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A COMPARATIVE STUDY OF THE PREDICTIVE VALUE OF STUDENTS’ ACADEMIC PERFORMANCE USING JAMB SCORES AND CGPA (A STUDY OF NNAMDI AZIKIWE UNIVERSITY AWKA)

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A COMPARATIVE STUDY OF THE PREDICTIVE VALUE OF STUDENTS’ ACADEMIC PERFORMANCE USING JAMB SCORES AND CGPA (A STUDY OF NNAMDI AZIKIWE UNIVERSITY AWKA)

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ABSTRACT

The interest in this work is to study the predictive value of

students’ academic performance using JAMB scores and CGPA in

Nnamdi Azikiwe University Awka. In addition the level at which the

divergence in grades started is also of great importance to the

researcher. Four faculties out of nine faculties were selected, from

which two departments each were selected from the already

selected faculties. This made it a total of eight departments

altogether for the study. The (Mahalanobis) generalized distance

concept used to “measure” the intellectual distance between 21

and 22 students reveals that this distance at graduation is far

greater than that at entry point for all the departments studied.

And that there is a gap between these two groups of students at

graduation as well as at entry point. From the findings, it was

gathered that the divergence in grades started after year one,

that is, it rose in year one in most of the departments studied.

Then in the subsequent years, it either rose or fell. The multiple

regression analysis used shows that the entry point scores as well

as the yearly GPAs can be used to predict the FCGPA. A stepwise

regression analysis reveals that the yearly GPAs are the ‘best’

predictors of the FCGPA. The concept of generalized distance 2

p D

reveals that the intellectual distance between 21 and 22 graduates

both at entry point and at graduation is not the same which

means that the intellectual distance at graduation is far greater

than that at entry point. The concept of additional distance due to

extra variates shows that the inclusion of the extra q variates

increases the efficiency of discrimination between the two groups

(21 and 22). A correlation analysis shows that there is both positive

and negative weak correlation between the entry point scores and

the FCGPA for the two groups. Also the coefficient of multiple

determination reveals that over 90% of the total variations in the

FCGPA is accounted for by the yearly GPAs of the two groups.

From the hypotheses tested, it was observed that:

there exists a relationship between the entry point scores,

yearly GPAs and FCGPA for both 21 and 22 students

(graduates).

TABLE OF CONTENT

CHAPTER ONE: INTRODUCTION

1.1 Background of the study – – – – – 1

1.2 Statement of the problem – – – – – 3

1.3 Objectives of the study – – – – – 5

1.4 Basic Assumptions – – – – – 6

1.5 Hypothesis formulation – – – – – 7

1.6 Significance of the study – – – – – 8

1.7 Limitations of the study – – – – – 9

1.8 Organization of the study – – – – 10

viii

CHAPTER TWO: REVIEW OF RELATED LITERATURE

2.0 Introduction – – – – – – – 11

2.1 Review of the Literature – – – – – 11

CHAPTER THREE: RESEARCH DESIGN AND METHODOLOGY

3.0 Introduction – – – – – – – 24

3.1 Population of study – – – – – – 24

3.2 Sources of Data – – – – – – 27

3.3 Problems Encountered during Data collection – 27

3.4 The sampling Technique – – – – – 28

3.5 Concept, operation and Definition of terms – 30

3.6 Research procedures – – – – – 32

3.7 Methods of Data Analysis – – – – – 32

3.8 Distance concept (Mahalanobis D2 Statistic) – 34

3.9 Multiple Regression – – – – – – 38

3.10 Underlying assumptions for regression analysis 40

3.11 Product-moment coefficient of correlation – 41

3.12 Coefficient of Multiple Determination – – 42

3.13 A test for the Hypothesis of equality of two covariance

matrices – – – – – – – – 43

3.14 Test of the Equality of the two mean vectors – 44

3.15 Stepwise Regression – – – – – 45

3.16 Additional distance due to extra variates – – 46

CHAPTER FOUR: ANALYSIS OF DATA

4.0 Introduction – – – – – – – 48

4.1 Test of the equality of two dispersion (covariance)

matrices — – – – – – – – 48

4.2 Correlation Analysis – – – – – – 51

4.3 Multiple regression Analysis – – – – 53

4.4 Distance concept (Mahalanobis) analysis for

21 and 22 – – – – – – 62

4.5 Stepwise regression Analysis – – – – 91

4.6 Multiple regression Analysis Model summary – 95

4.7 Distance concept analysis between males and

females – – – – – – – – 98

4.8 Additional Distance due to Extra variates – – 128

4.9 Test of the equality of two mean vectors for male

and female – – – – – – – 131

4.10 Test of the equality of two mean vectors for

21 and 22 – – – – – – – 139

4.11 Hypothesis Testing – – – – – – 147

CHAPTER FIVE: SUMMARY OF FINDINGS,

CONCLUSIONS AND RECOMMENDATIONS

5.1 Summary of findings – – – – – 150

5.2 Conclusions – – – – – – – – 168

5.3 Recommendations – – – – – – 171

References – – – – – – – – 173

Appendix – – – – – – – – 182

LIST OF TABLES

1.0 The faculties, the departments and the number

of students (graduates) chosen for the study – 26

1.1 Result of correlation coefficients – – – 51

1.2 Result of the additional distance due to extra

variates – – – – – – – – 144

1.3 Result of the intellectual distance between

21 and 22 – – – – – – – – 150

1.4 Result of the intellectual distance between male

and female – – – – – – – 165

1.5 Result of correlation coefficient and coefficient

of multiple determination – – – – – 166

CHAPTER ONE

INTRODUCTION

1.1 Background of the study

Academic programme in Nnamdi Azikiwe University was

founded on the philosophy that knowledge should be

disseminated and propagated without hindrance.

Candidates are admitted into the first degree regular

programmes of the University through the Joint Admissions

and Matriculation Board (JAMB) examinations, direct entry,

pre-science programme, continuing Education Programme

(CEP), and inter-university transfer.

But the researcher based the study mainly on JAMB as a

mode of admission of students in the University. This is

because this examining body (JAMB) was established by the

Federal Government of Nigeria through Act 2 of 1978 to

regularize the intake of students into the Universities and

solve the problem of multiple admissions given to some

candidates at the expense of others. Like other examining

bodies in Nigeria, JAMB has been subjected to a series of

criticisms. The researcher is not interested in these criticisms.

But is interested in finding out at what level during the course

of study of students admitted through JAMB (with high or low

scores) did divergence in grades begin, when compared with

their yearly cumulative grade point averages.

Examination in Nigerian schools is dated back to the

advent of formal education. As a former British colony, the

system of examinations in Nigeria took after the British

system. The importance of examinations in the country’s

education system has been entrenched in the National policy

of education. In the University setting, success in an

examination is being assessed through the cumulative grade

point average obtained by students in all courses registered

from year one to the final year. As such, a student is deemed

to have performed very well to the level of second class

upper division if the cumulative grade point average is

between 3.50 and 4.49, or first class if cumulative grade

point average is 4.50 and above on a 5-point scale. Hence,

the cumulative grade point average determines the success

level of a student from one semester to another. The grading

of the cumulative grade point average is such that 4.50 and

above is first class, 3.50 to 4.49 is second class upper

division (21), 2.40 to 3.49 is second class lower division (22),

1.50 to 2.39 is third class, 1.00 to 1.49 is ordinary pass

degree while below 1.00 is failure.

1.2 Statement of the Problem

Over the years, students have been admitted into the

higher institution of learning in Nigerian Universities mainly

through JAMB. The students at the entry point with high or

low score in JAMB may graduate with a first class, second

class, pass or some may fail. At a certain level in their course

of study, there are divergences of grades / scores. This

implies that some students with high or low scores in JAMB,

at a certain year in their study made grade point averages

which are below or above expectations with regards to their

initial high/low score at entry point.

One wonders at what point/level did this divergence

start. This is the problem of the study. The researcher is

interested in only the students that graduated with a secondclass

upper division and a second-class lower division. To

address the stated problem, the following research questions

were raised:

At what level did the divergence in grades set in?
Is there any correlation between students’ grade point

at graduation and their entry point scores?

What is the between the entry point scores and the

yearly grade point averages of students who graduated

in some selected departments in some faculties with 21

and 22?

Is the ‘distance’ the same in all the selected

departments?

What is the ‘distance’ between the grade point averages

of students with 21 and those with 22?

Is the ‘distance’ the same in all the selected

departments?

What is the ‘distance’ between grade point averages of

male graduates and the grade point averages of female

graduates in the selected departments?

Is the ‘distance’ the same in the selected departments?

1.3 Objectives of the Study

At graduation, students are classified into those with 21 and

above, and those with 22 and below. The objectives of this

study are;

To measure the ‘intellectual distance’ between the two

groups

To determine when this ‘intellectual distance’ started to

appear in their course of studies by working backwards

and examining the contributions of their 4th year work,

3rd year work, their 2nd year work, their 1st year work,

and their JAMB scores which would represent their

“entry behaviour”

To see whether the FCGPA can be predicted on the basis

of the variables mentioned in (2) above;

To choose a subset of the independent variables which

“best” explains the dependent variable;

To measure the ‘intellectual distance ‘ between male

and female graduates;

To test the equality of their mean vectors;
To test the equality of the two covariance matrices for

21 and 22 students;

1.4 BASIC ASSUMPTIONS

The variables are quantitative and continuous;
JAMB scores (entry point scores) and the yearly

grade point averages are the independent variables

while the final cumulative grade point average is

the dependent variable.

The students’ previous study environment is

assumed to be the same with the University study

environment.

1.5 HYPOTHESES FORMULATION

For the purpose of this research, the following

hypotheses were formulated to aid in solving the

aforementioned problems and would be tested for rejection or

acceptance at 5% level of significance:

H0: there is no relationship between the entry point

scores, the yearly grade point averages and the final

cumulative grade point average of graduates with 21 ,

H1: There exists a relationship between their entry point

scores, the yearly grade point averages and the final

cumulative grade point average of graduates with 21;

H0: there is no relationship between the entry point

scores, the yearly grade point averages and the final

cumulative grade point average of graduates with 22 ,

H1: There exists a relationship between their entry point

scores, the yearly grade point averages and the final

cumulative grade point average of graduates with 22 ;

H0: Students (graduates) with 21 do not differ greatly

from those with 22 at graduation ,

H1: Students (graduates) with 21 differ greatly from

those with 22 at graduation.

1.6 SIGNIFICANCE OF THE STUDY

This study will go a long way to:

Provide an insight into students’ academic

performance that help to determine their final

cumulative grade point average ;

Create awareness to students on the dangers of

obtaining a low grade point average at any level in

the course of their study as this determines to a great

extent what their final cumulative grade point

averages will be;

iii. Help staff, academic advisers and lecturers in counseling and

advising students on the merits and demerits of high or low grade

point averages.

1.7 LIMITATIONS OF THE STUDY

The most difficult problems encountered is the volume

of data required. It involved collecting the results of

graduates who made second-class upper division (21), and

second-class lower division(22) from the examination’s office

in the administrative building of Nnamdi Azikiwe University

Awka. Entry point scores (JAMB) of graduates whose results

have been collected were also collected from the record’s

office of the university. As a result of the difficulties involved

in this collection, the researcher limited the data to only 30

graduates each from every selected department in the

faculties of the university. So because of this number, the

researcher did not include first class candidates (graduates)

as their number is not up to thirty. The multistage sampling

method was used.

1.8 ORGANIZATION OF THE STUDY

In this work, Chapter One deals with the introduction of

the study, statement of the problem, objectives of the study,

formulation of the hypotheses, significance and limitations of

the study.

Chapter Two reviewed the literatures related to the

study, whereas chapter three deals with the research design

CHAPTER ONE:

INTRODUCTION

1.1 Background of the study – – – – – 1

1.2 Statement of the problem – – – – – 3

1.3 Objectives of the study – – – – – 5

1.4 Basic Assumptions – – – – – 6

1.5 Hypothesis formulation – – – – – 7

1.6 Significance of the study – – – – – 8

1.7 Limitations of the study – – – – – 9

1.8 Organization of the study – – – – 10

viii

CHAPTER TWO: REVIEW OF RELATED LITERATURE

2.0 Introduction – – – – – – – 11

2.1 Review of the Literature – – – – – 11

CHAPTER THREE: RESEARCH DESIGN AND METHODOLOGY

3.0 Introduction – – – – – – – 24

3.1 Population of study – – – – – – 24

3.2 Sources of Data – – – – – – 27

3.3 Problems Encountered during Data collection – 27

3.4 The sampling Technique – – – – – 28

3.5 Concept, operation and Definition of terms – 30

3.6 Research procedures – – – – – 32

3.7 Methods of Data Analysis – – – – – 32

3.8 Distance concept (Mahalanobis D2 Statistic) – 34

3.9 Multiple Regression – – – – – – 38

3.10 Underlying assumptions for regression analysis 40

3.11 Product-moment coefficient of correlation – 41

3.12 Coefficient of Multiple Determination – – 42

3.13 A test for the Hypothesis of equality of two covariance

matrices – – – – – – – – 43

3.14 Test of the Equality of the two mean vectors – 44

3.15 Stepwise Regression – – – – – 45

3.16 Additional distance due to extra variates – – 46

CHAPTER FOUR: ANALYSIS OF DATA

4.0 Introduction – – – – – – – 48

4.1 Test of the equality of two dispersion (covariance)

matrices — – – – – – – – 48

4.2 Correlation Analysis – – – – – – 51

4.3 Multiple regression Analysis – – – – 53

4.4 Distance concept (Mahalanobis) analysis for

21 and 22 – – – – – – 62

4.5 Stepwise regression Analysis – – – – 91

4.6 Multiple regression Analysis Model summary – 95

4.7 Distance concept analysis between males and

females – – – – – – – – 98

4.8 Additional Distance due to Extra variates – – 128

4.9 Test of the equality of two mean vectors for male

and female – – – – – – – 131

4.10 Test of the equality of two mean vectors for

21 and 22 – – – – – – – 139

4.11 Hypothesis Testing – – – – – – 147

CHAPTER FIVE: SUMMARY OF FINDINGS,

CONCLUSIONS AND RECOMMENDATIONS

5.1 Summary of findings – – – – – 150

5.2 Conclusions – – – – – – – – 168

5.3 Recommendations – – – – – – 171

References – – – – – – – – 173

Appendix – – – – – – – – 182

LIST OF TABLES

1.0 The faculties, the departments and the number

of students (graduates) chosen for the study – 26

1.1 Result of correlation coefficients – – – 51

1.2 Result of the additional distance due to extra

variates – – – – – – – – 144

1.3 Result of the intellectual distance between

21 and 22 – – – – – – – – 150

1.4 Result of the intellectual distance between male

and female – – – – – – – 165

1.5 Result of correlation coefficient and coefficient

of multiple determination – – – – – 166

xii

CHAPTER ONE

INTRODUCTION

1.1 Background of the study

Academic programme in Nnamdi Azikiwe University was

founded on the philosophy that knowledge should be

disseminated and propagated without hindrance.

Candidates are admitted into the first degree regular

programmes of the University through the Joint Admissions

and Matriculation Board (JAMB) examinations, direct entry,

pre-science programme, continuing Education Programme

(CEP), and inter-university transfer.

But the researcher based the study mainly on JAMB as a

mode of admission of students in the University. This is

because this examining body (JAMB) was established by the

Federal Government of Nigeria through Act 2 of 1978 to

regularize the intake of students into the Universities and

solve the problem of multiple admissions given to some

candidates at the expense of others. Like other examining

bodies in Nigeria, JAMB has been subjected to a series of

criticisms. The researcher is not interested in these criticisms.

But is interested in finding out at what level during the course

of study of students admitted through JAMB (with high or low

scores) did divergence in grades begin, when compared with

their yearly cumulative grade point averages.

Examination in Nigerian schools is dated back to the

advent of formal education. As a former British colony, the

system of examinations in Nigeria took after the British

system. The importance of examinations in the country’s

education system has been entrenched in the National policy

of education. In the University setting, success in an

examination is being assessed through the cumulative grade

point average obtained by students in all courses registered

from year one to the final year. As such, a student is deemed

to have performed very well to the level of second class

upper division if the cumulative grade point average is

between 3.50 and 4.49, or first class if cumulative grade

point average is 4.50 and above on a 5-point scale. Hence,

the cumulative grade point average determines the success

level of a student from one semester to another. The grading

of the cumulative grade point average is such that 4.50 and

above is first class, 3.50 to 4.49 is second class upper

division (21), 2.40 to 3.49 is second class lower division (22),

1.50 to 2.39 is third class, 1.00 to 1.49 is ordinary pass

degree while below 1.00 is failure.

1.2 Statement of the Problem

Over the years, students have been admitted into the

higher institution of learning in Nigerian Universities mainly

through JAMB. The students at the entry point with high or

low score in JAMB may graduate with a first class, second

class, pass or some may fail. At a certain level in their course

of study, there are divergences of grades / scores. This

implies that some students with high or low scores in JAMB,

at a certain year in their study made grade point averages

which are below or above expectations with regards to their

initial high/low score at entry point.

One wonders at what point/level did this divergence

start. This is the problem of the study. The researcher is

interested in only the students that graduated with a secondclass

upper division and a second-class lower division. To

address the stated problem, the following research questions

were raised:

At what level did the divergence in grades set in?
Is there any correlation between students’ grade point

at graduation and their entry point scores?

What is the between the entry point scores and the

yearly grade point averages of students who graduated

in some selected departments in some faculties with 21

and 22?

Is the ‘distance’ the same in all the selected

departments?

What is the ‘distance’ between the grade point averages

of students with 21 and those with 22?

Is the ‘distance’ the same in all the selected

departments?

What is the ‘distance’ between grade point averages of

male graduates and the grade point averages of female

graduates in the selected departments?

Is the ‘distance’ the same in the selected departments?

1.3 Objectives of the Study

At graduation, students are classified into those with 21 and

above, and those with 22 and below. The objectives of this

study are;

To measure the ‘intellectual distance’ between the two

groups

To determine when this ‘intellectual distance’ started to

appear in their course of studies by working backwards

and examining the contributions of their 4th year work,

3rd year work, their 2nd year work, their 1st year work,

and their JAMB scores which would represent their

“entry behaviour”

To see whether the FCGPA can be predicted on the basis

of the variables mentioned in (2) above;

To choose a subset of the independent variables which

“best” explains the dependent variable;

To measure the ‘intellectual distance ‘ between male

and female graduates;

To test the equality of their mean vectors;
To test the equality of the two covariance matrices for

21 and 22 students;

1.4 BASIC ASSUMPTIONS

The variables are quantitative and continuous;
JAMB scores (entry point scores) and the yearly

grade point averages are the independent variables

while the final cumulative grade point average is

the dependent variable.

The students’ previous study environment is

assumed to be the same with the University study

environment.

1.5 HYPOTHESES FORMULATION

For the purpose of this research, the following

hypotheses were formulated to aid in solving the

aforementioned problems and would be tested for rejection or

acceptance at 5% level of significance:

H0: there is no relationship between the entry point

scores, the yearly grade point averages and the final

cumulative grade point average of graduates with 21 ,

H1: There exists a relationship between their entry point

scores, the yearly grade point averages and the final

cumulative grade point average of graduates with 21;

H0: there is no relationship between the entry point

scores, the yearly grade point averages and the final

cumulative grade point average of graduates with 22 ,

H1: There exists a relationship between their entry point

scores, the yearly grade point averages and the final

cumulative grade point average of graduates with 22 ;

H0: Students (graduates) with 21 do not differ greatly

from those with 22 at graduation ,

H1: Students (graduates) with 21 differ greatly from

those with 22 at graduation.

1.6 SIGNIFICANCE OF THE STUDY

This study will go a long way to:

Provide an insight into students’ academic

performance that help to determine their final

cumulative grade point average ;

Create awareness to students on the dangers of

obtaining a low grade point average at any level in

the course of their study as this determines to a great

extent what their final cumulative grade point

averages will be;

iii. Help staff, academic advisers and lecturers in counseling and

advising students on the merits and demerits of high or low grade

point averages.

1.7 LIMITATIONS OF THE STUDY

The most difficult problems encountered is the volume

of data required. It involved collecting the results of

graduates who made second-class upper division (21), and

second-class lower division(22) from the examination’s office

in the administrative building of Nnamdi Azikiwe University

Awka. Entry point scores (JAMB) of graduates whose results

have been collected were also collected from the record’s

office of the university. As a result of the difficulties involved

in this collection, the researcher limited the data to only 30

graduates each from every selected department in the

faculties of the university. So because of this number, the

researcher did not include first class candidates (graduates)

as their number is not up to thirty. The multistage sampling

method was used.

1.8 ORGANIZATION OF THE STUDY

In this work, Chapter One deals with the introduction of

the study, statement of the problem, objectives of the study,

formulation of the hypotheses, significance and limitations of

the study.

Chapter Two reviewed the literatures related to the

study, whereas chapter three deals with the research design.

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