

STANDARD DEVIATION RATIOS FOR REGRESSION EQUATIONS USED IN PREDICTION OF FIRST-SEMESTER AVERAGE FOR CHEMISTRY AND PHYSICS STUDENTS

H.S.R.

.911 1.96

=

.4648

Voc.

,9 H 16.10

-

.0566

-

.2066

P.R.

4 .4 1

A.P.

,9 H 4—64

s

.1963

E.U.

,9 H 2.99

=

.3047

Alg.

.911 4.53

a

.2011

Chem. S.

.911 46.49

=

.0196

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

JL*

Prediction of First-Semester Average from Regression Equations

In predicting the first-semester average for the School of Chemistry and Physics, six score-form regression equations were con­ structed.

The equations, their probable errors of estimate, and the

percentages of forecasting efficiency are given in Table VII. The first line of each equation indicates the predictive items used in the battery.

The second line gives the weight by which raw

scores for the items are multiplied.

Each weight is obtained by mul­

tiplying the beta weight for the corresponding item given in Table IV by the standard deviation ratio shown in Table VI.

For example, the

weight of .1836 for high school rank in Equation 1 was obtained by multiplying the beta weight for this variable, .3950, by the corre­ sponding standard deviation ratio, .4.648. In the first eo^uation, the prediction team is made up of high school rank, the five parts of the Moore-Nell examination and the Chemist scale of the Vocational Interest Blank. lation for this combination is .710.

The multiple corre­

This degree of relationship com­

pares favorably with results for predictive teams shown elsewhere in the literature of college predictions (7), (14)*

The accuracy with

which first-semester average may be predicted from Equation 1 is indi­ cated by a probable error of estimate of .43.

Therefore, first-semes­

ter average can be expected to fall within a range of predicted average fifty percent of the time.

±.43 of the

The percent of forecast-

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .

ing efficiency is shovm to be 29.6.

This indicates that the standard

error of estimate represents a reduction of the standard deviation for this population of 29.6 percent. When high school rank was omitted from the first equation, the multiple correlation was reduced to .610. forecasting efficiency dropped to 20.8.

Lilcevd.se, the percent of

The probable error of estimate

was extended to .4-9. A comparison of Equation 1 with Equation 2 re­ veals that high school rank adds materially to the accuracy of the prediction.

A further indication of the relative importance of high

school rank is demonstrated by the beta weight of .3950 shown in Table IV. Both high school rank and the Chemist scale of the Vocational Interest Blank were eliminated from Equation 3.

Thus, the multiple

correlation for the five test parts of the Moore-Nell examination was determined.

The multiple correlation was shown to be .593> with

a probable error of estimate of .49, and 19*5 percent of forecasting efficiency.

It is apparent that no significant difference exists

between the multiple correlations of the variables involved in Equa­ tions 2 and 3» The Chemist scale of the Vocational Interest Blank was in­ cluded in the first and second equations in order to discover whether a non-intellective factor, which correlated negligibly with most of the other variables and the criterion, would raise the multiple correlation.

When the Chemist scale is eliminated from Equation 1,'

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

the correlation drops only .004-.

This is illustrated in Equation 4-*

Vocabulary, Paragraph Reading and the Chemist scale were dropped from Equation 5«

That there is no appreciable loss in pre­

diction efficiency is evidenced by a difference of only .002 between the multiple correlations for Equations 4- and 5.

The lowering of

forecasting efficiency is 0.2 percent. When the prediction battery consisted only of three parts of the Moore-Nell examination, namely, Arithmetic Processes, English Usage and Algebra, the multiple correlation was found to be .5^9 and the probable error of estimate .50. 6.

This is illustrated in Equation

By comparison with Equation 3 it is seen that this smaller team

predicts virtually as well as the entire college aptitude examina­ tion for the School of Chemistry and Physics. In summary, Table VII shows that the addition of the Chemist scale of the Vocational Interest Blank to the prediction battery fails to increase the multiple correlation materially.

High school

rank represents the best predictive item in the battery by its sub­ stantial contribution to the multiple correlations.

The prediction

team represented by Equation 5 appears to be the most practical of those given in Table VII inasmuch as it yields a satisfactory corre­ lation with a minimum of predictive items.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

TABLE VII SCHOOL OF CHEMISTRY AND PHYSICS

REGRESSION EQUATIONS FOR PREDICTION OF FIRST-SEMESTER AVERAGE FOR CHEMISTRY AND PHYSICS STUDENTS N = 228 Equa­ tions Chem. S. -. 0016X7)

.43

29.6

Voc. .0032X2

P.R. -.OOO8X 3

A.P. .0452X4

E.U. .0I421X5

Voc. (.0045X2

P.R. -.0059X2

A.P. ,0528X3

E.U. .0528X 4

Chem. S. E Alg. .0593X5 -.0017X6) -2.7865

.610

.49

20.8

Voc. ( .0039Xi

P.R. -.0052X2

A.P. .0528X 3

E.U. .0552X4

Alg. K .0525X 5)-2.9724

.593

.49

19.5

H.S.R. (.1840X1

Voc. .0027X2

P.R. -.OOOIX3

A.P. .O45IX4

E.U. .0/140X 5

.706

*44

29.2

H.S.R. (.I846X1

A.P. .Q464X 2

E.U. .0488X 3

.704

.44

29.0

A.P. (.0535X2

E.U. .0609X2

Alg. K .O53IX3) -3.4060

.589

.50

19.2

Alg. K .0451X6) -3.1133

K -2.6352

P.E. Est.

H.S.R. (.1836X2

K Alg. .0455X4) -3.1296

Alg. .0509X6

Multiple R .710

Per­ cent Fore Eff.

VjJ 00

6.

Relationship between Six Predictive Measures and Individual Course Grades

Since the criterion in foregoing sections was uniformlytaken to be the first-semester average, the relationships between the prediction instruments and success in specific subject matter areas were not revealed.

It would seem important to know the dif­

ferential prognostic value of an instrument when separate courses are used as criteria. Table VIII presents the correlations obtained between each of the forecasting variables and grades in chemistry, mathematics and English courses.

Some of the relationships were not computed.

It will be noted that the correlations between the variables and semester average are repeated to facilitate comparisons with the individual course criteria. A horizontal examination of the table shows the relation of the prediction items to the criteria. The correlations between high school rank and the criteria vary from .376 with mathematics to .510 vdth first-semester average. Vocabulary correlates to about the same extent with semester average and chemistry.

However, there is a reliable difference between the

correlations vdth mathematics and English composition.

This dif­

ference tends to indicate, as would be expected, that Vocabulary hields a more accurate prediction of English composition grade than

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

of mathematics grade.

That this is true will be pointed out in the

section devoted to regression equations for individual course pre­ diction. Paragraph Reading shows low relationships with each of the course grades as well as with semester average.

It was thought that

Paragraph Reading would offer a valuable contribution to a team pre­ dicting success in English Composition I but would hot be of much worth to a battery for the prediction of mathematics achievement. The low correlations with all criteria demonstrates the ineffective­ ness of the Paragraph Reading test part in predicting the freshman performance of Chemistry and Physics students. Arithmetic Processes correlates to the extent of .550 with chemistry and

.438 with mathematics.

At a first glance it may appear

unusual that an arithmetical test part shows a higher relationship to chemistry than to mathematics.

An investigation of the subject matter

of the chemistry and mathematics courses discloses a partial explana­ tion of the difference.

It will be remembered that the mathematics

courses, are composed largely of algebra and trigonometry, whereas Chemistry I is mainly concerned with the solution of problems relating to the chemical formulae.

These latter problems are of the type in­

volving arithmetical reasoning and computation.

Since the final grade

in Chemistry I is established largely by a student’s written perfor­ mance on this type of material, it would be expected that Arithmetic Processes would convey some indication of success in the chemistry source.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .

Although there is no significant difference between the correlations of English Usage with semester average and with chem­ istry, there is a reliable difference between the correlations of English Usage with mathematics and English grades.

The correlation

with mathematics grade is .327 and with English grade, .547.

It is

indicated, therefore, that the English Usage test part has greater prediction value for English grade than for mathematics. The Algebra test part shows the same magnitude of relation­ ship with mathematics as it does for semester average.

The corre­

lations are substantial, being .4&4 and .485, respectively.

Alge­

bra and grade in chemistry correlate .449, which is a material rela­ tionship.

As might be expected, the Algebra test part yields a low

correlation with English composition marks.

The correlation is .281.

The Algebra test part, therefore, has greater value for the predic­ tion of mathematics grade than for the prediction of English Compo­ sition I grade. It will be remembered that the correlations with English grade have probably'been reduced by the elimination of subjects who were not allowed to schedule English Composition I. By examining Table VIII vertically, the correlations of the prediction item3 with individual criteria may be compared.

For exam­

ple, it can be seen that the correlations with semester average vary from .220 to .510.

High school rank gave the highest correlation and

'Paragraph Reading the lowest.

Correlations with Chemistry I grade

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.

range from .230 to .550, Paragraph Reading again occupying the low­ est position.

Arithmetic Processes offers the highest relationship

in this case.

When mathematics grade is the criterion, the highest

correlation, which is

is found -with Algebra.

is lowest with a .087 correlation.

Paragraph Reading

The relationships shown for Eng­

lish grade, as indicated by the coefficients of correlation, ranged from .161 for Paragraph Reading to .54-7 for English Usage. From the examination of this data, then, it is seen that the Vocabulary, English Usage and Algebra test parts possess differential prognostic value in the prediction of English Composition I and mathe­ matics grades.

Arithmetic Processes demonstrates some value for the

prediction of mathematics and Chemistry I grades. The use of the prediction items in regression equations will be demonstrated and discussed in a later section of this chapter.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

TABLE V I I I

CORRELATIONS BETWEEN PREDICTIVE MEASURES AND INDIVIDUAL COURSE GRADES FOR SCHOOL OF CHEMISTRY AND PHYSICS

Prediction Items

Chemistry I Grade

Mathematics Grade

English Composition I Grade#

Semester Average

H.S.R.

.440

.376

Voc.

.240

.148

.390

.283

P.R.

.230

.087

.161

.220

A.P.

.550

.438

E.U.

.408

.327

.547

.435

.449

.484

.281

.485

Alg.

.

.510

.487

I

* The number of cases used in these correlations was 195. The cases were all members of the original population of 228 used to compute the correlations given in the preceding sections.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

7.

Relation of Semester Average. Mathematics Grade and Chemistry Grade to Moore-Nell Four-Farts and to Moore-Nell Five-Farts

In Table VIII the substantial relations of the Algebra test part to mathematics and chemistry grade and to the first-semester average are shown.

The predictive value of the Algebra section is

further demonstrated in Table IX.

This table presents the correla­

tions of the mathematics and chemistry grades and semester average with the total Moore-Nell score and with the Moore-Nell score when Algebra is not included.

The reliability of these differences is

shown by the standard error ratios in the right-hand column. the differences are shown to be reliable.

Thus,

It is interesting to note

that Borow (2), using a highly generalized population, found that the inclusion of the Algebra test part did not add significantly to the predictive value of the Moore-Nell examination. A comparison of Table VIII with Table IX shows that Arithme­ tic Processes and Algebra correlate with semester average approximate­ ly as high as the total Moore-Nell score, and that Algebra correlates Y/ith Chemistry I grade approximately as high as the total Moore-Nell (five parts).

Arithmetic Processes is shown to have a higher corre­

lation with chemistry than the total Moore-Nell (five parts).

Alge­

bra and Arithmetic Processes show greater relationships to mathematics than does the total Moore-Nell score.

These findings suggest that the

f

less effective parts of the test tend to reduce rather than raise the correlation between the total test score and the several criteria when

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

the test parts are not optimumly weighted.

In the following pages

will be shown the relationships between the total test and the grade criteria when the tests are weighted in terms of their partial re­ gression coefficients.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

46.

TABLE IX

CORRELATIONS AND STANDARD ERROR RATIOS OF MOORE-NELL FOUR PARTS AND MOORE-NELL FIVE PARTS WITH FIRST-SEMESTER AVERAGE AND GRADE IN CHEMISTRY AND MATHEMATICS

Moore-Nell (four-parts)

Moore-Nell (five-parts)

d S D

Semester Average

./+OS

.494-

3*20

Chemistry Grade

.393

*466

3-04

Mathematics Grade

.263

.345

3*28

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

8.

The Prediction of Chemistry I Grade

Table X presents the variables which were used in the mul­ tiple correlations with Chemistry I grade as the criterion.

The pre­

diction items are given on the first line of each equation, and the corresponding partial regression coefficients are indicated on the second line.

The multiple correlation, probable error of estimate,

and percent of forecasting efficiency accompany each prediction team. Inspection of the first row shows that the first battery is composed of the transmuted high school rank and all five parts of the Moore-Nell examination. tion of .680.

This combination yields a multiple correla­

The probable error of estimate is .67 and the percent

of forecasting efficiency is 26.7.

Arithmetic Processes and the

transmuted high school rank are most heavily weighted with partial regression coefficients of .3578 and .3249.

The variables least heav­

ily weighted are Vocabulary and Paragraph Reading with coefficients of -.0117 and .0240, respectively.

Algebra and English Usage show an in­

termediate relationship with partial regression coefficients of .1591 and .1205. Examination of the second battery reveals that the omission of Vocabulary from the team does not result in a reduction of predic­ tive efficiency.

Likewise, the multiple correlation obtained with

the third battery is not decreased by the omission of both Vocabulary and Paragraph Reading.

The multiple correlations for batteries 1, 2

and 3 axe all found to be .680.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

With the elimination of high school rank in battery 4-, the multiple correlation is reduced to .602. of the difference is 1,37.

The standard error ratio

This ratio would be considerably higher

if, in the computation of the standard error of the difference, the fact that the correlations have an array in common was taken into consideration.

The array common to both relationships is Chemistry

I grade. To determine the relation between Chemistry I grade and a predictive battery consisting of a verbal test part and a mathemati­ cal test part, a team composed of English Usage and Arithmetic Pro­ cesses was selected.

The degree of this relationship is indicated

by a multiple correlation of .531. Comparison of the multiple correlations obtained with the fourth and fifth batteries reveals a difference of .021. ference is not significant.

This dif­

Practically, the fifth battery would be

the more efficient since it contains only two variables. Since Arithmetic Processes contributes highly to the predic­ tion, it might be inferred that arithmetic reasoning and computational ability are important for success in Chemistry I.

It can be seen from

Table VIII and X that achievement in verbal matter such as measured by the Vocabulary and Paragraph Reading parts of the Moore-Nell, do not contribute much to the prediction of Chemistry I grade.

If, how­

ever, a test of vocabulary and paragraph reading which was specific to the scientific subject matter dealt with in the School of Chemistry

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

and Physics.were administered, the contribution to the prediction might be higher.

This hypothesis will not be subject to investi­

gation here.

TABLE X PARTIAL REGRESSION COEFFICIENTS, MULTIPLE CORRELATIONS, PROBABLE ERRORS OF ESTIMATE AND PERCENTS OF FORECASTING EFFICIENCI FOR MOORE-NELL PARTS AND TRANSMUTED HIGH SCHOOL RANK USING THE CHEMISTRY I GRADE AS THE CRITERION

Items

R

.67

26.7

H.S.R. .324-9

A.P. .3578

E.U. .1205

Alg. Voc. .1591 -.0117

2

.3238

.3616

.1224-

.1601 -.0022

.680 .67

26.7

3

.3237

.3612

.1217

.1600

.680 .67

26.7

4

.3908

.1539

.1906

.602

.74

20.2

5

.4-595

.2089

.581

.75

18.6

1

P R* .0240 .680

P.E. Est.

Per­ cent Forecasting Eff.

I

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

TABLE X I

STANDARD DEVIATION RATIOS FOR REGRESSION EQUATIONS USED IN PREDICTION OF CHB1ISTRI I GRADE

High School Rank

- .2246

Algebra

t H- o 1

= .0480

English Usage

0**00

- *0554

Arithmetic Processes

= .1058 4*64

Table XI shov/s the standard deviation ratios used in com­ puting the weights for the equations in Table XII.

The use of this

ratio was explained on page 33*

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

s>. Evaluation of Two Prediction Equations for Chemistry I Grade

Two regression equations were developed in order to predict the most probable Chemistry I grade for a first-semester student in Chemistry and Physics.

The first row of Table 211 shows the compo­

nents of the prediction team; the weights by which the raw scores are to be multiplied are found on the second line.

The raw scores to be

inserted for any student are indicated by the symbol "X".

For exam­

ple, a freshman who earned twenty-eight points in Algebra would have this score substituted for Xg in the first equation and multiplied by its corresponding constant, .0450. The first equation of the table is composed of high school rank, Algebra, English Usage and Arithmetic Processes. This team cor­ relates ,680 with Chemistry I grade.

The probable error of estimate

is found to be .67j the percent of forecasting efficiency is 26.7. Although the multiple correlation and percent of forecasting efficiency are somewhat lower in the second battery, this team is serviceable in the prediction of success where the high school rank is not yet available.

Relative to the magnitude of the multiple cor­

relations, the probable errors of estimate of predictions obtained with both equations were high.

This was ascribable to the relatively

large standard deviation of the criterion.

The standard deviation of

Chemistry I grade was found to be I.36. In order to reduce the size of the standard deviation much further, the multiple correlation would have had to be extremely high.

It would probably be difficult

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

to obtain very high correlations with one course as the criterion, as the reliability of course grades are ordinarily lower than that of a semester or yearly average. It would appear that the foregoing probable errors of estimate are too great to warrant the use of these equations for guidance pur­ poses.

TABLE XII

PREDICTION EQUATIONS USING CHEMISTRY I GRADE AS THE CRITERION

Items 1

2

H.S.R. (.224.6X3.

R

Per­ cent ForeP.E. casting Est. Eff.

Alg. . 0/+S0X2

E.U. A.P. .0554X3 .1058X4)

K -5 .0 6 0 8

. 680 . 67

2 6 .7

(.0572X4

.0699X2 .1145X3)

- 5.3977

.602 .7 4

2 0.2

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

10. The Prediction of Grade in Mathematics

The efficiency of several combinations of the variables in predicting success in freshman mathematics was sought.

Table XIII

lists the partial regression coefficients, multiple correlations, probable errors of estimate and percentages of forecasting efficien­ cy, for the various batteries. It is seen that the correlations range from .4.63 to .609, the corresponding probable errors of estimate from .85 to .77, and the percentages of forecasting efficiency from 11.4 to 20.7. Reference to the table will show that the first team is com­ posed of the five test parts and the transmuted high school rank.

Para­

graph Reading was omitted from this combination for the second team. For the third battery both Paragraph Reading and Vocabulary were dropped. It is seen that neither the second nor third teams demonstrates any loss in predictive efficiency by the elimination of the Vocabulary and Para­ graph Reading test parts.

However, when the high school rank was exclud­

ed from the third team, the correlation was reduced from

.601 to .540*

Correspondingly, the percent of forecasting efficiency was lowered from 20.0 to 15.8.

The reliability of the difference between these correla­

tions is indicated by an approximate standard error ratio of .97.

Had

it been feasible to account for the correlation between the two multiple correlations, the resulting standard error ratio would have been larger and the precise reliability of the difference would hence have been shown to be somewhat greater.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

Two variables, Arithmetic Processes and English Usage, mate up the fifth battery.

This combination gave a multiple correlation

of .463> which is .077 lower than the multiple correlation found for the fourth team.

The approximate standard error ratio of the differ­

ence, was found to be 1,12.

Once again the more precise value would

have been higher had it been feasible to use the tail of the standard error of the difference formula. An analysis of the partial regression coefficients shows the net relation of each of the variables to the criterion as a member of a prediction battery.

The highest partial regression coefficients were

obtained for the Algebra test part.

The range was from .3069 to .3326,

depending partly upon the number of variables used in the equation. The next highest was Arithmetic Processes with partial regression co­ efficients between .2200 and .364-9*

In the fifth team only two var­

iables were used and the partial regression coefficient of Arithmetic Processes was found to be .364-9*

Those of Vocabulary and Paragraph

'

Reading were practically negligible in the equations for which they were used.

For English Usage the weights ranged from .04-56 to .1639.

The partial regression coefficients for high school rank were found to be higher than those of the test variables, with the exception of Al­ gebra.

The range for high school rank was from .2690 to .2736. A comparison of Table XIII with Table X reveals the difference

between the multiple correlations which result when the same variables are used to predict mathematics and chemistry grades.

The tables con-

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

tain identical combinations of prediction variables.

The first battery

for chemistry is seen to have a multiple correlation of .680, whereas the first battery for mathematics is .609. error ratio of this difference is 1.31. significance.

The approximate standard

This difference approaches

It is indicated, therefore, that this combination of pre­

diction items is more closely related to success in Chemistry I than to success in mathematics.

Whether the higher correlation with Chemistry

results from an intrinsically closer relationship with the material of the course or from the higher reliability of this course is not clear.

The same interpretation might be drawn from the results obtained with the second, third and fourth batteries. The greatest difference was obtained with the fifth battery which is composed of Arithmetic Processes and English Usage.

The multiple cor­

relation for this combination with chemistry was .581 and with mathema­ tics, .4-63.

The approximate standard error ratio of the difference was

found to be 1.74-

This is a significant difference.

This indicates that

the value of the English Usage and Arithmetic Processes test parts as a battery, is greater in the prediction of Chemistry I grade than of mathe­ matics grade.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

TABLE X I I I

PARTIAL REGRESSION COEFFICIENTS, MULTIPLE CORRELATIONS, PROBABLE ERRORS OF ESTIMATE AND PERCENTAGES OF FORECASTING EFFICIENCY FOR PREDICTION ITEMS USING MATHEMATICS GRADE AS CRITERION

P.E. Items

Ha.

1 2

3

A

5

H.S.R. Voc. P.R. A.P. E.U. .2690 -.024-9 -.0969 .244-2 .074-7

R Alg. .3132

Est.

Per­ cent Forecasting Eff.

.609

.77

20.7

H.S.R. Voc. A.P. E.U. Alg. .2736 -.0631 .2289 . .0668 .3094

.604.

.77

20.3

H.S.R. A.P. E.U. Alg. .2720 .2200 .04-58 .3069

.601 .77

20.1

A.P. .2AA%

E.U. Alg. .0729 .3326

.540

.81

15.8

A.P. •364-9

E.U. .1689

.4-63

.85

11.4-

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

57.

/

.

TABLE X IV

STANDARD DEVIATION RATIOS FOR PREDICTION EQUATIONS USING MATHEMATICS GRADE AS CRITERION

H.S.R.

A.P.

1.46 ^4^-

= .067S

E.U. 2.99

Alg.

hd& 4.53

= .0969

Table XIV contains the standard deviation ratios used in the regression equations shown in Table XV.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

11. Evaluation of Two Regression Equations For Prediction of Grade in Mathematics

Two regression equations for the prediction of the most probable grade in mathematics are given in Table

i XV.

Equation 3 was

.

chosen from Table XIII because it satisfied the criteria of contain­ ing the least number of variables and of having a relatively high per­ centage of forecasting efficiency when compared with the other equa­ tions.

Equation A was used for the other prediction team since it was

desired to determine the predictive value of the college aptitude test alone, that is, with the high school rank omitted.

Table XV presents

the two regression equations and the multiple correlations, probable errors of estimates and percents of forecasting efficiency which de­ rive from the use of these batteries. The probable error of estimate of the first equation is .77 and the percent of forecasting efficiency is 20.1, whereas the probable er­ ror of estimate of the second equation is .81 and the percent of fore­ casting efficiency is 15.8.

It would appear that these prediction equa­

tions are not practical for the counseling of freshmen.

The probable

errors of estimate are too high to permit effective use of these equa­ tions for the prediction of grades in mathematics.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

TABLE XV

PREDICTION EQUATIONS USING GRADE IN MATHEMATICS AS CRITERION

Eg.. 3 4

Items H.S.R. ' ' 1 Alg. E;U. (.19S5X! .0969X 2 .0219X3

R A.P. K .O676X 4 ) -4.2017

Alg. E.U. A.P. K (.1050X]_ .0349X2 .0754X3)-4.4993

P.E. Est.

Per­ cent Forecasting Eff.

.601 .77

20.1

.540

15.8

.81

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

12. Partial Regression Coefficients and Multiple Correlations for Prediction Batteries when English Composition Grade is the Criterion

It has already been seen that the freshman curriculum in %he School’ of Chemistry and Physics emphasizes technical or non-verbal subject matter.

It has been further demonstrated that two of the

three verbal sections, the exception being English Usage, of the MooreNell examination bear low relationships to semester average, Chemistry I and mathematics grades.

In order, then, to determine whether the

Vocabulary and Paragraph Reading test parts have any prognostic value for Chemistry and Physics students, it was decided to calculate the multiple correlation of a team comprising these test parts and English Usage with English Composition I marks.

In addition, the contribution

of a mathematical part to the multiple correlation was sought. It will be remembered that the population was restricted be­ cause of the fact that many students were not qualified to take English Composition I.

This reduced the complete population of 223 which was

used for the other parts of this study of the School of Chemistry and Physics to 195 for this particular group.

Table XVI gives both the

multiple correlations and the partial regression coefficients for the prediction items used in the equations. The battery comprising the three verbal test parts yields a multiple correlation of .563.

It was seen in Table VIII that the cor­

relation between English Usage and English Composition I grade is .547*

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

It is apparent, then, that the addition of the Vocabulary and Para­ graph Reading test parts does not improve the prediction materially. Examination of the second team reveals that the addition of the Algebra test part does not increase the efficiency of the pre­ diction, the multiple correlation being .565. From an examination of the partial regression coefficients in Table XVI, it is seen that the English Usage test part is weighted most, the partial regression coefficients being .4505 and .4964. weight of the Vocabulary test part is next in magnitude.

The

Apparently,

the Paragraph Reading section does not add much to the prediction of success in English composition when the English Usage section is used in the same battery.

This is evidenced by the negligible partial re­

gression coefficients for the Paragraph Reading test part.

It was

i

demonstrated previously that the Paragraph Reading test part does not contribute much to the prediction of grade in mathematics or chemistry.

TABLE XVI

PARTIAL REGRESSION COEFFICIENTS AND MULTIPLE CORRELATIONS USING ENGLISH COMPOSITION I AS CRITERION

Eo. 1

2

Items

Multiple R

Voc. .1798

E.U. .4905

P.R. -.0657

1

Voc. .1769

E.U. .4964

P.R. -.0643

Alg. -.0262

.568

1

.568

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

12,.

The Use of Certain Personality and Interest Measures in Pre­ diction of First-Semester Achievement

It has been proposed by other writers in the field of college prediction (3), (14), (21), that the measurement of non-intellective factors might add appreciably to the prediction of college success. In an attempt to investigate the predictive value of trait measures, it was decided to use the Bernreuter Personality Inventory and the Strong Vocational Interest Blank.

Thus, the relationship was sought

between first-semester average and certain personality traits, as measured by the Bernreuter Personality Inventory, and vocational in­ terests, as indicated by the Vocational Interest Blank.

The results

of the investigation are shown in Table XVII. Negligible results are shown for the correlations with the Bernreuter scales, stability, self-sufficiency, and dominance. run from -.032 to .013.

These

The correlations with the interest scales

were not much higher, these ranging from -.075 to .089.

It is demon­

strated that these measurements would add virtually nothing to the prediction equations for the School of Chemistry and Physics.

As was

disclosed previously, the Ghemist scale for the Vocational Interest Blank, when used in the regression equations shown in Table V, made no contribution to the prediction of first-semester average. It will be noticed that two correlations are listed for the (

Chemist interest scale.

Raw scores were used in the calculation of

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

the correlation which is given first and letter grades in the corre­ lation which appears second.

A comparison of these correlations dis­

closes that there is virtually no difference in the magnitude of the relationship when raw scores are used instead of the letter grades. Inasmuch as the results obtained by the use of these instru­ ments offered little to justify the expectation of high correlations with the other schools, it was decided to utilize another type of nonintellective measurement.

The instrument employed was an adaptation of

the Young-Estabrooks Studiousness Index Scale for the revised Voca­ tional Interest Blank. on pages 10 and 11.

A brief explanation of this scale was given

It was used for the Schools of Mineral Industries,

Lower Division, and Agriculture, and will be reported in later sections of this chapter.

TABLE XVII

CORRELATIONS OF PERSONALITY AND INTEREST MEASURES YflTH FIRST-SEMESTER AVERAGE FOR THE SCHOOL OF CHEMISTRY AND PHYSICS Semester Average Bernreuter Personality Inventory Bl-N, Reversed B2-S B4--D

-.0^1 .013

-.032

Chemist Scale (raw scores)

.085

Chemist Scale (letter grades) Life Insurance. Salesman Scale (raw scores)

.089 -.075

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

64.

C.

1.

THE SCHOOL OF ENGINEERING

Interrelationship of Eight Prediction Variables and Semester Average

Correlations obtained between the prediction variables and first-semester average for the School of Engineering are given in Table XVIII. An inspection of the first horizontal line shows the rela­ tionship of the prognostic items to first-semester average. itive correlations range from .160 to .4^0.

The pos­

The highest correlation

was found for the Algebra test part and the lowest for Paragraph Read­ ing.

Arithmetic Processes is seen to possess a correlation of .350

with semester average.

When this correlation is compared with the

.437 correlation of Arithmetic Processes with semester average for Chemistry and Physics students, it wild, be noted that the Arithmetic Processes test part is a poorer index of success in the first-semester of the Engineering School than in the School of Chemistry and Physics. While high school ranlc shows less prognostic value for the Engineering students than for the Chemistry and Physics students, its correlation of

.406 with the grade-point average is nevertheless substantial.

The

English Usage test part yielded a correlation of .326, a slightly lower relationship.

It is observed that the Vocabulary and Paragraph Reading

test parts show little prognostic value for first-semester average for the School of Engineering. spectively.

The correlations are .217 and .160, re­

Table III demonstrates that similar results were found

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

for the School of Chemistry and Physics. The Engineer and Life Insurance Salesman occupational scales of the Strong Vocational Interest Blank exhibit low correlations with semester average. in order of naming.

These correlations are found to be .191 and -.203 As mentioned previously (p. 24.), it is likely

that the skewness of the distribution of scores for these scales is partly responsible for the low correspondence. Further examination of Table XVIII shows the interrelationship among the prediction indices.

It is seen that high school rank shows

small relationship to the other prediction items.

The correlations

with the test parts of the Moore-Nell examination are as follows: Vocabulary, .143; Paragraph Reading, .061$ Arithmetic Processes, .159; English Usage, .242; and Algebra, .140.

The interest scales of Engi­

neer and Life Insurance Salesman correlate .066 and -.045 with high school rank. It would be supposed that the verbal parts of the Moore-Nell examination show higher relationships with each other than with the mathematical sections.

This expectation is corroborated in part by

inspection of the correlation of the Vocabulary test part with Para­ graph Reading as contrasted to that with Algebra. are .613 and .263, respectively.

These correlations

The correlations of Vocabulary with

English Usage and with Arithmetic Processes, however, does not show this significant difference. spectively.

These correlations are .437 and .379, re­

Paragraph Reading gives a fair correlation with Arithmetic

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

Processes, the magnitude of the correlation being ,4-08.

Algebra and

English Usage have approximately the same correlations with Paragraph Reading.

In order of naming these correlations are .300 and .327.

It is recalled that Arithmetic Processes and English Usage showed sim­ ilar relationships with Paragraph Reading for the Chemistry and Physics population. Since the zero-order correlations of high school rank, the Moore-Well test parts and the interest scales are too low to permit their use singly for effective prognosis, multiple correlations were computed and prediction equations were constructed for various combina­ tions of the variables.

*

The results will be presented in the following

pages.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

TABLE X V I I I

INTERRELATIONSHIP BETWEEN PREDICTIVE INDICES AND FIRSTSEMESTER AVERAGE FOR THE SCHOOL OF ENGINEERING

N = 333

Sem. Av. Sem. Av,

H.S.R,

.4-06

H.S.R. Voc.

P.R. A.P. 1 E.U. Alg.

1

Voc.

P.R.

A.P.

E.U.

Alg.

Eng .S. L.I.S,

.217

.160

.350

.326

.480

.191

-.203

•143

.061

.159

.242

.140

•066

-•045

.613

•379

•437

.268

.183

-.135

.40S

.327

.300

.085

-.085

.388

.496

.099

-.098

.408

.123

-.154

.093

-.153

Eng. S. L.I.S.S.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

2.

Partial Regression Coefficients of Prediction Batteries with Semester Average as Criterion

Table XIX presents the relations of the predictive indices to the criterion when the overlapping elements of the items have been controlled by the use of partial regression coefficients.

The con­

struction of this table is similar to that of Table IV. Mien high school rank, the five parts of the Moore-Nell and the Engineer occupational interest scale are combined as a team, the partial regression coefficients are highest for the Algebra test part and high school rank, and are lowest for Vocabulary, Paragraph Reading and Eng­ lish Usage.

In the sequence given, the values are .3586, .3170, .0188,

-.0507 and ,0619*

The magnitude of the partial regression coefficients

of the Arithmetic Processes test part and Engineer occupational inter­ est scale are similar, these being .1024- and .1198, respectively. This pattern of ■relationship remains practically constant for the second row from which the Engineer scale was omitted.

However,

with the exclusion of high school rank from the third and fourth teams, greater changes are effected.

In the third row, the partial regression

coefficient of the English Usage test part is increased from .0592 to .1175, whereas only slight increases are effected in the remaining items.

In the fourth row, when both high school rank and the Engineer

scale are omitted, the English Usage partial regression coefficient is increased to .1225.

The remaining variables show slight increases.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

It is of interest to note here that the relationships of the Paragraph Reading and Vocabulary test parts with the criterion are negligible when the influence of the other variables is held constant. This was suggested previously by the low zero-order correlations of these items.

Since the relationships shown for these two variables

are approximately equal to zero, they were omitted in row five and Life Insurance Salesman vocational scale and high school rank were add­ ed.

The items used, then, are high school rank, Arithmetic Processes,

English Usage, Algebra and Life Insurance Salesman scale.

In order of

naming, the partial regression coefficients are .324-6, .094-0# .0502, .34-93 and -.1179.

In view of the relatively low partial regression coefficients shorn for Life Insurance Salesman scale in Table XIX, it is apparent that the Life Insurance Salesman scale does not add materially to this multiple correlation.

Therefore, it is omitted in the sixth row.

The

items which remain show essentially the same pattern and values as in row five. The partial regression coefficients of a team composed of Arith­ metic Processes, English Usage and Algebra are shown in row seven.

These

are the items for which the highest zero-order correlations with the cri­ terion were obtained.

The values shown in Table XIX are .1164-, .1302 and

.3690 for the respective parts. In order to determine the net relationship of the mathematical sections of the Moore-Nell examination plus the high school rank to se-

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

mester average, partial regression coefficients were obtained.

They

are high school rank, .3357, Arithmetic Processes, .1085, and Algebra, .3792. It will be remembered that the zero-order correlations of the Algebra and Arithmetic Processes test parts with semester average were found to be

.480 and .350. It is shown in row nine that the partial

regression coefficients of the Algebra and Arithmetic Processes sub­ tests are respectively, .4-064 and .1484. Thus in a two-variable team, the Algebra test part appears to take a great deal of the force away from the Arithmetic Processes test part. In addition to demonstrating the relationships between the pre­ diction items and the criterion when the effect of the overlapping of the variables has been eliminated, these values are used in the computa­ tion of the regression equations shown in Table XXII.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

71

TABLE XIX

PARTIAL REGRESSION COEFFICIENTS OF PREDICTION VARIABLES FOR THE SCHOOL OF ENGINEERING

Eq.

H.S.R.

Voc.

A.P.

E.U.

Alg.

1

.3170

.0188 -.0507

.1024

.0619

.3586 .1198

2

.3218

.0435

-.0566

.1009

.0592

.3658

3

.0436

-.0774

.1231

.1175

.3705

4

.0675

-.0852

.1258

.1225

.3750

P.R.

5

.32^6

.0940

.0502

.3493

6

.3250

.0943

.0630

.3620

.1164

.1302

.3690

7

8 9

.3357

.1085

.3792

.1484

.4064

Eng.S

L.I.S.

.1286

-.1179

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

2..

Means and Standard Deviations of First-Semester Average and the Prediction Measures

The means and standard deviations of first-semester average and of the prediction items for the Engineering population are shown in Table XX.

This table will be compared with the tables of means and

standard deviations for the other schools in the summary section of the study. The mean first-semester average for the School of Engineering is 1.30 and the standard deviation is .78.

This grade point average

is somewhat higher than the first-semester average for a typical entire freshman class; furthermore, it is

.30 higher than the minimum standard

for satisfactory college work. For the transmuted high school rank the mean is placed at 3*20. Eeference to Table II shows that this figure is located between the first and second fifths. high school rank, is

The standard deviation, in terms of transmuted

2.19.

The mean of the Vocabulary test part is 58.24, the standard de­ viation 15.80.

For the Paragraph Reading test part the mean and stan­

dard deviation are 32.30 and 5.17, respectively.

Arithmetic Processes

and EngLish Usage have mean scores of 26.61 and 28.59, in order of naming.

The standard deviations, in the same order, are 4.39 and 3.09.

The Algebra test part possesses a mean score of 29*20 and a standard deviation of

3 *47.

The fact that the means of the Moore-Nell test parts are high

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.

and the variabilities are low is possibly attributable to the selec­ tiveness of the population. For the interest scales the following means and standard de­ viations were obtained: the mean of Engineer scale, .379.90 and the standard deviation, 4-7.71, the mean of the Life Insurance Salesman scale, 275.73 and the standard deviation,

4-5.00.

TABLE XX

MEANS AND STANDARD DEVIATIONS FOR FIRST-SMESTER AV­ ERAGE AND PREDICTION VARIABLES FOR THE SCHOOL OF ENGINEERING

_Sem. Av.

H.S.R. Voc.

P.R.

Mean

1.30

3.20

58.24 32.30

S.D.

.78

2.19

15.80

5.17

A.P.

E.U.

Alg.

Eng.S. L.I.S.

26.61

28.59

29.20

379.90 257.73

4-39

3.09

3.47

47.71

45.00

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

TABLE XXI

STANDARD DEVIATION RATIOS FOR REGRESSION EQUATIONS FOR PREDICTION OF FIRST-SEMESTER AVERAGE

H.S.R. Voc.

= .3562 .73 15.30

P.R.

= .0-494

r .1059

5*17

A.P.

.m i m

E.U.

■£&

= .2524

Alg.

-i?i 3.47

= .2243

Eng. S* *

I.i .s .

47.71

45.00

*

s .0164

= .0173

The standard deviation ratios used in developing the scoreform regression equations for the prediction of first semester aver­ age are listed in Table XXI.

The explanation of the use of these

ratios is given on Page 35.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.

Evaluation of the Regression Equations Used for the Prediction, of First-Semester Average

The relationships of the prediction indices to the criterion were shown in the first part

of this section.

A comparison was made

of the partial regression coefficients for the items when they were combined into various teams.

The means and standard deviations of the

prediction variables and the criterion were given in Table XX.

Fin­

ally, the standard deviation ratios which were used in the regression equations were listed.

The prediction batteries are not presented,

with their multiple correlations, probable errors of estimate and per­ cents of forecasting efficiency. An examination of the first column at the right of Table XXII shows the multiple correlations to range from .4-96 to .612. responding probable errors of estimate vary from

.46 to *42.

range of percents of forecasting efficiency is from

The cor­ The

13.2 to 21.0.

The score-form regression equation shown in row one consists of high school rank, the five parts of the Moore-Nell and the Engineer occupational interest scale.

This combination yields a multiple cor­

relation of .612 with first-semester average. estimate for this equation is .42.

The probable error of

The predictive effectiveness of

this equation is indicated by a percent of forecasting efficiency of

21.0. It will be observed from the second equation that the omission

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

of the Engineer occupational interest scale does not reduce the mul­ tiple correlation significantly.

The multiple correlation is .600.

With the elimination of high school rank from Equation 1, however, the multiple correlation is reduced from .612 to .530. is shown in Equation 3»

This

The probable error of estimate is .4-5 for

the third equation as compared with .4-2 for Equation 1. of forecasting efficiency is reduced to

The percent

15.2.

In the fourth equation, the five parts of the Moore-Hell are used as the prediction team.

The multiple correlation, probable

error of estimate and percent of forecasting efficiency for this com­ bination are shown to be .515, .4-5, and 14.3, respectively.

It will

be noticed that these values are not substantially different from those shown in Equation 3-

Hence, it is seen that the contribution of the

Engineer vocational scale to the multiple correlation is slight. As was previously stated on page 69, the Paragraph Reading and Vocabulary test parts of the Moore-Nell appear to contribute negli­ gibly to the multiple correlations.

This was,observed by an inspec­

tion of the beta weights shown in Table XEX. test parts are eliminated.

In Equation 5 these

The battery consisted of high school rank,

the Arithmetic Processes, English Usage and Algebra test parts and the Life Insurance Salesman scale.

The magnitude of the multiple corre­

lation is .611, the probable error of estimate is .42, and the percent of forecasting efficiency is

20.9»

A suggestion was offered on page 69 concerning the negligible

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

value of the Life Insurance Salesman scale as a member of a pre­ diction battery.

This suggestion is substantiated by the results

shown in Equation

6. Inspection of this equation reveals that the

omission of the scale did not result in an appreciable reduction in the strength of the relationship.

The multiple correlation is .599)

the probable error of estimate, .4-2, and the percent of forecasting efficiency,

20.00.

In Equation 7 the three test parts of the Moore-Nell which possessed the highest zero-order correlations with the criterion were combined in a team.

The multiple correlation was .510.

A comparison

of this team with the fourth battery, which contains all the test parts of the Moore-Nell, reveals no difference in the size of the multiple correlation.

This further demonstrates the ineffectiveness of the Vo­

cabulary and Paragraph Reading test parts as instruments for the pre­ diction of academic success in the School of Engineering.

When the Arithmetic Processes and Algebra test parts and high school rank are. combined, the multiple correlation is .596.

This com­

bination shows a probable error of estimate of .-42 and a percent of forecasting efficiency of 19.7.

Thus, the English Usage test part can

be omitted from Equation 6 with little loss in prognostic efficiency. With the elimination of high school rank from Equation correlation drops from .596 to .496, a substantial loss.

8, the

This is seen

by reference to Equation 9, which is composed simply of the Arithmetic and Algebra test partsj this team possesses a probable error of estimate

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

of .4-6, and a percent of forecasting efficiency of

13.2.

From the score-form regression equations which are listed for each of the combinations of prediction indices, it appears that the eighth battery is the most efficient.

Since it is composed of only

three variables and shows a substantial correlation with the criter­ ion, it would seem to be the most practical of the equations pre­ sented.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

SCHOOL OF ENGINEERING SCORE—FORM REGRESSION EQUATIONS, MULTIPLE CORRELATIONS, PROBABLE ERROR OF ESTIMATE AND PERCENTS OF FORECASTING EFFICIENCY FOR PREDICTION OF FIRST-SEMESTER AVERAGE FOR ENGINEERING STUDENTS

Eg..

Items

H.S.R. A.P. Alg. Eng.S. K Voc. P.R. E.U. (.1129X1 .0009X2 -.0077X3 .OI82 X4 .OI56X5 .0806X6 .OO2CEX7 ) -2.5722 H.S.R. Voc. 2. P.R. A.P. E.U. Alg. K .0179X4 .OI49X 5 .0822X6) -2.2212 (.1146X1. .0021X2 -.OO85X3 Voc. A.P. E.U. Eng.S. K P.R. Alg. 3 (.0022X! -.0117X2 .0297X4 .0219X3 .0021X6) -3.0088 .O833X 5 Voc. E.U. P.R. A.P. Alg. K k (.0033X! -.0129X2 .0309X4 .0224 X3 .0843X5) -2.4190 H.S.R. A.P. E.U. Alg. L.I.S. K 5 (.1156X-L .OI67X 2 . 0127X2 .0785X4 -.OO2QX5) -1.6428 H.S.R. 6 A.P. E.U. Alg. K .O8I4 X4 ) -2.3470 .OI59X3 (.1158X1. .Ol68X 2 A.P. E.U. Alg. K 7 (.0207X! .0329X2 .O83 CK3 ) -2.6120 8 H.S.R. A.P. Alg. K ( .1196X! .0193X2 .O852X3) -2.0846 A.P. Alg. K 9 ( .0264X! •0914X2) -2.0691

P.E.

Per­ cent Forecasting

Est.

Eff.

.612

.42

21.0

.600

.42

20.0

.530

.4-5

15.2

.515

.45

14.3

.611

.42

20.9

.599

.42

20.0

.510

•A5

14.0

.596

CM >*.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

TABLE XXII

19.7

•496

.46

13.2

R

1

!•

Relationships between Predictive Items and Grade in Mathematics

In the preceding parts of this section, relationships between the predictive measures and the first-semester average were presented. This part will present the relationship of the variables to grade in mathematics. Table XXIII lists the coefficients of correlation of the pre­ dictive indices with first-semester average and mathematics grade. The correlations with semester average are repeated to facilitate com­ parison. Examination of the first column reveals that the Algebra test part shows the highest relationship with mathematics grade. efficient of correlation is .4.60.

The co­

This is in accordance with the ex­

pectation that a ma.thematical test part would correlate highest with mathematics grade.

The next highest relation in shown with another

mathematical test part, Arithmetic Processes.

The correlation is .341*

Success on the verbal test parts shows slight correspondence to success in mathematics.

This is indicated by the coefficients of

correlation of .096, .117 and .230 for Vocabulary, Paragraph Reading and English Usage, respectively. High school rank correlates moderately low with mathematics, the correlation being .316. Scores on the Engineer occupational scale show little relation to mathematics grade. is .162.

The coefficient of correlation with this cale

Life Insurance Salesman scale gives a correlation of -.1SS.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

This negative relationship is not a significant one.

Again, the

skevmess of these scales may he offered as a partial explanation of the low degrees of correspondence. A- comparison of the two columns reveals that the correlations of the forecasting variables are somewhat higher with semester aver­ age.

Since the semester average is a grade point average for a number

of courses, it may justifiably be considered to be more reliable than the grade in a single course.

TABLE XXIII

CORRELATIONS BETWEEN PREDICTIVE MEASURES, GRADE IN MATH­ EMATICS AND FIRST-SEMESTER AVERAGE

Mathematics Grade

Semester Average

H.S.R.

.316

.4-06

Voc.

.096

.217

P.R.

.117

.160

A.P.

.341

.350

E.U.

.230

.326

Alg.

.4.60

.7,30

Eng. S.

.162

.191

-.183

-.203

L.I.S.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

6. Effect of the Algebra Test Part on Correlations with First-Semester Average and Grade in Mathematics

Table XXIII shows the marked relation of the Algebra test part to semester average and mathematics grade.

Table XXIV presents the

correlations of semester average and mathematics gra.de with the total Moore-Nell score and with the score when Algebra test part is omitted. The reliability of the differences is shown by the standard error ra­ tios.

It is seen that these differences are significant.

Thus, for

the School of Engineering as well as for the School of Chemistry and Physics, the importance of the Algebra section of the Moore-Nell ex­ amination is demonstrated.

TABLE XXIV

CORRELATIONS OF MOORE-NELL FOUR PARTS AND MOORE-NELL FIVE PARTS WITH SEMESTER AVERAGE AND MATHEMATICS GRADE

N = 338

Moore-Nell Four

Moore-Nell Five

Semester Average

*324

.388

6.4.

Mathematics Grade

.220

.292

7.2

1

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.

7.

Evaluation of Different Combinationa of Predictive Items and the Partial Regression Coefficients for Each When Mathematics Grade is the Criterion

The predictive value of several combinations of the test parts and high school rank in forecasting freshman mathematics grade was sought for the School of Engineering.

Table XXV presents the partial

regression coefficients and the multiple correlations. The right column of the table shows a range of .4-7& to .550 for the multiple correlations.

Horizontal examination of the table

shows the prediction variables and the partial regression cqeffipients of each team.

Inspection of the third row -reveals that the team which

gives the highest multiple correlation is composed, of high school rank, all the test parts of the Moore-Nell except Vocabulary and Paragraph Reading, and the Engineer vocational interest scale.

The second row

demonstrates that the multiple correlation is not reduced significantly when the Engineer scale is omitted. The sixth team, which yields the lowest multiple correlation, consists of the Arithmetic Processes, English Usage and Algebra test parts.

A comparison of the sixth battery with the seventh battery in­

dicated that the presence of the English Usage test part in the battery failed to increase the accuracy of the prediction. High school rank and the five test parts of the Moore-Nell correlate .54-3 with mathematics grade.

This is shovm in the first row.

When high school rank, Arithmetic Processes and Algebra are combined

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

in a team the resulting multiple correlation is .536.

Thus, the cor­

relation of the three variable battery is not significantly lower than the correlation obtained with the six variable team shown in the first row.

This indicates that the Vocabulary, Paragraph Reading and Eng­

lish Usage test parts contribute little to prediction of mathematics grade. By a comparison of the correlations of the prediction batteries listed in Table XIII with those listed in Table XXV, it is seen that the multiple correlations with mathematics grade for the School of Chemistry and Physics are somewhat higher than those for the School of Engineering. An analysis of the partial regression coefficients in Table XXV demonstrates that Algebra and Arithmetic Processes contribute signi­ ficantly to the multiple correlations.

The first column discloses the

importance of high school rank in the prediction teams. Thus, it is seen once more that, of the prediction indices used, high school rank, Arithmetic Processes and Algebra are the most impor­ tant for the forecasting of freshman mathematics grade.

It will be

remembered that the same results were found for the School of Chemistry and Physics.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

85.

TABLE XXV

PARTIAL REGRESSION COEFFICIENTS AND MULTIPLE CORRELATIONS FOR THE PREDICTIVE ITEMS USING MATHEMATICS GRADE AS CEETERION N s 338

Eg.

Items H.S.R.

Voc.

P.R.

A.P.

R E.U.

Alg.

Eng.S.

1

.2518 -.0861 -.0219

.1558

-.0020

.3779

.543

2

.2486

.1432

-.0227

.3806

.540

3

.2447

.1442

-.0295

.3771

4

.2515

.1283

-.0349

.3754

.537

5

.2456

.1204

.3659

.536

.3805

.478

.3858

.478

-.0654

6

.1451

7

.1496

.0184

.1060

.550

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

TABLE XXVI

MEANS AND STANDARD DEVIATIONS FOR PREDICTIVE ITEMS AND GRADE IN MATHEMATICS

N = 333

Mathematics Grade

H.S.R. _____

A.P. ____

Alg. ____

Mean

1.08

3.20

26.61

29.20

S.D.

1.31

2.19

-4.39

3.47

The means and standard deviations of mathematics grade and the prediction variables used in forecasting grade in mathematics are shown in Table XXVI.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

TABLE XXVII

STANDARD DEVIATION RATIOS FOR REGRESSION EQUATIONS FOR PREDICTION OF MATHEMATICS GRADE

H.S.R.

= .5982

A.P.

^

= .2984

Alg.

i*|i

= .3775

Table XXVII presents the standard deviation ratios used in the prediction equation shown in Table XXVIII.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

8 . Examination of Score-Form Regression Equation Constructed for the Prediction of Mathematics Grade

A score-form regression equation for the prediction of fresh­ man mathematics grade was constructed with the three variables shown to be most effective in the foregoing discussion.

These items were

high school rank, Arithmetic Processes and Algebra.

This equation,

the multiple correlation, probable error of estimate and percent of forecasting efficiency are presented in Table XXVIII. The probable error of estimate of a mathematics grade pre­ dicted by this equation is .75* is 15.6.

The percent of forecasting efficiency

The probable error of estimate is too high to permit effec­

tive use of the equation in the prediction of mathematics grade for Engineering students.

The same conclusion, it is recalled, was drawn

for the School of Chemistry and Physics.

TABLE XXVIII

SCORE-FORM REGRESSION EQUATION FOR THE PREDICTION OF GRADE IN MATHEMATICS N « 338

H.S.R. (.H69X;l

A.P. .0359X 2

Alg. .I38IX3)

K -4.3796

R .536

P.E. Eff.

Per­ cent Forecasting Eff.

.75

15.6

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

9.

Comparison of Personality and Interest Measures with Semester Average

The data in Table XXIX are similar to those presented in Table XVII for the School of Chemistry and Physics.

The Engineer

scale of the Vocational Interest Blank was substituted for the Che­ mist scale.

It should be recalled that these measures of non-in­

tellective factors were investigated in order to determine whether such indices would increase the effectiveness of the prediction bat­ teries. The results show that the personality traits measured by the Bernreuter Personality Inventory correlate negligibly with semester average. The Engineer occupational interest scale has little relation to success in the first semester in the School of Engineering.

Simi­

larly, the Life Insurance Salesman scale demonstrates a lack of signi­ ficant relationship. On the whole, these results are in agreement with those found for the School of Chemistry and Physics.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

TABLE XXIX

CORRELATIONS BETWEEN PERSONALITY AND INTEREST MEASURES AND SEMESTER AVERAGE

Semester Average Bernreuter Personality Inventory Bl-H

.099

B2-S

-.010

B4-D

-.070

Engineer

Scale

Life Insurance Salesman Scale

.191 -.203

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

D.

1.

THE SCHOOL OF MINERAL INDUSTRIES

Interrelationship between Eight Predictive Measures and FirstSemester Average for the School of Mineral Industries

The correlations of the predictive items with first semester average for the School of Mineral Industries are given in the first row of Table XXX.

In the remaining rows of this table are listed the

inter-correlations of the predictive variables. An inspection of the first row reveals that the best correla­ tion with grades is secured with the Algebra test part, and the poor­ est with the Vocabulary test part.

These correlations are .567 and

.287, respectively. Following the pattern of results obtained for the School of Chemistry and Physics and the School of Engineering, the English Us­ age and Arithmetic Processes test parts are related to success in the first semester of the Mineral Industries School to about the same de­ gree.

In the order given, the correlations are .5-44- and .513 • For

the Vocabulary and Paragraph Reading test parts relatively low corre­ lations with the criterion are shown.

High School rank, with a corre­

lation of .529, is closely related to achievement in the first semester of the School of Mineral Industries.

This was likewise the case for

the Schools of Engineering and Chemistry and Physics. Significant zero-order correlations with the criterion are shown for the Chemist vocational interest scale and the Studiousness

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

92. I

Index.

These correlations are .354 and .336, respectively.

These

relationships are impressive when they are compared with t he low pre­ dictive values frequently reported in the literature for similar trait measures (7).

It is recalled that personality and interest scores

showed negligible correlations with academic success for students in both tiie School of Chemistry and Physics and the School of Engineering. Investigation of the second row reveals that high school rank is not markedly related to scores on the Paragraph Reading and Vocabu­ lary test parts.

The degree of correspondence with achievement on the

Arithmetic Processes, English Usage and Algebra test parts is appreci­ ably higher. Close relationship is shown between the Vocabulary and Para­ graph Reading test parts in the third row.

The correlation of .637 be­

tween these test parts is higher than was found between the same test parts for the Schools of Engineering and Chemistry and Physics.

The

low relationship between the Vocabulary and Algebra test parts is ex­ hibited again by a correlation of .221 for this population.

From an

examination of the fourth row it is seen that the Paragraph Reading test part shows a reliably higher relationship to Arithmetic Processes test part than with English Usage.

In order of sequence these correlations

are .519 and .373. It is apparent from the correlations in the fifth row that Arithmetic Processes shows a stronger tendency to vary concomitantly with the Algebra section than with the English Usage section.

These

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

correlations are .495 and .303, respectively. the same for the School of Engineering.

This relationship is

It was pointed out previous­

ly, however, that for the School of Chemistry and Physics, the differ­ ence between these two correlations is not so clearly marked.

English

Usage test part shows a lower correlation with the Algebra test part for this population than it does for the Schools of Engineering and Chemistry and Physics. From the results given in the seventh column, it is seen that scores on the Chemist occupational interest scale Show little rela­ tionship to the five parts of the Moore-Nell examination.

It is noted

that the highest correlation of the Chemist scale for the Mineral In­ dustries School is with the Vocabulary test part, whereas the highest correlation fpr this scale with the School of Chemistry and Physics is with the Algebra test part.

The explanation of this difference is

not clear. Examination of the findings in the last column reveals the lack of relationship between the Studiousness Index and the other pre­ diction items with the exception of the English Usage test part.

The

correlation with the English Usage section is .277. These predictive indices were combined into various forecast­ ing teams, and regression equations were constructed for each combina­ tion.

The data necessary for these computations and the resulting re­

gression equations are presented on the following pages.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

TABLE XXX

INTERRELATIONSHIP BETWEEN EIGHT PREDICTIVE ITEMS AND FIRST-SEMESTER AVERAGE FOR THE SCHOOL OF MINERAL INDUSTRIES N - 78

Sem.Av. H.S.R.

Sem.Av. H.S.R. Voc. P.R. A.P. E.U. Alg.

'

.529

Voc.

P.R.

A.P.

E.U.

Alg.

V.I.B. V.I.I Chem. S.I.

.237

.334

.513

.544

.567

.354

.336

.107

.107

.310

.306

.279

.215

.223

.637

.353

.370

.221

.290

.165

.519

.373

.324

.114

.097

.303

.495

.130

.096

.319

.209

.277

.225

.053

V.I.B. Chem.

.002

V.I.B. S.I.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

2.

The Partial Regression Coefficients of the Predictive Teams

The partial regression coefficients necessary for the de­ velopment of the regression equations and for the computation of the multiple correlations are listed in Table XXXI. The relative magnitude of the partial regression coefficients for the same variable, when it is used in a number of different teams, is disclosed by an examination of the columns.

Thus, it is seen that

high school rank and the Algebra and English Usage test parts have re­ latively high partial regression coefficients.

The Arithmetic Pro­

cesses test part, the Chemist interest scale and the Studiousness In­ dex have somewhat lower weights. The partial regression coefficients of the Vocabulary and Para­ graph Reading test parts are negligible.

Similar results were found

for the School of Chemistry and Physics.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

96.

TABLE XXXI

PARTIAL REGRESSION COEFFICIENTS FOR PREDICTIVE ITEMS USING FIRST-SEMESTER AVERAGE AS CRITERION N - 78

Eg.

Factors H.S.R.

Voc.

P.R.

A.P.

E.U.

Alg.

V.I.B. Chem.

V.I.B, S.I.

.1763

.1863

1

.2394

-.0570

-.0220

.1932

.2468

.2807

2

.2697

.0048

-.0084

.1884

.2643

.2981

3

.2439

.1862

.2382

.2836

4

.2692

.1811

.2616

.3091

5

.2970

.1817

.3032

.2975

.2374

.3660

.3328

6

i

.1673 .1634

.1810 .1682

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

2»

Means and Standard Deviations of Predictive Items and Semester Average

The data contained in Table XXXII are the means and standard deviations of the first-semester average and of the forecasting var­ iables for the School of Mineral Industries.

This table will be com­

pared with similar tables of the other schools in the summary section of this chapter.

TABLE XXXII

MEANS AND STANDARD DEVIATIONS FOR PREDICTIVE ITEMS AND SEMESTER AVERAGE N = 78

Sem.Av. H.S.R. Voc. ____________ ______ Mean S.D.

1.33

2.46

.943 2.04

P.R. ____

A.P. ____

E.U. ____

64.23 33-53

27.22

29.51

17.62

5.09

3-95

Alg. ____

V.I.B. V.I.B. Chem. S.I.

29.38 368.65 258.73

2.78 . 3.13

46.22

52.81

In Table XXXIII are shown the same data obtained from a popu­ lation of one hundred cases.

It will be observed that the means and

standard deviations are similar to those shown in Table XXXII.

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

TABLE XXXIII

MEANS AND STANDARD DEVIATIONS FOR PREDICTIVE ITEMS AND FIRST-SEMESTER AVERAGE N = 100

Sem. At .

H.S.R. Voc. _____

P.R.

A.P.

E.U.

Alg. V.I.B. Math. Chem. Chem.________ _____

Mean

1.28 2.59

63.4-7 33.34 26.92 29.44 29.19 365.17'

S.D.

.901 2.10

IS.52 4.93

3.96

2.75

3-25

48.46

.90

.75

1.53 1.44

In Table XXXIV are presented the standard deviation ratios used in converting the partial regression coefficients to the form necessary for developing score-form regression equations.

TABLE XXXIV

STANDARD DEVIATION RATIOS FOR REGRESSION EQUATIONS SHOWN IN TABLE XXXV N = 78

H.S.R. Voc. P.R. A.P.

.4-623

E.U.

.942. 2.78 -

.3392

•0535

Alg.

•942^ 3.13

.3013

5.09 =

.1853

•942 V.I.B. 52.31 = Chem.

.0179

-*242 . 3.95

.2387

V.I.B. S.I.

•942 _

2.04 •943 _ 17.62 " •943

•942

46.22 “

.0204

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

4*

Prediction of First-Semester Average from Six Score-Form Regression Equations

In Table XXXV are presented the score-form regression equations for the prediction of first-semester average for the School of Mineral Industries.

The multiple correlations, probable errors of estimate

and percent of forecasting efficiency for each team are also listed. Each of the prediction batteries shows a high relationship to the criterion.

The multiple correlations range from .714 to .797.

These correlations approach in magnitude the highest reported in the literature (7), (14).

The probable errors of predictions developed

from the regression equations vary from .33 to .45; the percents of forecasting efficiency vary from 39.6 to 30.0. It will be observed that despite the high correlations obtained, the probable errors of estimate are relatively high. partly

This is at least

ascribable to the large standard deviation of the semester

average for this school.

Comparison of Table XXXV with:Tables XXXII

and XXX will malce this clear. Analysis of the rows in Table XXXV discloses the indices that were combined into the various teams.

Thus, it is seen that the first

battery comprises the high school rank, the five parts of the Moore-Nell examination, the Chemist interest scale and the Studiousness Index.

The

multiple correlation obtained with this team is .797; the probable error of estimate and percent of forecasting efficiency are .3^ and

39*6, re­

spectively .

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

In the second team the Chemist interest scale was omitted. The predictive effectiveness for this battery is somewhat lower, the multiple correlation being .779, and the probable error of estimate .4.0. i t is apparent that the use of the interest scale is of some importance in the prognosis of grades, although its contribution to the battery is not a substantial one.

Practically no loss in predic­

tive value is found when the Vocabulary and Paragraph Reading test parts are omitted from the team. row three.

This is shown by an inspection of

Row four reveals that when the Vocabulary and Paragraph

Reading test parts and the Chemist interest scale are eliminated from the team, the multiple correlation is reduced to .781. In the fifth battery, high school rank, the Arithmetic Pro­ cesses, English Usage and Algebra test parts and the Studiousness In­ dex are retained.

This battery gives a multiple correlation of .764.

By a comparison of the fourth and fifth batteries, it is seen that the multiple correlation is reduced by .017 and the probable er­ ror of estimate by .01 when the Studiousness Index is omitted. loss is not large.

This

With the omission of high school rank from the

fifth battery, an appreciable loss in the multiple correlation is ef­ fected.

This battery, consisting of Arithmetic Processes, English Us­

age and Algebra is shown in row six.

The multiple correlation is seen

to be ,714» In order that the difference in prognostic efficiency of the team composed of high school rank, and the Arithmetic Processes,

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

English Usage, and Algebra test parts may be seen for the various technical schools, the following multiple correlations and probable errors of the predictions are listed below: School

R

P.E. Est.

Chemistry and Physics

.704

.44

Engineering

.599

.42

Mineral Industries

.764

.41

It is seen that the prediction is slightly more accurate for the School of Mineral Industries.

It is interesting to note that

on the basis of the probable errors of estimate the battery is a more efficient forecaster for the Engineering students than for the Chemistry and Physics students.

However, when comparison is made on the

basis of the multiple correlations, the order of the schools is re­ versed.

The probable error of estimate may be a better standard than

the multiple correlation to evaluate the precision of the forecasting teams.

The reason for this lies in the fact that the multiple corre­

lation is directly affected by the magnitude of the standard deviations, whereas the probable error of estimate is not.

Hence the latter is a

more uniform measure of the effectiveness of the prediction batteries.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

REGRESSION EQUATIONS, MULTIPLE CORRELATIONS, PROBABLE ERRORS OF ESTIMATE AND PERCENTS OF FORECASTING EFFICIENCY FOR MINERAL INDUSTRIES STUDENTS N = 73

Eg. 1

Items H.S.R.

(.UOTXi H.S.R ( .12A7X1 H.S.R.

(.1128X1 H.S.R.

(.1245XX H.S.R.

Voc.

P.R.

.0030X 2 -.OO4IX3 Voc.

P.R.

.OOO3X 2 -.OOI6X3 A.P.

E.U.

.0444X 2 A.P.

.O808X3 E.U.

.0432X 2 A.P.

.O887X3 E.U.

A.P.

E.U.

.O46IX4

.0837X5

.0846X 5

E.U.

Alg.

A.P.

Alg.

-°4-50X4 .0897X5 ■.0898X 5 Alg.

.0854X4 Alg.

.O93IX4 Alg.

(.1373Xx

.0434X2

•1028X 3

(.056^!

E.U. .1241X

Alg. K .1003X 3)-6.8221

2

R

VIB-Chem. VIB-SI

.0029X 5 VIB-SI

VIB-Chem. VIB-SI

Eff.

K

.OO32X7.OO38X3)-6.9957 VIB-SI

P.E. Est.

Per­ cent Fore­ casting

.797

.38

39.6

.779

.40

37.3

.796

.38

39.5

.781

.40

37.5

.764. .4X

35.5

.714

30.0

K

.0034X7)-6.2226 K

.0037X6)-7.1174 K

.OO34X5)-6.2847 K

.O896X4)-5.8569

.45

102

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

TABLE XXXV

£•

Relationship Between Predictive Indices and Specific Course Grades

In Table XXXVI are listed the correlations between the predic­ tive indices and chemistry, mathematics and English composition grades. In the right .harid column the zero-order correlations with semester av­ erage are repeated. A horizontal examination of the table reveals the relationship of the forecasting items with the criteria.

It is seen that high school

rank shows about the same degree of correspondence to Chemistry I grades and semester average, and shows a somewhat lower correspondence with grades in mathematics. spectively.

The correlations are .4-94-, .500 and .4-30, re­

The correlation with English Composition I grade was not

computed. The correlations of the Vocabulary test part with chemistry and English composition grades and semester average are approximately the same, being .367,

.385 and .34-3, respectively.

As was found for the

School of Chemistry and Physics and the School of Engineering, the Vocabulaiy test part is not related significantly to mathematics grade, the correlation being .178.

Low relationship with the criteria is

found with the Paragraph Reading test part also.

The Arithmetic Pro­

cesses test shows an appreciable relationship to all the criteria.

The

correlations vary from .4-55 to .508, the highest being with semester average and the lowest with English composition. i

It will be observed that the correlations of the English Usage test part with Chemistry I grades and with mathematics grades are prac­ tically the same.

The correlations are .4-85 and .483.

Higher rela­

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

I

104.

tionships axe shown for this test part with English composition grade and semester average, the correlations being .522 and .556, respective­ ly.

For the School of Chemistry and Physics, however, there was a

greater difference between the correlations of English Usage with Eng­ lish Composition I grade and with grade in mathematics than for this school. There is an appreciably better relationship between the Algebra i test part and success in mathematics than is found between the Algebra test part and success in English Composition I or Chemistry I. In addition to showing the relationships between the predictive indices and the criteria, the horizontal analysis of the table dis­ closes that the following indices have differential predictive value. Vocabulary and Paragraph Reading show greater predictive value for chemistry than for mathematics.

The Algebra test part has greater

efficiency in predicting success in mathematics than in chemistry or English composition. By examining the columns, the relationships of the predictive items with each criteria is disclosed.

Thus it is seen that the range

of the correlations with Chemistry I grade is from .367 to .494, Vocabulaiy being the lowest and high school rank the highest.

For

freshman mathematics grade, the correlations vary from .17# to .569, Vocabulary being the lowest and Algebra the highest.

The English Us­

age test part gives the highest correlation with English composition, and Paragraph Reading the lowest.

These correlations are .522 and

Reproduced with permission ofthe copyright owner. Furtherreproduction prohibitedwithout permission.

.364., as presented.

The .Algebra test part yields the best correla­

tion with first-semester average and the Vocabulary test part the poorest.

The correlations are .530 and .34-3, respectively.

Multiple correlations resulting from various combinations of these predictive indices are shown on pages 107, 110 and 113-

The

partial regression coefficients necessary for the computation of re­ gression equations are given in the following pages.

In addition,

the partials are presented in order to demonstrate the relationships of the variables used in the team when the force which each receives from the others are in turn held constant.

TABLE XXXVI

INTERCORRELATIONS BETWEEN PREDICTIVE MEASURES AND INDIVIDUAL COURSE GRADES N = 100 Chemistry Grade H.S.R.

,/+94

Mathematics Grade

English Grade*

*430

Semester Average .500

Voc.

.367

.173

.335

.343

P.R.

.378

.299

.364

.360

A.P.

.491

*466

.455

.508

E.U.

.485

*483

.522

.558

Alg.

.465

.569

.400

.580

*The N for this group was 78.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

6. The Multiple Correlations and Partial Engression Coefficients of Various Forecasting Batteries when Grade in Chemistry I is the Criterion

Table XXXVII shows the multiple correlations and the partial regression coefficients of various batteries for the prediction of Chemistry I grade. Inspection of the right hand column reveals that the multiple correlations vary from .54-2 to .679.

The highest relationship is ob­

tained with a team comprising the five parts of the Moore-Nell examina­ tion and high school rank.

In this team the size of the partial re­

gression coefficients of the Vocabulary and Paragraph Reading test parts indicates that these test parts contribute very little to the multiple correlation.

High school rank with a coefficient of .3160 contributes

most, then follows the English Usage, Arithmetic Processes and Algebra test parts with partial regression coefficients of .1935,

.1901 and

•1537, respectively. 'When the Vocabulary and Paragraph Reading test parts are omitted, the correlation and the relative importance of the remaining items re­ main substantially the same.

It is shown in row two that the multiple

correlation of this team is .674-.

With the omission of nigh school

rank from the team, the correlation is reduced to .609. appreciable loss.

This is an

The importance of the English Usage test part to the

team is demonstrated in the fourth row.

It is seen that there is a

substantial loss in the multiple correlation when the English Usage test part is dropped from the battery.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

TABLE X X X V II

PARTIAL REGRESSION COEFFICIENTS AND MULTIPLE CORRELATIONS FOR PREDICTIVE MEASURES WHEN CHEMISTRY GRADE IS THE CRITERION

Eg.

H.S.R.

P.R.

Voc.

A.P.

E.U.

Alg.

1

.3160

.0757

.0406

.1901

.1985

.1537

.679

.2312

.2230

.1626

.674

3

.2793

.3090

.1793

.609

4

.3362

.2774

.542

2

■

.3119

R

TABLE XXXVIII

STANDARD DEVIATION RATIOS FOR REGRESSION EQUATIONS USED IN THE PREDICTION OF CHEMISTRY I GRADE N = 100

H.S.R.

1.53 2.10

P.R.

1.53 4.93

"

Voc.

1.53 18.52

"

.7285

A.P.

1-33 3.96

"

.3103

E.U.

1.53 2.75

"

.0826

Alg.

IsSSL _ 3.25 "

.3863 .5563 .4707

The standard deviation ratios shown in Table XXXVIII were used in the regression equations for the prediction of Chemistry I grade.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

TABLE XXXIX

REGRESSION EQUATION, MULTIPLE CORRELATION, PROBABLE ERROR OF ESTIMATE AND PERCENT OF FORECASTING EFFICIENCY FOR THE PREDICTION OF CHEMISTRY I GRADE FOR THE SCHOOL OF MINERAL INDUSTRIES N = 100

Items H.S.R.

A.P.

( .2 1 3 %

.O84IX2

E.U.

. 1194X3

R Alg.

. 0720X4)

P.E. Est.

Per­ cent Forecasting Eff.

K

- 7 . 684.9 .674 .72

26.2

In Table XXXIX is presented the most practical score-form re­ gression equation for the prediction of Chemistry I marks. It will be noted that the probable error of estimate is .72. As was found for the School of Chemistry and Physics, it is impracti­ cal to use this equation for counseling purposes because of its low accuracy.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

7.

Partial Regression Coefficients and Multiple Correlations for Prediction Batteries Using Mathematics Grade as Criterion

In Table XL are given the partial regression coefficients of the prediction variables when mathematics grade is used as the criter­ ion.

The multiple correlations are shown in the last column. Analysis of the results shown in the table reveals that the

Algebra test part shows the highest relationship with the criterion when the other variables of the team are held constant. Reading and Vocabulary show the lowest relationship.

Paragraph

It is interesting

to note that English Usage, a non-mathematical test part, shows a high­ er net relation to the criterion than does Arithmetic Processes,

High

school rank has a relatively high partial regression coefficient. Inspection of the last column discloses that the multiple cor­ relations vary from .597 to .701.

The best correlation is obtained

when a team composed of high school rank and the five parts of the Moore-Nell examination is used.

When the Paragraph Reading and Vocab­

ulary test parts are omitted from the team, the multiple correlation is not reduced appreciably.

The multiple correlation is .6&0.

With

a battery composed of Arithmetic Processes, English Usage and Algebra the multiple correlation is .644When the mathematical test parts sire combined the multiple correlation is not significantly higher than the zero-order correla­ tion of the Algebra test part.

The correlations are .597 and .569#

respectively.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

110.

An examination of the corresponding batteries in Tables XIII and XXV reveals that the highest relationship with mathematics grade was obtained for the School of Mineral Industries, the lowest for the School of Engineering.

The School of Chemistry and Physics shows an

intermediate relationship.

TABLE XL

PARTIAL REGRESSION COEFFICIENTS AND MULTIPLE CORRELA­ TIONS FOR PREDICTIVE MEASURES M E N MATHEMATICS GRADE IS THE CRITERION

R

A.P.

E.U.

Alg.

.134-3

.2483

.3645

.701

.1294

.2097

.3500

.680

3

.1662

.2709

.3625

.644

4

.2156

.4487

.597

Eg..

1

2

•

H.S.R.

P.R.

•24-89

.1194-

Voc. -.2324-

.2359

TABLE XLI

STANDARD DEVIATION RATIOS FOR REGRESSION EQUATIONS USED IN PREDICTION OF MATHEMATICS GRADE N = 100 H.S.R.

A.P.

Idk

2.10 H I 3.96

«

.6857

E.U.

i # 2.75

-

=

*3636

Alg.

H I 3*25

-

*0720

The standard deviation ratios shown in Table XLI were used in the regression equations for the prediction of mathematics grade.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

8 . Score-Form Regression Equation for the Prediction of Mathematics Grade

In Table X U I is given the selected score-form regression equa­ tion for the prediction of mathematics grade. the prediction is .74*

The probable error of

As was found for the Schools of Chemistry and

Physics and Engineering, the low degree of accuracy of the prediction makes it impractical to use the regression equation for the prediction of mathematics grade.

TABLE XLII

REGRESSION EQUATION, MULTIPLE CORRELATION, PROBABLE ERROR OF ESTIMATE AND PERCENT OF FORECASTING EFFICIENCY FOR THE PREDICTION OF GRADE IN MATHEMATICS FOR THE SCHOOL OF MINERAL INDUSTRIES N = 100

Items

R

H.S.R. P.R. Voc. A.P. E.U. Alg. K (.lSl3Xi .0370X3-.0192X 5.0519%. .I38IX5.1716X6)-10.0594- .701

P.E. Est.

Per­ cent Fore­ casting Eff.

.74-

28.7

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

2*

Partial Regression Coefficients and Multiple Correlations for Prediction Batteries using English Composition Grade as Criterion

It will be remembered that multiple correlations were computed with English composition grade for the Chemistry and Physics students in order to determine the magnitude of the relation between the verbal test parts and English Composition I.

It was thought that with English

grade as criterion the Vocabulary and Paragraph Reading test parts »

would have relatively higher weights than with the other criteria.

It

has been shown for the Chemistry and Physics School that Paragraph Reading has a low weight then combined with Vocabulary and English Us­ age.

In addition to demonstrating similar relationships for this

group, the partial regression coefficients and multiple correlations for other combinations of the predictive variables are shown in Table XLIII. It is seen by examination of the first row that the relation­ ships of the predictive indices used in this team are similar to those shown for the Chemistry and Physics group.

The multiple correlation

of this battery, which is composed of Vocabulary, Paragraph Reading and English Usage, is .566.

The multiple correlation of the same

batters- for the School of Chemistry and Physics is .56S. Inspection of the results in the second row reveals that when English Usage is omitted from the team, the partial regression co­ efficients are .2002 for Paragraph Reading and .2575 for Vocabulary. The multiple correlation is .415*

■

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

In the third row it is seen that a combination of the mathe­ matical test parts yields a multiple correlation of .4-97.

Thus the

prediction of English Composition I grade is somewhat better with a team composed of the mathematical test parts than with a team com­ prising verbal material. The multiple correlation obtained with the five test parts is .633.

TABLE XLIII

PARTIAL REGRESSION COEFFICIENTS AND MULTIPLE CORRELATIONS FOR PREDICTIVE. MEASURES "WHEN ENGLISH GRADE IS CRITERION N = 7S

Voc.

P.R.

E.U.

1

.1656

.0985

.4235

2

.2575

.2002

.1639

-.0474-

Alg.

R

.566 .415

3 5

A.P.

.3602

.3404

.2315

.497

.2399

.1452

.633

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

10.

Relation of Personality and Interest Measures to First—Semester Average

In order that the possibility of obtaining greater precision in predicting semester average might be investigated, the prediction batteries were augmented by certain personality and interest measures. The zero-order correlations of these measures are listed in Table XLIV.

■ Examination of the findings discloses that the personality

traits measured show no significant relationship to success in the first semester of the School of Mineral Industries. Higher correlations are found with the interest measures of the Vocational Interest Blank.

In each case, raw scores are used in

I

the computation.

The Life Insurance Salesman scale correlates nega­

tively with the criterion, the correlation being -.299*

This negative

relationship is in agreement with the results of other investigators (15).

A similar finding has been reported for the Engineering School

(Table XXIX).

However, with the Chemistry and Physics population the

correlation was negligible (Table XVII). No relationship is found be­ tween the Lawyer occupational scale and the criterion.

It might have

been expected that this scale would yield a negative correlation since, like the Life Insurance Salesman Scale, it is a measure of interest in common with men engaged in a non—technical vocation.

There is a reli­

able correspondence between scores on the Chemist interest measure and first-semester achievement for this group.

The correlation is .354*

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

Although tliis zero-order correlation may be considered satisfactory for this type of instrument, the amount by which the inclusion of the scale increases the effectiveness of the prediction team is not great. This is demonstrated in Table XXXV. Since unsatisfactory results are obtained with the use of per­ sonality and interest measures, the possibility of improving the pre­ diction battery by the inclusion of a measure of studiousness was ex­ amined.

That there is a significant relationship between scores on

the Studiousness Index and academic achievement is indicated by the correlation of .336.

Moreover, the precision of the forecasting bat­

teries is increased somewhat when this measure is included.

This is

shown in Table XXXV. It will be observed that for the personality measures and the Engineer and Lawyer interest scales a population of one hundred is used, whereas the population for the other measures is seventy-eight. This discrepancy is explained by the fact that scores for the Studious­ ness Index scale were available for only seventy-eight cases.

Since it

was desired to use the measure of studiousness in a prediction team, this smaller population of seventy-eight was employed in the development of multiple correlations and regression equations for the School of Min­ eral Industries.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

TABLE XLIV

CORRELATIONS OF PERSONALITY AND INTEREST MEASURES WITH FIRST-SEMESTER AVERAGE

Semester Average

N

Bl-N

.033

100

B2-S

-.151

100

B4-D

.024

100

Engineer Scale

.194

19®

Lawyer Scale

’

*029

Chemist Scale Life Insurance SalesmanScale Studiousness Index Scale

*354 -.299

100 ^ 7S

.336

In Tables XLV to XLVIII are presented the data for the larger population of the School of Mineral Industries.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

TABLE XLV.

INTERRELATION SHIP BETWEEN SIX PREDICTIVE MEASURES AND FIRST-SEMESTER AVERAGE N = 100

Sera.A y .

H.S.R.

Vo c .

P.R.

A.P.

E.U.

Alg.

V.I.I Chem,

Sem.Av. H.S.R.

Voc. P.R. A.P.

.500

.348

.360

.508

.558

.580 .309

. .207

.143

.279

•333

.249

.214

.655

• .393

.417

.342

.267

.519

.335

•359

.164

.360

.558

.147

E.U.

.420 .173

Alg.

*224

V.I.B. Chem.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

TABLE XLVI

PARTIAL REGRESSION COEFFICIENTS FOR -PREDICTION BATTERIES FOR THE SCHOOL OF MINERAL INDUSTRIES N s 100

H.S.R.

Voc.

A.P.

P.R.

E.U.

AlRv

1

.2719

-.0382

.0409

.1519

.2712

.2850

2

.2893

-.0106

.0370

.1453

.2706

.3036

3

.0167

-.0025

.2006

.3463

.3178

4

-.0219

.0060

.2042

.3409

.2925

.2.761

.3039

.3507

.3190

5

.2866

.1591

6

-.1780

Chem.S .1214

.1593

TABLE XLVII

STANDARD DEVIATION RATIOS USED IN REGRESSION EQUATIONS SHOWN IN TABLE XLVIII N = 100 H.S.R.

df5

E.U.

■

Voc.

.

.0^6

Alg.

.1827

V.I.B. Chem.

P.R.

-^225 4.93

=

A.P.

.9005 3.96

_

-2005 .

,3275

-2771

'

-°186

.2274

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

TABLE

XLVIII

REGRESSION EQUATIONS FOR PREDICTION OF FIRST—SEMESTER AVERAGE FOR MINERAL INDUSTRIES STUDENTS N = 100

Factors

Eg.1.

2.

3-

4-

5.

6.

Fore­ cast­ ing Eff. P.E. PerEst. cent

H.S.R. (.H6&!

Voc. -.0019X2

P.R. .OO75X3

A.P. .0345X4

E.U. .O888X 5

Alg. .0790X6

H.S.R. (.12A1X!

Voc. -.0005X2

P.R. .OO6SX3

A.P. .0330X4

E.U. .O886X 5

Alg. .0841X6)

Voc. (.OOOSX]^

P.R. -.OOO5X 2

A.P. .0456X3

E.U. .II34X4

Alg. .0881X5)

K -5.8930

Voc. (-.0011X!

P.R. .00HX2

A.P. .0464X3

E.U. . I H 6X4

Alg. .O8H X 5

VIB-Chera .0030X6)

H.S.R. (.1229X!

A.P. .0362X2

E.U. .0904X3

Alg. .O842X 4)

A.P. (-.0405Xi

E.U. .1149X2

Alg. .OS84X 3)

K -3-5913

K -5.1319

VIB-Chem .0023X 7) K -5.1875

K -6.6720

K -5.9262

.754

.40

34.4

.745

.41

33.3

.696

.44

28.2

.712

.43

29.8

.745

.41

33.3

.696

.44

28.2

5

E.

1.

THE SCHOOL OF LOWER DIVISION

Relationship Between the Prediction Indices and Fir S't-Semester Av­ erage for Lower Division Students

The relationships between the forecasting variables and firstsemester average for the Lower Division students are presented in Table XLIX.

It will be noted that the Algebra test part is omitted

from this table.

This is explained by the fact that the Algebra sec­

tion of the Moore-Nell examination is not administered to students en­ rolled in non-technical curricula. From the zero-order correlations shown in the first row it is evident that high school rank, with a correlation of .513, is the best single forecaster of freshman achievement for this group of students.

It is also clear that the parts of the Moore-Well examination do not differ widely in the degree to which they are related to the criterion. In contrast to this finding, the technical schools revealed considerable variation among the correlations of the Moore-Nell test parts with se­ mester average. Of the test parts, English Usage and Vocabulary possess the highest predictive value with correlations of .4-00 and .395; Arithmetic Processes, with a correlation of .351 possesses the lowest value.

The

Paragraph Reading test part correlates slightly better than the Arith­ metic Processes test part.

These results are markedly different from

those of technical schools for which the Vocabulary and Paragraph Read-

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

ing test parts were shown to yield the lowest relation to firstsemester achievement. Further analysis of the table reveals the following inter­ correlations among the predictive items: high school rank shows fair relationship to the Vocabulary and English Usage test parts and slightly lower relationship to the Arithmetic Processes and Paragraph Reading test parts.

The Vocabulary section possesses the highest

correspondence with Paragraph Reading and has appreciably lower corre­ lations with Arithmetic Processes and English Usage.

The Paragraph

Reading test part correlates substantially with Arithmetic Processes and English Usage. cantly related.

Arithmetic Processes and English Usage are signifi­

The general patterns of interrelationship are similar

to those found for the technical schools. As in the case of the foregoing schools, the zero-order corre­ lations and intercorrelations for the Lower Division population are used to obtain the partial regression coefficients necessary for cal­ culating multiple correlations and developing regression equations.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

TABLE XLIX

INTERRELATIONSHIP BETWEEN PREDICTIVE I T M S AND FIRSTSEMESTER AVERAGE FOR THE SCHOOL OF LOWER DIVISION N = 208

Sem.Av. Sem.Av. H.S.R. Voc. P.R. A.P.

H.S.R. .573

Voc.

P.R. -

A.P.

E.U.

M-N 4

.395

.366

.351

.400

.485

.278

.217

.230

.303

.34-6

.542

.308

.330

•434

.468 .425

E.U.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

2 • Partial Regression Coefficients for Prediction Batteries

In Table L are presented the partial regression coefficients for three prediction teams.

Inspection of the first battery, con­

sisting of the high school rank and four parts of the Moore-Nell ex­ amination reveals that high school rank receives the heaviest partial regression coefficient and Vocabulary the second heaviest. weights are .4471 and .1507, respectively.

These

English Usage and Arith­

metic Processes have respective weights of .1305 and .1123.

As in

the case of each previously discussed school, Paragraph Reading, with a weight of .0770, is lowest.

It is noted that Vocabulary has a rel­

atively large weight for this group, whereas for the technical schools the weights for this test part are small.

When high school rank is

dropped, the Moore-Nell test parts maintain their relative positions. This is shown in the second row.

In the third row it is seen that the

high school rank shows a somewhat greater contribution to the multiple correlation than the total unweighted Moore-Nell score when these items make up a two-variable team.

TABLE L PARTIAL REGRESSION COEFFICIENTS FOR PREDICTIVE MEASURES USING SEMESTER AVERAGE AS CRITERION

N = 208 Eg.

H.S.R.

Voc.

P.R.

A.P.

E.U.

1

•4471

.1507

.0770

.1123

.1305

.2381

.0647

.1576

.2258

2 3

.4602

*3258

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

£.

Means and Standard Deviations for Semester Average and Prediction Items

Table LI shows the means and standard deviations of the fore­ casting measures and first-semester average.

These data are used in

the development of the score-form regression equations and will he compared with similar data of the other schools in the summary section of this chapter. It may he noted here that the mean and standard deviation of the first-semester average for this group of students are lower than was found for the technical groups. school rank is somewhat lower.

Furthermore, the mean of the high

This suggests that the typical student

who enters one of the science or engineering schools of the college is academically somewhat superior to the typical Lower Division freshman. This matter is further discussed in the summary section.

TABLE LI

MEANS AND STANDARD DEVIATIONS FOR PREDICTIVE ITEMS AND SEMESTER. AVERAGE N =

Sem.Av. Mean S.D.

1.10 .765

208

H.S.R.

Voc.

P.R.

A.P.

E.U.

M-N 4

4-.02

54.38

31.28

23.33

28.05

4.49

2.15

17.88

4.91

5.54

2.97

2,01

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

The standard deviation ratios used in constructing the scoreforra regression equations are listed in Table LII. that tiie ratios for two populations are shown.

It will be observed

The second set is used

in developing the regression equations shown in Table LVIII.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

TABLE LII STANDARD DEVIATION RATIOS USED IN REGRESSION EQUATIONS SHOW IN TABLE LIII AND LVIII to 0

It

H.S.R.

01

N

N = 107

.765 2.15

"

.3558

■ M-N

4

Voc.

.765 17.88 =

.04.28

H.S.R..

P.R.

.765 4.91 =

.1558

V.I.B. SI

A.P.

.765 5.54 "

.1381

E.U.

.765 2.97 "

.2576

M-N 4

.765 2.01 “

.3806

.728 2.09

"

.728 2.10

~

.728 63.57

=

.3483 •3467 .1145

I

I I I

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

TABLE LIII

REGRESSION EQUATIONS, MULTIPLE CORRELATIONS, PROBABLE ERRORS OF ESTIMATE AND PERCENTS OF FORECASTING EFFICIENCY FOR PREDICTION OF FIRST-SEMESTER AVERAGE OF LOWER DIVISION STUDENTS N = 208

Eg .

1

2

R

Items

P.E. Est.

H.S.R. Voc. P.R. A.P. E.U. K (.1591X-L .oo64X2 .0120X2 .0155X4 .0336X5)-1.5741 .660 .39 Voc.

P.R.

A.P.

E.U.

H.S.R. M-N 4K (.1637X1 .I24QX2)-.0650

24-9

K

(.0102X! .0101X2 .0212X3 .0582X4 )-1.8516 .512 .44

3

Per­ cent Forecasting Eff.

.64-9 .39

14-1

23.9

1

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

128.

k'

Score-Form Regression Equations for Prediction of First-Semester Average

The three score-form regression equations which were construct­ ed for the prediction of first-semester average in the School of Lower Division are given in Table LIII.

The multiple correlations, correspond­

ing probable errors of estimate and percents of forecasting efficiency are listed on the right-hand side of the table. Analysis of the table reveals that the multiple correlation ob­ tained with the first battery, comprising high school rank and the weighted parts of the Moore-Nell, is virtually the same as for the third battery, which comprises high school rank and the total unweighted score of the Moore-Nell.

Likewise, the probable error is .39 in both cases.

Thus, it is demonstrated that weighting the college aptitude test parts fails to increase the accuracy of predictions made for Lower Division students.

When high school rank is omitted from the first team, the

multiple correlation drops from .660 to .512.

That the second battery

is a distinctly poorer forecaster is further shown by the relatively high probable error of estimate.

This is .44*

In order to compare the prognostic efficiency of a team selected as most practical for Lower Division with the selected most practical teams of the technical schools, the following batteries, multiple cor­ relations, and probable errors of estimate are listed in Table LIV.

Only

teams which are composed of the high school rank and the Moore-Nell exam­ ination are included in this table.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

TABLE LIV

COMPARISON OF A SELECTED BATTERY FOR LOWER DIVISION WITH A SELECTED BATTERY FOR EACH OF THE FOREGOING SCHOOLS

Schools

Batteries

R

P.E. Est.

Lower Division

H.S.R.

M-N 4 (unweighted)

.649

•39

Mineral Industries

H.S.R.

A.P.

.764

.41

Engineering

H.S.R.

A.P.

.596

.42

Chemistry and Physics

H.S.R.

A.P.

.704

•44

E.O.

Alg.

Alg. E.U.

Alg.

Inspection of the probable errors of estimate for the various schools discloses that the prediction of first-semester average by these batteries is more accurate for the Lower Division group than for the technical groups.

In the third column it is seen that the multiple

correlation for Lower Division is appreciably lower than that of Mineral Industries and somewhat lower than the multiple correlation for Chemis­ try and Physics.

Despite this fact, the probable error of estimate is

smaller than those for the other schools.

This finding may be at least

partially attributed to the smaller standard deviation of the Lower Di­ vision group.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

5“ Intercorrelations of the Prediction Measures Including Studiousness Index and Semester Average

In Table LV are presented the intercorrelations of the MooreNell total score (four parts unweighted), high school rank, the Studious­ ness Index and semester average. It is seen in the first row that the correlation of the total Moore-Nell score (parts unweighted) with semester average is .574*. Referaice to Table XLIX reveals that this is .089 higher than the correla­ tion obtained with the larger Lower Division population.

The correla­

tion between high school rank and semester average is similar to that found for the larger group, the difference being merely .019.

Inspec­

tion of the second row reveals that the Moore-Nell examination is re­ lated significantly to high school rank.

The correlation is .4-21.

The

Studiousness Index scale shows some relationship with the total score on the Moore-Nell examination and with high school achievement.

These

correlations are .251 and .356 ^ respectively. From the correlations in this table were obtained the partial regression coefficients necessary for computing the multiple correla­ tions.

These are given in Table LVI which follows.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

TABLE LV

INTERRELATIONSHIP BETWEEN MOORE-NELL (EOUR PARTS), HEGH SCHOOL RANK, THE STUDIOUSNESS INDEX AND SEMESTER AVERAGE N = 107

Sem.Av. M-fl 4 ____ ____ Sem.Av. M-N 4 H.S.R.

.574

H.S.R. ____

V.I.B. SI

.554

-201

.421

.251 .356

V.I.B. SI

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

6. Partial Regression Coefficients for Two Forecasting Teams for Lower Division Students

Table LVI presents the partial regression coefficients for the members of two prediction batteries.

The first team, comprising the

total unweighted Moore-Nell score, the high school rank and the Stu­ diousness Index, shows sizable weights for the first two of these var­ iables and a negligible weight for the third.

The total unweighted

Moore-Nell score and the high school rank, which together make up the second battery, possess somewhat similar partial regression coefficients, contributing approximately equally to the prediction of freshman grades for this population.

TABLE LVI

PARTIAL REGRESSION COEFFICIENTS FOR PREDICTIVE MEASURES I

WHEN SEMESTER AVERAGE IS THE CRITERION N = 208

H.S.R.

M-N 4

V.I.B. SI

1

.3931

•4196

-.0443

2

•3V96

.4H2

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

TABLE LVII

MEANS AND STANDARD DEVIATIONS FOR THREE PREDICTIVE ITEMS AND FIRST-SEMESTER AVERAGE N = 107

Sem.Av.

Mean S.D.

The means vision population

1.15 .723

H.S.R.

M-N 4-

4-05

4.31

256.00

2.10

2.09

63.57

'

V.I.B. SI

and standard deviations for the larger Lower Di­ are shown in Table LVII.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

7.

Two Regression Equations for the Prediction of First-Semester Success in the School of Lower Division

Of the personality and interest’measures listed in Table LVIII, it was thought that the Studiousness Index might be of some value in improving the efficiency of the battery consisting of high school rank and 'the total weighted Moore-Nell score.

In order to in­

vestigate this possibility, two regression equations were developed for the above-mentioned battery, the first of which included the Stu­ diousness Index.

Table LVIII shows the equations, their corresponding

multiple correlations, probable errors of estimate and percents of forecasting efficiency. It will be seen that the probable error of the prediction and the percents of forecasting efficiency are the same for both teams. They .are .36 and 25.8, respectively.

Comparison of the second team in

this table with the comparable team in Table LIII reveals that the probable error of the prediction is .03 lower for this sample than that found for the larger population.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

TABLE LVIII

REGRESSION EQUATIONS FOR PREDICTION OF FIRSTSEMESTER AVERAGE FOR LOYffiR DIVISION STUDENTS N = 107

Ed . 1

2

11shis H.S.R. (.1363X-L

M-N 4.I4.6IX2

VIB-SI -.0051 )

H.S.R. (.1316X1

M-N 4K .1443X 2 ) -.004-3

R K -.0930

Per­ cent ForeP.E. casting Est« Eff«__

. 671 .36

25.8

. 670 .36

25.3

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

8 . Relation between Personalitv and Interest Measures and FirstSemester Average

The final part of the investigation of the Lower Diva,sion students consisted of an attempt to improve the prediction by the ad­ dition "of non-intellective measurements to the forecasting battery. In Table LIX are listed the correlations between the trait measures investigated and the first-semester average.

The highest correlation

obtained with any of the interest measures is .175 for Group X.

This

group includes the Advertising Manager, Lawyer, and Author-Jcurnalist occupations. Letter* grades were used in correlating the interest scales with semester average.

That the use of raw scores does not increase

the relationships is indicated by a comparison of the two correlations listed for the Life Insurance Salesman Scale, the first of which en­ tails raw scores and the second letter grades. It is seen that the Studiousness Index scale is employed for 107 subjects, whereas the population for the other items is 208.

This

is explained by the fact that Studiousness Index scores were not avail­ able for the entire group.

Since it was not known whether the smaller

group was a random sample of the larger population, means and standard deviations of each predictive item were calculated for this group. results are shown in Table LVII.

The

A comparison of the corresponding

items in Tables LI and LVII reveals that the results are very similar with the exception of the standard deviation of semester average.

For

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

the smaller group, the standard deviation is somewhat reduced, the difference being .037.

The results of the study based upon the smaller

population are given in Tables LVI and LVIII.

TABLE LIX

CORRELATIONS BETWEEN PERSONALITY AND INTEREST MEASURES AND FIRST-SEMESTER AVERAGE N = 20S

Semester A vera g e Bl-N (reversed)

.012

B2-S

.111

B4-D

.061

V.I.B.

-

V.I.B. -

Engineer

.025

Life Insurance

Salesman (raw score) .020

V.I.B.

-Life Insurance Salesman

V.I.B.

-

V.I.B. -

-.001

Sales Manager

.009

Real Estate Salesman

.04-6

Group X

.175

Group IX

•021

Group VIII

.064

Group V

.123

V.I.B.

-Studiousness Index* «

.201

*N = 107

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

- F.

i*

THE SCHOOL OF AGRICULTURE - NOR-TECHNICAL

Interrelationship betv;een Predictive Items and First-Semester Average for the School of Agriculture (Non-Technical)

In Table LX are presented the intercorrelations of seven forecasting variables and first-semester average for the general group of the School of Agriculture.

It will be remembered, that the students

of the school are divided into the following groups: non-technical, scientific or technical, and two-year.

The findings for the last two

groups will be presented in later sections of this chapter. Examination of the first row of this table reveals that, of the forecasting measures, high school rank is the best single item. The correlation is .458.

The Vocabulary and Paragraph Reading test

parts are -the poorest itemsj the Arithmetic Processes and English Us­ age parts occupy intermediate positions.

The correlations of the Moore-

Nell test parts range from .189 to .314? Paragraph Reading yielding the lowest and English Usage the highest relationship.

When this table is

compared vdth the corresponding table for Lower Division (XLIX), it is seen that the Moore-Nell test parts show substaitially smaller rela­ tionships with semester average for the non-technical group of the School of Agriculture.

As before, the non-intellective measures, Stu­

diousness Index and Life Insurance Salesman scale, show little tendency to vary with first-semester average. Inspection of the second row shows a lack of significant cor-

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

responden.ce between high school rank and the Moore-Well test parts. In the third row it is seen that the Vocabulary test part correlates substantially higher with the other verbal test parts, Paragraph Read­ ing and English Usage, than with the arithmetical test parts.

Para­

graph Reading is more closely related to English Usage than to Arith­ metic Processes.

It will be noted in the fifth row that the correla­

tion of Arithmetic Processes with English Usage is .4-08.

The relation­

ships among the test parts found for this group are similar in pattern to those found with the other groups. The Studiousness Index shows the highest correlation with high school rank and the lowest with Paragraph Reading, the correlations being .269 and -.OSO.

The correlations with the Life Insurance scale

are shown in the seventh column.

It will be observed that all the cor­

relations with the scale are negative, the highest negative relation being with the Studiousness Index scale and the lowest with Paragraph Reading.

These correlations are -.315 and -.053> respectively.

Reproduced with permission ofthe copyright owner. Furtherreproduction prohibitedwithout permission.

TABLE IX

INTERRELATIONSHIP BETWEEN PREDICTIVE ITEMS AND FIRSTSEMESTER AVERAGE FOR THE SCHOOL OF AGRICULTURE (NON-TECHNICAL)

N = 105

Sem.Av. Sem.Av. H.S.R.

Voc. P.R. A.P. E.U. VIB-SI

H.S.R.

Voc. P.R.

A.P.

E.U.

VIB-SI

L.I.S.

.458

.198

.189

.245

.3U

.205

-.181

.090

.020

.107

.129

.2.69

-.162

.562

.2.54

• m

.137

-.214

.313

.-456 -.030

-.053

.408

.077

-.103

.074

-.103 -.315

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

2.

Relative Wei gilts of the Predictive Indices Used in the Regression Equations for the School of Agriculture (Non-Technical)

From a general analysis of the partial regression coefficients, it is seen that high school rank has the highest weights in the various batteries, and that Vocabulary and Paragraph Reading have the lowest. In the fifth battery, it is seen that the Studiousness Index and Life Insurance Salesman scale have higher weights than the Vocabulary test part.

In general, the non-intellective measures have relatively low

weights.

The dominance scale, however, possesses a fair-sized weight

in the sixth team. These partial regression coefficients are utilized in the de­ velopment of the score-form regression equations shown in Table LXIV.

TABLE LSI

PARTIAL REGRESSION COEFFICIENTS FOR PREDICTIVE INDICES USED IN REGRESSION EQUATIONS FOR THE SCHOOL OF AGRICULTURE NON-TECHNICAL

N - 105 Voc.

P.R.

A.P.

E.U.

1

.4-002 -.0125

.0983

.1859

2

.4207

.0793 .0560

.1031

.i860

.1339 .1100

.2308 .1968

.1090

.1870

H.S.R.

3

.0134 .0434 .0381

.0175

M-N 4 VIB-SI L.I.S. B4-D .0854

4 5 6 7

.4-173 .3921 .3866 .3929

.2607 .2618

8

.3995

.2735

.0163

.0508 -.0913 -.0335 -.1569 -.0564

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

2.* Means and Standard Deviations of First-Semester Average and the Predictive Indices for the School of Agriculture - Non-Technical

The means and standard deviations necessary for the construc­ tion of the score-form regression equations are shorn in Table LXII. The mean and standard deviation of first-semester average for this group are similar to those found for the Lower Division.

As was sta­

ted previously, tables shovdng these data for the various schools will be compared in the summary section of this chapter.

TABLE LXII

MEAN AND STANDARD DEVIATIONS FOR PREDICTIVE ITEMS AND FIRST-SEMESTER AVERAGE FOR THE SCHOOL OF AGRICULTURE NON-TECHNICAL N = 105

Sem. H.S.R.

Voc.

P.R.

A.P.

E.U. M-N 4 VIB-SI L.I.S. Chem.

_____ ____________ ____________ Av._______ _____________,

43.70 29.31 22.63 27.3S 5.28

Mean 1.18

3.71

S.D.

2.10 14.24 4-92

.79

4-50

3.29 1.71

S*

B4-D ____

275-74 278,89 315-36 4.88 53-23

40.43

49-68 I .96

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

The standard deviation ratios necessary for deriving the score-forru regression equations are given in Table LXIII.

TABLE LXIII

STANDARD DEVIATION RATIOS USED IN SCORE-FORM REGRESSION EQUATIONS FOR PREDICTION OF SEMESTER AVERAGE FOR THE SCHOOL OF AGRICULTURE - NON-TECHNICAL N = 105

H.S.R. Voc.

-4? 2•10

=

-3762

E.U.

^-4?

=

-0555

VIB-SI

14* •24-

P.B.

a -p -

^

5 •27 -4|

= .2/+01 = .0143

5 J/ •

=

tOo=

.1606

L.I.S.

-1756

Bi-D

. .0195

tM

=

-4031

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

4*

Prediction of First-Semester Average for the School of Agriculture Non-Technical - trjr the Use of Eight Score-Form Regression Equations

The score-form regression equations developed from the data in the foregoing tables are given in Table LXIV. tiple correlations,

probable errors of

casting efficiency are shown on the

The corresponding mul­

estimate andpercents of fore­

right-hand sideof the table.

The multiple correlations of the eight forecasting batteries shown in this table

range from .34-2 to

.555.

first column on the

right-hand side of

the table.

team consists

Theseare given in the The best prediction

of the high school rank, total Moore-41ell score (four

parts), Life Insurance Salesman scale and the dominance scalej the poorest team consists Of the four weighted parts of the Moore-Nell test. Examination of the first and, second rows reveals that the multi­ ple correlation is reduced from .5-44 to .538 when the Studiousness In­ dex is omitted from the first team.

It is noticed in the third row that

the four parts of the Moore-Nell yield a multiple correlation of .342. In Table LXV it is seen that the unweighted Moore-Mell total score gives a correlation of .362.

The reason for this discrepancy is not clear,

although it is probably a chance finding. A comparison of the second and fourth teams shows that 'the omission of the Paragraph Reading test does not reduce the multiple cor­ relation appreciably.

From the fifth row it is seen that the addition

of the Studiousness Index and Life Insurance Salesman measures to the fourth battery increases the multiple correlation from .536 to .544*

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

In the sixth row 'the unweighted total Moore-Nell score has replaced the test parts, and the dominance scale has replaced the Studiousness Index.

The multiple correlation of this combination is .555.

When

the dominance scale is omitted from the sixth battery the multiple correlation is reduced to .533*

This is shown in the seventh row.

A comparison of this row with the eighth row reveals that the same correlation is obtained with the omission of the Life Insurance Sales­ man scale from the battery. It is seen that the probable errors of the prediction are .4-5 for all the teams except the third and sixth.

The probable error of

estimate of the third team, which is composed entirely of the MooreNell test parts, is .50.

The sixth team, composed of the high school

rank, unweighted total Moore-Nell score, Life Insurance Salesman scale and dominance scale, is the most accurate forecaster of first semester success for this group of students.

The probable error of estimate of

this team, which is .UU, is slightly smaller than those of the other teams.

However, the eighth battery, which consists of the high school

rank and unweighted total Moore-Nell score, may be considered the most practical since it involves only two prediction items and predicts al­ most as well as the sixth team. A perusal of the last column reveals that the percents of fore­ casting efficiency are relatively low.

When the probable errors of the

predictions and percents of forecasting efficiency are compared with those of the other schools, it is seen that the predictions for this group are the least accurate.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

TABLE LXIV

REGRESSION EQUATIONS, MULTIPLE CORRELATIONS, PROBABLE ERRORS OF ESTIMATE AND PERCENTS OF FORECASTING EFFICIENCY FOR THE SCHOOL OF AGRICULTURE - NON-TECHNICAL

N = 105 Equations

R

1

H.S.R.

Voc.

(.1506X-L -.0007X2

2

H.S.R.

(.1583X-L 3

4

6

P.R.

A.P.

.OO9OX3

.OiaiX^

P.R.

A,P.

E.U.

.0028X2

.0235X3

.0554X 4)

Voc.

A.P.

E.U.

.OI93X3

.0473X4)

H.S.R.

H.S.R.

.0021X2 Voc.

A.P.

E.U.

(.147%

.0009X2

.OIOIX3

.0449X4

H.S.R.

M-N 4 .1204X2

L .I .S . -.OOO7X3

M-N 4 .1210X2

L.I.S.

K

-.OOIIX3)

+.3000

H.S.R.

( .1473X1.

8

Voc.

.0007X2

Voc.

(.1454% 7

A.P.

,0173X4

(.0024X-]

(.1570X! 5

P.R.

.OI2.7X3

H.S.R.

(.1503X!

K M-N 4 .1264X2) -.0447

B4-D -.O632X4)

E.U.

.0446X5 E.U.

.0447X5)

VIB-SI

.OplSXg)

P.E. Est.

Per­ cent Forecasting Eff.

K

-1.7090

.544

.45

16.1

.538

.4-5

15.7

.342

.50

6.1

.536

.45

15.6

.544

.45

16.1

.555

.44

16.9

.533

.45

15.4

.533

.45

15.4

K

-1.3662

K

-1.0980 K

-1.2598 L.I.S.

-.0018X 5

VIB-SI

,0008X6)

K

-.8072

K

+.4954

146.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

' ’

5.*

Relationship Between High School Rank, Moore-Nell Total Score (Four Farts Unweighted), Life Insurance Salesman Scale and the Dominance Scale and First-Semester Average

•

In Table LXV are shown the intercorrelations of high school rank, total unweighted Moore-Nell score, Life Insurance interest scale, the dominance scale and first-semester average. This table is presented to show the interrelationships among the items used in the sixth, seventh and eighth forecasting teams (Table LXIV). The items winch have not appeared heretofore and which are presented in this table are Moore-Nell examination (parts not weighted) and the dominance personality trait measure.

The first row

reveals that the unweighted total Moore-Nell score correlates .362 and the dominance scale -.200 with first-semester achievement.

In­

spection of the interrelations among the forecasting items reveals that these indices are not related to each other significantly.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

L48.

TABLE LXV

INTERRELATIONSHIP BETWEEN FIRST-SEMESTER AVERAGE AND HIGH SCHOOL RANK, MOORE-NELL TOTAL SCORE (FOUR PARTS), LIFE INSURANCE SALESMAN SCALE AND THE DOMINANCE SCALE OF THE BERNREUTER PERSONALITY INVENTORY N = 105

Sem.Av. H.S.R.

L.I.S.

M-N 4

L.I.S.

B4-D

.458

.362

-.181

-.200

.214

-.162

-.065

-.233

1

M-N 4

H.S.R.

1-•

Sem.Av.

.154

B4-D

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

6 . Relation of Personality and Interest Measures to First-Seme ster

Average for the School of Agriculture (Non-Technical)

The relationship of the non-intellective factors investigated with first-semester achievement is shown in Table LXVI. It is seen in this table that the personality traits are not significantly related to the criterion.

Despite the fact that the

dominance scale shows a small negative relation to semester average, the correlation being -.200, it was seen in Table LXIV that this mea­ sure adds some value to the battery in which it is used. Examination of the interest measures investigated reveals that these, too, are not related significantly to the criterion.

The

correlations range from -.131 for the Life Insurance Salesman scale to .177 for the Chemist scale. listed for the Farmer scale.

It is noted that two correlations are For the first correlation, raw.scores

were used; for the second, letter grades were used.

The correlations

l

are .073 and .108.

For this scale, then, the correlation is not re­

liably increased by the use of raw scores instead of letter grades. Further inspection of the table reveal,3 that the Studiousness Index scale is not related significantly to first-semester average. It will be remembered that in Table LXIV, this instrument was employed I

in an attempt to increase the efficiency of a prediction battery and that it was found to have no value for this purpose.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

TABLE LXVI

RELATION OF PERSONALITY AND INTEREST MEASURES TO FIRST-SEMESTER AVERAGE FOR THE SCHOOL OF AGRICULTURE - NON-TECHNICAL N = 105

Semester Average Bernreuter Personality Inventory Bl-N (reversed)

-.100

B2-S

.044-

B4-D

-.200

Life Insurance Salesman Scale

-.181

Lawyer Scale

-.060

Social Science Teacher Scale

.055

Farmer Scale

(raw scores)

.073

Farmer Scale

(letter grades)

.108

Chemist Scale

.177

Studiousness Index

.205

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

G.

THE SCHOOL OF AGRICULTURE - SCIENTIFIC

1 . Interrelationships Between the Predictive Indices and First-

Semester Average for the School of Agriculture (Scientific)

In this section the results of the investigation for the tech­ nical or scientific group of students of the School of Agriculture are given.

Table LXVII presents the interrelationships of the forecasting

variables and first-semester average for this group. Inspection of the first row of this table reveals that the Algebra test part is most highly correlated with the criterion, the correlation being .597. is next.

High school rank, with a correlation of .4-77,

The Vocabulary and Arithmetic Processes test parts are next

in order of relationship to first-semester achievement, showing corre­ lations of .386 and .301, respectively.

The Paragraph Reading and

English Usage test parts are most poorly related to the criterion, their respective correlations being .236 and .230.

Studiousness Index

and the Chemist interest scale, the two trait measures used, correlate .304 and .344-, respectively, with the criterion.

It may be noted that the correlation between the Paragraph Reading test part and the Arithmetic Processes test part is reliably higher than the correlation between Paragraph Reading and English Us­ age, another verbal test part.

Although this difference likewise ex­

ists for the Engineering and Mineral Industries schools, it is diffi­ cult to give a ready explanation for this finding.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

To the left of the dotted line in the table are presented the probable errors of the correlations between the prediction mea­ sures and seme ster-average. Ovdng largely to the restricted size of this population, the probable errors of the correlations are high. Hence, many of these correlations are unreliable, and interpretations are to be made with caution.

. . TABLE LXVII

INTERRELATE OH SHIP BETWEEN PREDICTIVE INDICES AND EERSTSEMESTER AVERAGE FOR THE SCHOOL OF AGRICULTURE - SCIENTIFIC N = 30

Sem.Av.

P.E.

.4-77

.386

.236 .301 .230 .597

.344

-.136 .069 .388 .309 -.131 .117

.025

2 H.S.R.

.097

3

Voc.

.106

.668 .385 .419 .4-57

.268 .268 -.273

4

P.R.

.118

.510 .186 .265

.035 .034- -.289

5 A.P.

.114-

.184. .4-81

.083 .116 -.007

6 ■E.U.

.118

.226

.280 •073 -.538

7

Alg.

.080

•4-91 .118 -.317

8

Ghem.S.

.110

.4-53 --532

.113

-.244

9 VIB-SI 10

L.I.S.

-.025

P.R. A.P. E.U. Alg. Chem. VIB- L.I.S SI S. 1 m 0 t 1 m• 1 1

Sem.Av.

Voc.

! cT cn •

1

H.S.R.

.110

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

2.

Partial Regression Coefficients of the Predictive Indices Used For the School of Agriculture - Scientific

From the intercorrelations of the variables, the partial re­ gression coefficients required for the development of regression equa­ tions shown in Table LXXI were computed.

The partial regression co­

efficients of the various batteries are listed in Table LXVIII. It is seen in the first and fifth columns that high school rank and the Algebra test part have substantial weights.

The Vocabulary test

part, shoYai in the second column, makes somewhat smaller contributions to the multiple correlations.

As seen in the third, fourth and sixth

columns, the Arithmetic Processes, English Usage and Paragraph Reading test parts add very little to the efficiency of the forecasting batteries . Examination of the seventh, eighth and ninth columns reveals that most of the partial regression coefficients of the non-intellective measures are positive and moderately high.

Negative partial regression coefficients

are found for the Life Insurance Salesman scale in the ninth battery and for the Chemist scale in the tenth battery.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

TABLE LXVIII PARTIAL REGRESSION COEFFICIENTS USED IN PREDICTION BATTERIES FOR THE SCHOOL OF AGRICULTURE - SCIENTIFIC

E.S.R. Voc. 1 2

A.P. 3

E.U. 4

Alg. 5

P.R. 6

Chem. 7

L.I.S. VIB-SI 8 9

.0366 .H22 .504-0 -.1414.

1

.1765

2

.1217 -.0141 -0608 .5343

3

.1458 -.0133

.5367

4

.1431

.5316

5

.3638 .2195

.3843

6

.4064 .2040

.2834

.1714

7

.4341 .2344

.2458

.2241

8

.33S9 .1675

.3953

9

.3633 .1539

.3429

10

.3863 .1912

.3256

.0906

.1728 -.1748

.1373

-.2042

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

2.« Means and Standard Deviations of First-Semester Average and the Predictive Indices for the School of Agriculture - Scientific

Table LXIX gives the means and standard deviations of firstsemester average and the forecasting variables employed in the predic­ tion batteries for this group.

It will be noted that the mean semes­

ter average is 1.13 and the standard deviation of this average is .32,, The mean transmuted high school rank is 3.21.

Reference to Table LXII

discloses that these findings are similar to those found for the gen­ eral group of the School of Agriculture. In the summary section, these results will be compared with the corresponding findings of the foregoing groups.

I

TABLE LXIX

MEANS a nd STANDARD DEVIATIONS FOR PREDICTION INDICES AND FIRST-SEMESTER AVERAGE FOR THE SCHOOL OF AGRICULTURE- SCIENTIFIC

Sem.Av.H.S.R.

Voc.

P.R.

Mean

1.13

3*27 53-93 31-17

S.D.

.82

2.20 19.80 5.10

A.P.

E.U. A.lg.

VIB-SI

Chem. L.I.S.

24.63 23.87 26.13 292.4-0 258.86 269.10

A.20

2.70 4-57

57.26

32.20 37.23

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

In Table LXX are listed the standard deviation ratios used in developing the score-form regression equations for the prediction of first-semester average in the scientific agricultural curricula.

TABLE LXX

STANDARD DEVIATION RATIOS USED IN SCORE-FORM REGRESSION EQUATIONS FOR PREDICTION OF FIRST-SEMESTER AVERAGE FOR SCHOOL OF AGRICULTURE - SCIENTIFIC N = 30

T0°-

W M

■

Alg-I

x i

■ •179°

A-p-

x §

H.S.R.

—

.3727

E.U.

—

.0220

P.R.

L.I.S. S.

2.20

-x~ ~ |

= =

-°i H

VIB-SI

°h m ■ S - 32^20

— 57.26

=

‘

2.70 j

-°255

- -1952 =

-3037 -

-1608

• -* -w

.0020

I

I

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

4-

Score-Form Regression Equations for the Prediction of FirstSemester Average for the School of Agriculture — Scientific

The score-form regression equations developed from the data shown in the foregoing tables are listed in Table LXXI.

The multiple

correlations, probable errors of estimate and percents of forecasting efficiency are given in the right-hand side of the table.

A glance at the column of multiple correlations discloses the prognostic effectiveness of the various batteries. range from .616 to .72-4-

The correlations

The last two columns reveal that the cor­

responding probable errors range from .38 to .4-4 and the percents of forecasting efficiency from 20.8 to-32.2.

Reference to the correspond­

ing column in Table LXI indicates that the semester average is fore­ cast more accurately for this group than for the general group of the School of Agriculture. An analysis of the first four batteries discloses that they have practically the same prognostic efficiency. comprises the five test parts.

The first battery

In the second battery Paragraph Read­

ing is eliminatedj in the third Paragraph Reading and English Usage are omitted.

The fourth battery is composed of two variables, the Vo­

cabulary and Algebra test parts.

The probable error of estimate for

these batteries is .44 i^ each case.

When high school rank is added

to the Vocabulary and Algebra test parts, the multiple correlation is increased from .610 to .698 and the probable error of estimate is re­ duced from .44 to .40.

This is shown by a comparison of the fourth

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

and fifth teams.

The effect of augmenting the fifth team with the

Chemist, interest scale and Studiousness Index is seen in the sixth row.

The correlation is increased to .727 and the probable error of

the prediction is lowered to .38. It will be noted that the correla­ tions of the seventh battery, which includes the Chemist interest scale; the eighth battery, in which the Studiousness Index is included, are virtually the sane as the sixth team where both measures are in­ cluded.

The ninth battery comprises the high school rank, the Vocabu­

lary ancf Algebra test parts, the Life Insurance Salesman scale and the Studiousness Index.

This battery possesses the highest correlation,

.735, with semester-average, but fails to yield a smaller probable error of estimate than was found for the three preceding teams.

It

is seen in the tenth row that a battery comprising the Vocabulary and Algebra test parts, high school rank and the Life Insurance Salesman scale gives a multiple correlation of .724. Of the forecasting batteries listed in this table, the most practical and economical is the fifth team, since it satisfies the criterion of containing few items and of having a relatively small probable error of estimate.

Reproduced with permission ofthe copyright owner. Furtherreproduction prohibitedwithout permission.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

TABLE LXXI SCORE-FORM REGRESSION EQUATIONS, MULTIPLE CORRELATIONS, PROBABLE ERRORS OF ESTIMATE AND PERCENTS OF FORECASTING EFFICIENCY FOR THE SCHOOL OF AGRICULTURE - SCIENTIFIC N = 30 i.

Equations

1 2 3 u

5

6 7 a 9 10

R

Voc. (.0073X!

A.P. .0071X2

E.U. .0432X3

Alg. .0904X4

P.R. -.0227X5)

Voc. (.0050X-!

A.P. -.OO28X 2

E.U. .OI85X3

Alg. .0959X4 )

K -2.1122

Voc. (.OO6OX1

A.P. -.0026X2

Alg. .0963X3)

K -2 .34I3

K -I.648O

K -1.6780

Per cent ForeP.E. casting Est. Eff.

.616

.44

21.3

.614

.44

21.1

.610

.44

20.8

.610

.44

20.8

.698

.40

28.4

.727

.38

31.4

Voc. (.0059Xx

Alg. .0954X2)

H.S.R. (.1356X±

Voc. .0091X2

Alg. .0689X3)

H.S.R. (1515X-L

Voc. .OO84X 2

Alg. .OSOSX^

Chem.S. .OO44X4

H.S.R. (.161SX!

Voc. .0097X2

Alg. .O44IX3

Chem.S. .OO57X4 )

-2.5523

.722

.38

30.9

H •5 •R* (.1263XX

Voc. .0069X2

Alg. .0709X3

VIB-SI .OO25X4)

K -2.2341

.718

.38

30.4

H.S.R, (,1354X1

Voc. .OO64X 2

Alg. .O6I5X3

L.I»S. -.OO38X4

.735

.38

32.2

H.S.R. (.UXCK-l

Voc. ■.0079X2

Alg. .05843

L.I.S. -.OO45X4 )

.724

.38

31.1

K -1.6055 VIB-SI .0013X5)

K -2.6590

k:

VIB-SI .OO2OX5) K -.0842

K -.8031

5-

Relationship of Personality and. Interest Measures with FirstSemester Average for the School of Agriculture - Scientific

The correlations of the Personality and interest measures with first-semester average for this group of students are given in Table' LXXII,

^

Similar to the results obtained for the other schools, the personality traits are shown to possess negligible relationship with the criterion for this population also.

Two of the interest scales,

however, yield correlations with first-semester achievement which approach reliability.

These are the Chemist and Life Insurance Sales­

man scales; the correlations are .34-4 and -*350, respectively.

The

Farmer interest scale fails to demonstrate any value for the predic­ tion of first-semester average.

Inspection of the last item in the

table discloses that scores on the Studiousness Index scale correlate

.304 with achievement in the first semester, this correlation approach­ ing significance.

Raw scores were used in computing the foregoing cor­

relations . Since the correlations obtained with the Chemist, Life Insurance Salesman and Studiousness Index scales approached significance, it was thought that their inclusion in the prediction batteries was warranted. It' -was seen in Table LXII that the probable error of estimate was re­ duced from .4,0 to .38 with the addition of these items to a team con­ sisting of high school rank, Vocabulary and Algebra test parts.

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

TABLE LXXII

RELATIONSHIP OF PERSONALITY AND INTEREST MEASURES TO FIRSTSEMESTER AVERAGE FOR THE SCHOOL OF AGRICULTURE - SCIENTIFIC

Semester Average Bernreuter Personality Inventory Bl-N (reversed)

-.0 0 3

.041

B2-S

-.0 4 5

B4-D

.344

Chemist Scale

-.3 5 0

Life Insurance Salesman Scale Farmer Scale

.051

VIB-SI

.304

I

I

Reproduced with permission ofthe copyright owner. Furtherreproduction prohibitedwithout permission.

H.

THE SCHOOL OF AGRICULTURE TWO-YEAR

1. Interrelationships of Prediction Indices and First-Semester Average for the Two-Year Curriculum in Agriculture

The intercorrelations of first-semester achievement and the forecasting variables used in the prediction batteries for the two-year group of the School of Agriculture are presented in Table LXXIII.

The

probable errors of the correlations between the prediction measures and the criterion are given in the column to the left of the dotted line. Examination of the first row discloses that high school rank, the Vocabulary and Arithmetic Processes test parts correlate reliably with semester average for this group; the correlations are .34-0, .406 and .4.80, respectively.

The English Usage and Paragraph Reading test

parts are not closely related to success in the first semester.

Fur­

ther Inspection of this row reveals that the dominance scale and Life Insurance Salesman scale have low negative correlations with the cri­ terion. From the intercorrelations of the test parts, it is seen that each of the verbal parts correlates more highly with the others than with the mathematical part, Arithmetic Processes.

It is noted by in­

spection of the sixth column that the dominance scale is not related significantly

to

high school rank and the test parts.

Similarly,

inspection of the seventh column discloses that the Life Insurance Salesman interest measure does not correlate significantly with high

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

school rank and the test parts.

However, there is some relationship

between the Life Insurance Salesman interest scale and the dominance scale.

This is indicated by a correlation of .304> a figure which

approaches significance. These correlations were employed to obtain the partial re­ gression coefficients necessary for the developing of score-form re­ gression equations.

TABLE LXXIII

INTERRELATIONSHIP BETWEEN PREDICTIVE INDICES AND FIRSTSEMESTER AVERAGE FOR THE SCHOOL OF AGRICULTURE - TWO-YEAR N = 51

Sem.A.v. Sem.Av

P.E.

H.S.R.

.08A

Voc.

.079

P.R.

.093

A.P.

.073

E.U.

.090

B4.-D

.087

L.I.S.

.088

H.S.R.

Voc.

P.R.

A.P.

E.U.

B4--D

L .I.S

•34-0

.4-06

.122

.480

.230

-.288

- .269

.090

-.071

.062

.186

.215

- .206

.506

.254-

.414

.030

.001

.198

•44-9

.155

.160

.287

-.234- - .123 .107

.042 .304

Reproduced with permission ofthe copyright owner. Further reproduction prohibitedwithout permission.

2«

Partial. Regression Coefficients of Prediction Batteries Developed for the Two-Year Curriculum in Agriculture

Table LXXIV lists the partial regression coefficients of the items used in various forecasting teams. It is seen in the first row that the Arithmetic Processes and Vocabulary test parts possess the highest weights in a team composed of the four test parts.

In this same team the English Usage test part

has a negligible weight; the Paragraph Reading test part possesses an appreciable negative weight.

When Paragraph Reading is omitted from

the team, the remaining test parts maintain the same relative posi­ tions; this is seen in the second row.

The third team comprises the

Vocabulary and Arithmetic Processes test parts, the latter part again possessing a somewhat higher weight -than the former.

Examination of

the fourth row reveals that high school rank has been added to the two-variable team.

In this combination, the Vocabulary test part and

high school rank'have approximately the same weights, and both possess lower weights than the Arithmetic Processes test part.

When the Life

Insurance Salesman interest measure and dominance scale are added to the combination of Arithmetic Processes, Vocabulary and high school rank in the fifth and sixth teams, appreciable negative weights result. The score-form regression equations for these teams are list­ ed in Table LXXVII.

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

TABLE LXXIV PARTIAL REGRESSION COEFFICIENTS OF THE ITEMS IN THE PREDICTION BATTERIES FOR THE TWO-YEAR CURRICULUM IN THE SCHOOL OF AGRICULTURE N = 51 Voe.

A.P.

E.U.

P.R.

1

.37014

•A087

.0315

-.1 6 0 4

2

.3088

•A057

-.0142

3

.3037

•A029

A

.2806

.3908

.2895

5

.289A

.3696

.2547

-.1 7 1 3

6

.2689

•A873

.3 AAA

-.3 1 4 6

H.S.R.

L.I.S,

BA-D

-.1018

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

2_. Means and Standard Deviations for Fir st-Semester Average and the Prediction Indices for the Two-Year Curriculum in Agriculture

The data given in Table LXXV are the means and standard de­ viations of the first-semester average and the prediction items for the two-year curriculum in the School of Agriculture.

It was stated

in the description of the subjects that, relative to the populations of the other schools of the college, this group of students is of in­ ferior academic quality and the academic standards are not high.

The

comparatively low mean semester average indicates the inferior academ­ ic achievement of this group. low mean high school rank.

A further indication is found in the

Though the two-year students in agriculture

are not strictly comparable to the other populations studied, the re­ sults of the investigation for this group will nevertheless be compared with those obtained for the other schools in the summary section of this chapter.

TABLE LXXV MEANS ADD STANDARD DEVIATIONS FOR PREDICTION INDICES AND FIRST-SEMESTER AVERAC-E FOR THE SCHOOL OF AGRICULTURE - TWO-YEAR N s 51 Sem.Av.

H.S.R.

Voc.

P.R.

A.P.

E.U.

L.I.S.

B4-D

Mean

.996

5.16

31.61

25.57

19-63

25-43

278,90

4.88

S.D,

.811

1.61

9.86

4-.80

3.94

3.31

35.43

1.59

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

The standard deviation ratios required for the development of the score-form regression equations are given in Table LXXVI.

TABLE LXXVI

STANDARD DEVIATION RATIOS USED IN SCORE-FORM REGRESSION EQUATIONS FOR PREDICTION OF FIRST-SEMESTER AVERAGE FOR SCHOOL OF AGRICULTURE - TWO-YEAR

Voc.

=

.0823

H.S.R.

9.86 A.P. E.U.

P -K -

3.94

- .5037 1.61

=

.2058

= .2450

z i i 3- -

L.I.S. B4-D

35.43

= .°229 = *5101

-169°

Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission.

4*

Regression Equations for Prediction of First-Semester Average for the Two-Year Curriculum in Agriculture

The score-form regression equations, multiple correlations, probable errors of estimate and percents of forecasting efficiency are given for six forecasting teams in Table LXXVII. The first team in the table is composed of the four test parts.

In the second team, Paragraph Reading has been omitted.

The

third team consists of two variables, the Vocabulary and Arithmetic Processes test parts.

Inspection of the corresponding multiple cor­

relations and probable errors of estimate for these teams discloses that the forecasting precision of the two and three variable teams are practically as high as that of the four variable team.

The mul­

tiple correlations are .573 for the first team and .562 for the sec­ ond and third teams, whereas the probable error of estimate is .45 for each of the three teams.

With the inclusion of the high school rank

in the battery composed of the Vocabulary and Algebra test parts, the accuracy of the prediction is somewhat increased.

It is seen in the

fourth row that the combination of these three variables yields a mul­ tiple correlation of .634-. team is .42.

The probable error of estimate for this

The addition of the Life Insurance Salesman interest

scale to the foregoing team increases the multiple correlation to .653 and, correspondingly, reduces the probable error of estimate to .41* A substantial improvement in forecasting first-semester average for this group of students is obtained by including the Life Insurance Salesman

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

and dominance measures in the team composed of high school rank, Vocabulary and Arithmetic Processes test parts.

By examination of

the sixth row, it is seen that the team yields a multiple correla­ tion of .757 and predicts the semester average with a probable error of .35-

Inspection of the last column shows that the corresponding

percents of forecasting efficiency for these teams range from 17.3 to 34*7.

TABLE LXXVII

REGRESSION EQUATIONS, MULTIPLE CORRELATIONS, PROBABLE ERRORS OF ESTIMATE AND PERCENTS OF FORECASTING EFFICIENCY FOR THE TWO-YEAR CURRICULUM IN THE SCHOOL OF AGRICULTURE

Equations

1 2 3 45

6

.P.R. Voc. (.0305X! -.0271X2

A.P. .O84IX3

E.U. K .0077X4)-1.1217

R.

Per­ cent ForeP.E. casting Est. Eff♦

.578

.45

18.4

Voc. (.0254X1

A.P. E.U. K .0835X2 -.0035X3)-!.3577

.562

.45

17.3

Voc. (.0250X!

A.P. K .O829X 2)-1.4215

.562

.45

17.3

H. S.R. (.14-5SX!

Voc. .0231X 2

A.P. K .O8O4X 3)-2.0650

.634

*4-2 22.7

H.S.R. (.12S3X!

Voc. .0238X2

A.P. .O76IX3

.653

.41

24.3

H.S.R. (.1735X!

Voc. .0221X2

K A.P. L.I.S. B-4D .IOO3X3 -.OO72X4 -.0519X5)--.3055 .757

.35

34.7

L.I.S. K .OO39X4)-.8182

1 R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

5.-

Relation of Personality and Interest Measures to First-Semester Average for the Two-Year Curriculum in Agriculture

The relations between freshman achievement and the personality and interest measurements for this group are shown, in Table LXXVIII. It ■wall be noted that the personality traits show low negative relationships with first-semester achievement.

Reference to the prob­

able errors of the correlations reveals that these relationships approach significance. As was found for the other two groups of students in the School of Agriculture, the Farmer 'interest scale is not related significantly to success in the first semester.

The Life Insurance Salesman interest

scale is somewhat negatively correlated with first-semester achievement. This correlation is approximately three times its probable error. It was seen in Table LXXVII that the inclusion of the dominance personality trait measure and the Life Insurance Salesman interest mea­ sure in a forecasting battery for this group of students effected a substantial increase in the accuracy of the prediction.

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

TABLE LXXVIII

RELATION OF PERSONALITY AMD INTEREST MEASURES TO FIRST-SEMESTER AVERAGE FOR THE TWO-YEAR CURRICULUM IN THE SCHOOL OF AGRICULTURE N = 51 Sem. Av. Bernreuter Personality Inventory Bl-N (reversed)

P.E.

-.261

.088

B2-S

-.244

.089

B4-D

-.288

.087

*135

.093

-.269

.088

Fanner Scale Life Insurance Salesman Scale Production Manager Scale

*845

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

172.

I.

SUMMARY SECTION

In this section are presented tables which bring together many of the findings presented in the foregoing sections of this chapter.

There is also a description of the distribution for the

various schools on the Strong Vocational Interest Blanlt.

The tables

are not discussed in detail.

1.

Relationships of the Moore-Nell Test Parts. the Moore-Nell Total Test Score (Parts Unweighted) and the Total Test Score (Parts Weighted) with First-Semester Average for the Seven Populations

In Table LXXIX are presented the relationships obtained be­ tween the Moore-Nell examination and the first-semester average for each population investigated.

Correlations obtained with the indi­

vidual test parts are given in columns two to six.

Column seven shows

the correlation of grades with the total test when the test parts are weighted optimumly.

The relationship of first-semester average to the

total Moore-Nell score with the parts unweighted can be found for each group in the eighth column.

In the last row the median correlation

calculated for the five parts of the test are given. It is seen in the second column that the correlations of the Vocabulary test part with first-semester average range from .198 for the non—technical group in the School of Agriculture to .4-06 for the two-year students in the School of Agriculture.

The median correlation

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

is .287.

In the third column the correlations vdth the Paragraph

Reading test part are listed.

These correlations range from 122 to

.366, the Agriculture Two-Year group possessing the lowest and the

Lower Division group the highest. test part is .220.

The median correlation for this

The low median correlation would seem to indicate

that this test part in its present form has little validity as a fore­ caster of first-semester freshman grades for the populations investi­ gated.

The correlations of the Arithmetic Processes test part with

semester average are given in the fourth column.

These correlations

range from .2.45 to .513, the lowest correlation being vdth the Agri­ culture - Non-Technica.l - group and the highest with Mineral Industries. The median correlation obtained with this test part is .351-

The cor­

relations with the English Usage test part are listed in the fifth column.

The highest correlation, .544-, was obtained vdth the Mineral

Industries population and the lowest, .230, for the two-year and sci­ entific grovips of the School of Agriculture.

The median correlation

of .326 was found for the Engineering students.

For the Algebra test

part the correlations range from .480 for the School of Engineering to .597 for the scientific group in the School of Agriculture.

The median

correlation for this test part is .526. A comparison of the seventh and eighth columns discloses that

1

the correlations obtained vdth the weighted Moore-Nell examination are substantially higher than those found for the unweighted examination for all the populations vdth the exception of the Lower Division and Agriculture - Non—Technical — groups.

,

R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

174.

CO

W O EH O

s

o

H

EH

Ph

P h CO

H M i «si i is Eh gi O

~ o> 'i•f

to to PI •

CP

tM

-t •

o v£) cp •

1 —1 Z> -t •

o to Pi •

Pi - t CP •

SO H

to

fca Eh

O Ph

Cp o

Pi

ip

»

in to

•

3

z r•

m

Pi

H

lf\ •

H cp •

•

£>P •

W

CO CO

§

EH

Ph

Pi