statistical modelling of factors affecting students

i

STATISTICAL MODELLING OF FACTORS AFFECTING STUDENTS ACADEMIC

PERFORMANCE IN THE SECOND CYCLE INSTITUTIONS. A CASE SYUDY OF

NSAWAM- ADOAGYIRI MUNICIPALITY, GHANA.

BY

SARKODIE KURTIS OSAFO

(10441973)

THIS THESIS IS SUBMITTED TO THE UNIVERSITY OF GHANA, LEGON IN

PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE AWARD OF THE

MPHIL STATISTICS DEGREE

JUNE 2015

University of Ghana http://ugspace.ug.edu.gh

ii

DECLARATION

Candidate’s Declaration

This is to certify that this thesis is the result of my own work and that no part of it has been

presented for another degree in this University or elsewhere.

SIGNATURE………………………….. DATE……………………………

SARKODIE KURTIS OSAFO

(10441973)

Supervisors’ Declaration

We hereby certify that this thesis was prepared from the candidate’s own work and supervised in

accordance with guidelines on supervision of thesis laid down by the University of Ghana.

SIGNATURE……………………………. DATE………………………..

DR.EZEKIEL N.N. NORTEY

(Principal Supervisor)

SIGNATURE………………………….. DATE…………………………..

DR.FELIX O. METTLE

(Co – Supervisor)


iii

ABSTRACT

Academic performance is vital in education as it helps in the selection and placement of students

from one stage to the other on academic ladder. However, academic performance of students in

the second cycle institutions has continually declined over the last decade. In 2014, approximately

28 percent of the students who sat for the WASSCE had grade A1 to C6 in all the core subjects.

This study identifies statistically significant factors that influence students’ academic performance

in the second cycle institutions in the Nsawam-Adoagyiri Municipality, Ghana. Data was

collected from Seven hundred and forty-four (744) final year students in the two schools located

in the municipality. From a well itemized structured questionnaire that was administered by Mixed

Methods Sampling, information vital to student’s performance was collected on the 744 students.

Factor Analysis with Principal Component Analysis (PCA) was used to reduce the dimensionality

of the data and summarise the critical factors that influence academic performance in the selected

second cycle institutions. The factors were scored based on weights assigned to the variables. The

factor scores were then used to predict the academic performance of the students. The students’

academic performance was measured using the variable Cumulative Continuous Assessment

Marks (CCAM) categorised into two “poor” (CCAM between 0-49%) and “good” (CCAM

between 50-100%). A binary logistic regression model was fitted to the data for all the core

subjects in both schools. The study revealed that teacher instructional strategies is the main factor

influencing academic performance in Nsawam-Adoagyiri Municipality, Ghana. Based on the

mean mark of the two schools in each core subjects, it was established that St. Martin’s Senior

High School performed relatively better in all Core Subjects than Nsawam Senior High School.

The study recommended that, in order to improve students’ academic performance parents are

encouraged to have family size they can adequately cater for, while government among other

things is encouraged to provide schools with adequate learning materials.


iv

DEDICATION

This work is dedicated to my lovely grandmother Comfort Acheampomah and my dearest mother

Mavis Ama Osei. I say thank you very much for your prayers and support.


v

ACKNOWLEDGEMENT

I thank the Almighty God who has given me care, knowledge and the opportunity to pursue

education up to this level.

This work would not have been possible without great support accorded me by various individuals.

I render my sincere gratitude’s to my supervisors; Dr E.N.N. Nortey and Dr. F.O. Mettle for their

countless guidance advice and constructive criticism throughout this work.

I would also thank, Mr Abeku Asare-Kumi and Kwabena Asare all of Department of Statistics

University of Ghana for their services and pieces of advice throughout this work. To Regina

Amissah, Miss Georgina Akoto-Nsiah and my siblings Fredrick Owusu Sarkodie, Prince Amoako

Atta and Bridget Anowa Sarkodie, for their financial assistance and advice, I say the good Lord

continue to bless you.

Lastly, great appreciation to the Assistant Headmasters (Academics) of St. Martin’s Senior High

School (Nsawam) and Nsawam Senior High School and all my friends especially 2015 batch of

MPhil statistics students University of Ghana.


vi

TABLE OF CONTENTS

CONTENT PAGE

Title Page i

Declaration ii

Abstract iii

Dedication iv

Acknowledgement v

Table of Contents vi

List of Tables xii

List of Figures xv

CHAPTER ONE

INTRODUCTION

1.0 Background of the study………………………………………………………….……… 1

1.1 Statement of Problem……………………………………………………………………. .5

1.2 Objectives of the study…………………………………………………………………… 6

1.3 Research Question…………………………………………………………………………6

1.4 Methodology…………………………………………………………………………….…7

1.5 Significance of the study…………………………………………………….…………..... 7

1.6 Limitations………………………………………………………………….………………7

1.7 Organisation of the study…………………………………………………….……………..7

CHAPTER TWO

LITERATURE REVIEW

2.0 Introduction ……………………………………………………………..………………..9


vii

2.1 Theoretical Framework……………………………………………….………………....9

2.2 Empirical Review……………………………………………..…………….………......11

2.3 Factor Analysis…………………………………………………………….….………...16

2.4 Factor scores…………………………………………………………………………….17

2.5 Binary Logistic Regression……………………………………………………………. 18

CHAPTER THREE

METHODOLOGY

3.0 Introduction…………………………………………………………………..……….. 20

3.1 Research Design………………………………………………………………..………20

3.2 Study Population……………………………………………………………….………20

3.3 Determination of Sample size………………………………………………….………21

3.4 Source of Data………………………………………………………………….………22

3.5 Sampling Procedure……………………………………………………………….…...22

3.6 Data Collection …………………………………………………………………….….23

3.7 Method of Data Analysis………………………………………………………………24

3.7.1 Description of Data…………………………………………………………….…..24

3.7.2 Test of Reliability………………………………………………………………….24

3.7.3 Data Analysis…………………………………………………………………..……24

3.7.3.1 Factor Analysis………………………………………………………………...…. 25

3.7.3.1.1 Model Definition and Assumptions………………………………………...…..26

3.7.3.1.2 Methods of Estimating Factor Loadings…………………………………….…29

3.7.3.1.3 Principal Component Method……………………………………….………….30

3.7.3.1.4 Measures of Appropriateness of Factor Analysis…………………………........33

3.7.3.1.5 Choosing Number of Factors to Retain ………………......................................35


viii

3.7.3.1.6 Factor Rotation………………………………………………………………....36

3.7.3.1.7 Factor Scores……………………………………………………………………39

3.7.3.2 Regression Analysis …………………………………………………………….. 41

3.7.3.2.1 Binary Logistic Regression Model and Assumptions……………………….… 41

3.7.3.2.2 Odds and Odds ratio…………………………………………………………… 43

3.7.3. 2.3 Wald Statistics ………………………………………………………………... 46

3.7.3.2.4 Likelihood Ratio Test……………………………………………………….......47

3.7.3.2.5 Test for Goodness of Fit……………………………………………………...... 47

3.7.3.2.6 Pseudo R-square……………………………………………………………….. 48

CHAPTER FOUR

RESULTS OF DATA ANALYSIS

4.0 Introduction……………………………………………………………………………49

4.1 Preliminary Analysis………………………………………………………………. ... 49

4.1.1 Demographic Description………………………………………………………......49

4.1.1.1 Responses on Gender…………………………………………………………… 51

4.1.1.2 Age of Respondents……………………………………………………………... 50

4.1.1.3 Responses on Religion…………………………………………………………... 50

4.1.1.4 Reponses on Region of Birth and Region of JHS………………………………...50

4.1.1.5 Responses on Locality of Residence and

Location of JHS………………………………………………………………….52

4.1.1.6 Responses on Ownership of JHS………………………………………………….52

4.1.1.7 Responses on BECE Aggregate………………………………………………….. 53

4.1.2 Educational, Social and Economic Description……………………………………..53

4.1.2.1 Responses on Current School…………………………………………………….53


ix

4.1.2.2 Responses on Course of study…………………………………………………….53

4.1.2.3 Responses on Mode of Residence…………………………………………………54

4.1.2.4 Responses on Participation in Sporting and

Affiliation to Societies/Clubs……………………………………………………...54

4.1.2.5 Hours spend on the Clubs/Societies and Sporting Activity……………………….55

4.1.2.6 Use of mobile phone and Access to Internet………………………………………56

4.1.2.7 Device use when on Social Media and

Minutes spend on Social Media…………………………………………………..56

4.1.2.8 Hours spend on Television………………………………………………………..57

4.1.2.9 Responses on Mothers and Fathers Age……………………………………….....58

4.1.2.10 Responses on Number of Siblings……………………………………………….59

4.1.2.11 Respondent’s Position of Birth in the Family……………………………………59

4.1.2.12 Respondent’s Parent’s living together……………………………………………59

4.1.2.13 Marital status of Respondents Parents’…………………………………………...60

4.1.2.14 Responses on whom respondents live with……………………………….............60

4.1.2.15 Highest level of Education of respondents’ Parents………………………………61

4.1.2.16 Mothers status of Employment…………………………………………………....61

4.1.2.17 Fathers status of Employment…………………………………………………….62

4.1.2.18 Sponsors of respondents Education……………………………………………….63

4.1.2.19 Respondents responses on Number of Textbooks

in all Subjects…………………………………………………………………….63

4.1.2.20 Distribution of number of Textbooks……………………………………………...63

4.1.2.21 Responses on Extra Classes……………………………………………………….64

4.1.2.22 Number of Hours spend in week on Extra Classes………………………………..64

4.1.2.23 Responses on Place Study…………………………………………………………65


x

4.1.2.24 Responses on Amount of Money spend in a Week………………………………66

4.2 Main Analysis………………………………………………………………………….67

4.2.1 Reliability of the scale……………………………………………………………….67

4.2.2 Factor Analysis………………………………………………………………………68

4.2.2.1 Analysis of the value of KMO…………………………………………………….68

4.2.2.2 Analysing the value of the Bartlett’s test of Sphericity……………………………68

4.2.2.3 Analysis of eigenvalues……………………………………………………………69

4.2.2.4 Rotation sums of squared loadings…………………………………………….......70

4.2.2.5 Analysis based on scree plot……………………………………………………. ...71

4.2.2.6 Determining the number of factors…………………………………………………72

4.2.2.7 Factor Rotation…………………………………………………………………. …73

4.2.2.8 Factor interpretation………………………………………………………………..74

4.2.2.9 Calculating the factor score…………………………………………………………75

4.2.2.10 Summary of results from the Factor Analysis…………………………………….76

4.2.3 Analysis on Binary Logistic Regression……………………………………………..77

4.2.3.1 Summary of Students’ Academic Performance…………………………………..77

4.2.3.1.1 Respondents Performance in Core Subjects (Nsawam SHS)…………………..77

4.2.3.1.2 Respondents Performance in Core Subjects (St. Martin’s SHS)………………..78

4.2.3.2 Descriptive Statistics of students’ Academic Performance………………………..78

4.2.3.2.1 Descriptive Statistics of St. Martin’s SHS………………………………………78

4.2.3.2.2 Descriptive Statistics of Nsawam SHS………………………………………… 79

4.2.3.3 The Model Building………………………………………………………………. 81

4.2.3.3.1 Model Building for Core Mathematics (St. Martin’s SHS)……………………..81

4.2.3.3.2 Model Building for Integrated Science (St. Martin’s SHS)……………………..85

4.2.3.3.3 Model Building for English Language ((St. Martin’s SHS)…………………….88


xi

4.2.3.3.4 Model Building for Social Studies (St. Martin’s SHS)…………………………..91

4.2.3.3.5 Model Building for Core Mathematics (Nsawam SHS)………………………….93

4.2.3.3.6 Model Building for Integrated Science (Nsawam SHS)…………………………..96

4.2.3.3.7 Model Building for English Language (Nsawam SHS)…………………………...98

4.2.3.3.8 Model Building for Social Studies (Nsawam SHS) ………..................................100

CHAPTER FIVE

SUMMARY, CONCLUSION AND RECOMMENDATION

5.1 Summary………………………………………………………………………………103

5.2 Discussion……………………………………………………………………………...104

5.3 Conclusion ……………………………………………………………………………..106

5.3 Recommendation……………………………………………………………………….107

References………………………………………………………………………………….109

Appendix I: Questionnaire…………………………………………………………………114

Appendix II: Results from field data………………………………………………………119

Appendix III: Results from factor analysis……………………………………………..… 126

Appendix IV: Results from binary logistic regression………………………………….…127


xii

LIST OF TABLES

Table Title Page

4.1.1.1 Responses on Gender 50

4.1.1.2 Age of Respondents 51

4.1.1.3 Responses on religion 51

4.1.1.4 Responses on region of birth and region 52

Of JHS

4.1.1.5 Responses on locality of residence and location of JHS 53

4.1.1.6 Responses on ownership of JHS 53

4.1.1.7 Responses on BECE Aggregate 54

4.1.2.1 Responses on current school 54

4.1.2.2 Responses on course of study 54

4.1.2.3 Responses on mode of residence 55

4.1.2.4 Responses on participation in sporting activity and societies/clubs 55

4.1.2.5 Hours spend on the club/societies and sporting activities 56

4.1.2.6 Use of mobile phone and access to internet 57

4.1.2.7 Device use when on social media and minutes spend on social media 58

4.1.2.8 Hours spend on television 59

4.1.2.9 Responses on Mother’s and Father’s Age 60

4.1.2.10 Response on number of siblings 60

4.1.2.11 Responses on position of birth in the family 61

4.1.2.12 Respondent’s parent’s living together 61

4.1.2.13 Marital status of respondent’s parent’s 61

4.1.2.14 Responses on whom respondents live with 62


xiii

4.1.2.15 Highest level of education of respondents parents 62

4.1.2.16 Mother’s status of employment 63

4.1.2.17 Father’s status of employment 64

4.1.2.18 Sponsors of respondents education 65

4.1.2.19 Respondents responses on number of textbooks 65

4.1.2.20 Distribution of number of textbooks 65

4.1.2.21 Responses on extra classes 66

4.1.2.22 Number of hours spend in week 66

4.1.2.23 Responses on place of study 67

4.1.2.24 Responses on amount of money spend in a week 67

4.2.2.1 KMO and Bartlett’s test 69

4.2.2.3 Total variance Explained 69

4.2.2.4 Rotation sums of squared loadings 71

4.2.2.7 Varimax transformation matrix 74

4.2.3.1.1 Respondents performance in core subjects (Nsawam SHS) 77

4.2.3.1.2 Respondents performance in core subjects (St. Martin’s SHS) 78

4.2.3.2.1 Descriptive statistics of St. Martin’s SHS 79

4.2.3.2.2 Descriptive statistics of Nsawam SHS 80

4.2.3.3.1a Classification Table 82

4.2.3.3.1b Classification Table 82

4.2.3.3.1c Variables in the equation 83

4.2.3.3.31d Variables in the equation 84





xiv








4.2.3.3.5b Variables in equation 95


4.2.3.3.6b Variables in the equation 97


4.2.3.3.7b Variables in the equation 99



xv

LIST OF FIGURES

Figure Title

Figure 1 The scree plot for extracted factors 72


1

CHAPTER ONE

INTRODUCTION

1.0 Background of the study

Etymologically, the word "education" is derived from the Latin educatio ("A breeding, a bringing

up, a rearing") from educo ("I educate, I train") which is related to the homonym educo ("I lead

forth, I take out; I raise up, I erect") from e- ("from, out of") and duco ("I lead, I conduct")

(Ety.com, 2011).

Education in its general sense is a form of learning in which knowledge, skills and habits of a

group of people are transformed from one generation to the next through teaching, training or

research. It frequently takes place under the guidance of others, but may also be autodidactic. Any

experience that has formative effect on the way one thinks, feels or acts may be considered edu-

cational.

According to (Opolot and Enon, 1990), education is the basic human right to which every

individual should have access. To many, the key function lies in its ability to offer and hold the

chance to rise in the economic hierarchy. A right to education has been recognised by some

governments. At the global level, Article 13 of the United Nations’ 1966 International Covenant

on Economic, Social and Cultural Rights recognizes the right of everyone to education. Education

is compulsory in most countries (at least the basic level). For various personal, and socio-

economic reasons, some students are not always in school, and some parents choose other forms

of education such as home – schooling and e-learning for their wards. The very nature of education

creates in the minds of those who receive it, attitude, expectation, evaluations and aspiration about

what they study and their future world (Dewey, 2008). Education can take place in formal or

informal educational settings.


http://en.wikipedia.org/wiki/Etymologically

http://en.wikipedia.org/wiki/Homonym

http://en.wiktionary.org/wiki/en:e-#Latin

2

Informal learning is one of three forms of learning defined by the Organisation for Economic Co-

operation and Development (OECD). Informal learning occurs in a variety of places, such as at

home, work, and through daily interactions and shared relationship among members of society.

For many learners this includes language acquisition, cultural norms and manners. It is not

necessarily planned to be pedagogically conscious, systematic and according to subjects, but

rather unconsciously incidental, holistically problem related, and related to situation management

and fitness for life (Dpoulous, 2010). It is experienced directly in its natural function of everyday

life and is often spontaneous.

Formal education is the system of schooling which involve institutionalised teaching and learning

in relation to a curriculum, which in itself is established according to predetermined purpose of

the schools in the system. School systems are sometimes also based on religion which often

influences the curricula used in these schools.

Marret and Tang (1994) reported that formal education appears to overshadow informal

education. They added that, nature of schooling and the way schools have been structured so that

pupils are taught in groups of varying sizes presupposes that someone should be expert in the

management of such groups in order to bring about good examination results.

Every country designs education that will be suitable for its citizens so as to achieve as a whole,

the country’s educational aims and objectives.

Education in Ghana was mainly informal before the arrival of European settlers, who built a

formal education system addressed to the elites. With the independence of Ghana in 1957,

universal education became an important political objective. The magnitude of the task as well as

economic difficulties and political instabilities have slowed down attempted reforms. The

Education Act in 1987, followed by the Constitution of 1992, gave a new impulse to educational

policies in the country. In 2011, according to the ministry of education the primary school net


http://en.wikipedia.org/wiki/Ghana

3

enrolment rate was 84%, described by UNICEF as "far ahead" of the Sub-Saharan average. In its

2013-14 report, the World Economic Forum ranked Ghana 46th out of 148 countries for education

system quality. In 2010, Ghana's literacy rate was 71.5%, with a notable gap between men (78.3%)

and women (65.3%).

Education indicators in Ghana reflect a gender gap and disparities between rural and urban areas,

as well as between southern and northern parts of the country. Those disparities drive public action

against illiteracy and inequities in access to education. Eliminating illiteracy has been a constant

objective of Ghanaian education policies for the last 40 years; the difficulties around ensuring

equitable access to education is likewise acknowledged by the authorities. Public action in both

domains has yielded results judged significant but not sufficient by national experts and

international organizations. Increasing the place of vocational education and training and of ICT

within the education system are other clear objectives of Ghanaian policies in education. The

impact of public action remains hard to assess in these fields due to recent implementation or lack

of data.

The Ministry of Education and Ghana Education Service (GES) is responsible for the

administration and the coordination of public action regarding Education. Its multiple agencies

handle the concrete implementation of policies, in cooperation with the local authorities (10

regional and 216 municipal and district offices). The State also manages the training of teachers.

Many private and public colleges prepare applicants to pass the teacher certification exam to teach

at the primary level. Two public universities and other private university colleges offer special

curricula leading to secondary education teacher certification.

According to NUFFIC (2013), education in Ghana is divided into three phases: basic education

(kindergarten, primary school, and lower secondary school), secondary education (upper

secondary school, technical and vocational education) and tertiary education (universities,

polytechnics and colleges). Thus education is compulsory between the ages of four and fifteen


http://en.wikipedia.org/wiki/UNICEF

http://en.wikipedia.org/wiki/Sub-Saharan_Africa

http://en.wikipedia.org/wiki/World_Economic_Forum

4

(basic education). The language of instruction is mainly English. The academic year usually runs

from September to July inclusive.

The Ghanaian education system from Kindergarten up to an undergraduate degree level takes 20

years.

The ratio of females to males in the total education system was 96.38% in 2011. The adult literacy

rate in Ghana was 71.5% in 2010, with males at 78.3% and females at 65.3%.The youth female

and male ages 15–24 years literacy rate in Ghana was 81% in 2010, with males at 82% and females

at 80% (World Bank, 2013). Since 2008, enrolment has continually increased at all level of

education (pre-primary, primary, secondary and tertiary education). With 84% of its children in

primary school, Ghana has a school enrolment "far ahead" of its sub-Saharan neighbour’s.

Infrastructure has increased consequently in the same period. Vocational Education (in "TVET

institutes", not-including SHS vocational and technical programs) is the only exception, with an

enrolment decrease of 1.3% and the disappearance of more than 50 institutions between the years

2011/12 and 2012/2013. This drop would be the result of the low prestige of Vocational Education

and the lack of demand from industry (GES, 2013).

The contribution of education in both developed and developing countries cannot be

underestimated. It is the key to the doors of every organisation and development of human

resource for both public and private sectors of the economy. Before the Europeans came to Africa,

we were practising indigenous education where emphasis was placed on the individual, and for

that matter, no one was regarded failure (Moumouni, 1991).

With the arrival of the Europeans, a new system was introduced which was titled “training people

for white collar jobs”. This new system of education resulted in the selection of the best product;

this examination was established as a yardstick for this selection.

With this, students who excel in their final examination were made to pursue further those who

fail to perform creditably were made to acquire vocation and other handy-skills. But the number


5

of students who fail to perform creditably continues to rise. Out of the 242,162 candidates who

wrote the West Africa Senior Secondary Certificate examination in the year 2014, 68,062 of them,

representing 28.11 percent, made grades A1 to C6 in at least six subjects, including English

Language and Core Mathematics and are therefore eligible for admission to tertiary institutions

(Teye-Cudjoe, 2014).

A growing concern for government and educationist is the large number of second cycle students

who fail the West Africa Senior Secondary Certificate Examination (WASSCE). Also of concern

is the fact that the proportion of students leaving prior to the completion of study.

Ghana Education Service (GES) which is mandated to monitor the performance of students in

second cycle institutions are increasingly interested in the rationale behind the abysmal students’

performance over the past years, this gives rise to the need to research, collate, analyse and

interpret data, in order to have evidence to inform academic policies that are formulate to improve

student performance, quality teaching and support resource or creating intervention strategies to

mitigate factors that will positively affect student performance at large. This desire for high level

of achievement puts a lot of pressure on students, teachers and schools and in general the

educational system itself. There is no more denying fact that the whole system of education

revolves round the academic achievement of students, though various other outcomes are also

expected from the system. Hence, a lot of the school resources are committed to help students

achieve better in their scholastic endeavours.

1.1 Statement of Problem

Academic performance plays very important role in education. It helps in the selection and place-

ment of students from one stage to another on academic ladder. In most Organisations

and tertiary institutions such as Universities, Polytechnics, Colleges and other research institu-

tions it is used as criteria for awarding qualification and promotion (Frempong 2007). On the job

market, academic performance serves as guideline for which required applications are selected.


6

According to World Bank (2014) government of Ghana, pumps a lot of resources in educational

sector. Ghana in the past decade spends around 25% of its annual budget on education (World

Bank, 2014). But the academic performance of students has continually decline. In 2014, out of

242162 candidates who sat for West Africa Secondary School Certificate Examination

(WASSCE), 68062 representing 28.11 percent made grades A1 to C6 in at least six subjects,

including English Language and Core Mathematics and are therefore eligible for admission to

tertiary institution (Teye – Cudjoe, 2014). The study, therefore anticipate finding out factors that

contribute to the performance of students at the second cycle institutions in Nsawam – Adoagyiri

Municipality, Ghana.

1.2 Objectives of the study

The study aims at modelling factors that affect students’ academic performance in the second cycle

institution. A case study of Nsawam-Adoagyiri Municipality, Ghana.

Specific Objectives

a) Examine the specific factors that affects students’ academic performance.

b) Examine if there exists some association between the factors that affect the students’ aca-

demic performance.

c) Fit a statistical model to identify the relationship between academic performance and

the identified covariates.

1.3 Research Questions

In line with the above objectives, the study poses the following research question:

a) What are the specific major factors that affect students’ academic performance in the sec-

ond cycle institutions in Nsawam-Adoagyiri Municipality?

b) What is the relationship between these factors and students’ academic performance


7

1.4 Methodology

Basically, the study seeks to use two statistical tools, thus Factor Analysis and Binary Logistic

Regression. Statistical software such as Excel (2013) and SPSS 20 were used for the study. In

addition, Cumulative Continuous Assessment Marks of the final year students’ of the second cycle

schools in the Municipality were useful for the analyses.

1.5 Significance of the Study

a) The study is geared towards providing the necessary statistical justification regarding factors

influencing academic performance in the municipality.

b) The study will furnish decision makers and other stakeholders with information regarding spe-

cific major factors that affect students’ academic performance in the second cycle institution in

Ghana as a whole.

1.6 Limitations

Indisputable constraints such as financial and time, other uncontrollable constriction beyond the

control of the researcher may impinge restrictions on the conclusion of the study. Some of these

factors proposed to conflict the study may be data-gathering instruments. In as much as the study

would minimized occurrence of biasedness, unwillingness of respondents to disclose a validated

response to the given questionnaires could falter the true results of the analyses.

1.7 Organisation of the Study

The study comprises five chapters. The introductory chapter is the first and it presents the back-

ground of the study, problem statement, objective, research questions, methodology, significance

of the study and limitations of the study. Chapter two reviews some of the relevant literature re-

lated to the work. It is followed by chapter three which presents an in- depth discussion of the

methodology employed by looking at how the sample size was determined, sampling technique

used and the statistical tools used for the analysis of the data. In chapter four, the data collected is


8

analysed and presents a detailed discussion of the observed results. Summary, conclusion and

recommendation are captured in the fifth chapter.


9

CHAPTER TWO

LITERATURE REVIEW

2.0 Introduction

In this chapter, we will consider theoretical and empirical framework of factors affecting students’

academic performance of published studies at both international and national, review of factor

analysis, binary logistic regression and factor score as variables in subsequent analyses.

2.1 Theoretical framework

The term academic performance has been described by Daniel and Schouten (1970) and Asaolu

(2003) as the grades obtained in a course or group of courses taken by a student at any given time.

It also describes how a person is able to show his or her intellectual abilities. Kenteyky Adult

Education (KYAE) report on Managed Application Fiscal Year (MAFY,2009-10) defines

academic performance and retention as “a process where a student’s success in school is measured

to determine how they stand up to others in the same areas”. Owusu (2011) defined academic

performance as how students deal with their studies and how they cope with or accomplish

different tasks given to them by their teachers. Academic performance is the ability to study and

remember facts and being ask to communicate what is learnt in successful manner.

All schools, scholars and writers in sociology, psychology, educational sciences, statistics and

other disciplines have discussed factors affecting students’ academic performance and various

theories have come out with respect to these factors. Some researchers place emphasize on

individuals internal characteristics (e.g. intelligence, self - concept etc.) and some others consider

external characteristics (family, social status, educational environment etc.) important. On the

other hand, education is one of the most important variables that undermines development.

Developed countries usually have effective educational system but education lacks adequate

infrastructure in developing countries (Ali Poor, 2005).


10

In educational psychology, students’ performance is considered as a product of his learning and

for information on individual learning rate, one should refer to his visible behaviour or to be more

precise see his performance (Garkaza et al, 2011). According to Hillgard and Bauer, the distinction

between learning and performance is the same as the distinction between knowing how to do a

job and actually doing it. It is also believed that individual performance is highly affected by

motivation and emotion, environmental condition, tiredness and illness. So these factors may yield

a fairly accurate indicators of how much he is learning, unless he can show it well (Seif, 2009).

To evaluate students’ performance through their exam scores, Wooten (1998), suggest that one

should consider students talent through their scholastic aptitude test scores, their struggle through

their attendance in classes and their assignment and educational environment through asking about

course material, class hours and classrooms.

Arrington and Cheek (1990), have emphasized the relationship between interest in the field of

study and academic achievement. King and Kotrlid (1995) believe that students wishing to enter

university and their use of logical programs and physical and human equipment’s such as

professor, library and laboratory are among factors explaining academic achievement and quality

of educational institutions. Among these factors, interested in learning, he can handle other factors

and employ them for success and learning. Cheung and Kan (2002) have considered factors

relating to the students’ performance in Hong Kong and indicated that there is a positive

correlation between classroom instruction and previous experience in learning and students.

History tells us that, academic performance was often measured by ear than today. Observations

made by teachers’ in and out of the classroom constituted the chunk of the assessment, but in

recent years numerical methods of ascertaining how a student is performing is used. Functionally,

the tracking of academic performance, according to Owusu (2011), fulfils a number of purposes.

Areas of achievement and failure in students’ academic career need to be evaluated in order to

foster improvement and make full use of the learning process. Results provide a framework for


11

talking about how students fare in school, and constant standard to which all students are held.

Performance results also allow students to be ranked and sorted on a scale that is numerically

obvious, minimizing complaints by holding teachers and schools accountable for the components

of each and every grade.

2.2 Empirical Review

Some of the related studies on factors affecting students’ academic performance are reviewed

below.

AL-Mutairi (2010), conducted a study on the title “Factors Affecting Business Students’ Perfor-

mance in Arab Open University: The case of Kuwait”. In this study, all students who graduated

during the academic year 2009-2010 at AOU-Kuwait branch were the subject of study. Data was

obtained from the record of registration department at the university. Data collected included stu-

dent’s GPA in graduation, major of high school, grade in high school, gender, age, nationality and

occupation. Ordinary Least square (OLS) multiple regression model were conducted and the

model assumed that the student’s GPA depends on the other variables. Based on that the following

model was estimated in order to determine the factors affecting the academic performance of

AOU-Kuwait branch.

GPAt = 𝛽0 + 𝛽1HSS + 𝛽2HSB + 𝛽3AGE + 𝛽4NAT + 𝛽5GENDER + 𝛽6Smart +𝛽7Work + 𝜖𝑡

Where:

GPA = Overall Grade Point Average of the student in graduation

HSS = Score in secondary school certificate examination; expressed in a percentage form

HSB = Branch of study (stream) in secondary school (sciences =1, arts =2, courses 3)

AGE = Age of student upon admission to college (Young < 30, mature > 30).

NAT = A dichotomous variable representing student's nationality (Kuwaiti = 1, Non-Kuwaiti =

2).

Gender = Gender of student (male = 1, female = 2).


12

Smart = Marital status of student (single = 1, married = 2).

Work = A dichotomous variable representing student's occupation (work = 1, Not work = 2).

𝜖𝑡 = The random residuals.

In conclusion, the results revealed that younger students perform better than mature students and

non- national students perform better than male counterparts in line with a significant number of

previous empirical studies. More importantly, the results of the analysis indicated that marital

status plays a significant role in determining the student’s performance by confirming that married

students perform better than non-married counterparts.

In a similar work, Gonzalez-Pieda, et al (2002), used the structural equation model (SEM)

approach to test a model hypothesizing the influence of parental involvement on students’

academic achievement. The theoretical model was contrasted in a group of 12 to 18 years old

adolescents (N=261) attending various educational centres. The results indicate that (a) parental

involvement had a positive and significant influence on the participant’s measured characteristics;

(b) causal attribution was not causally related to self – concept or academic achievement when the

task involved finding causes for success, but, self – concept and causal attribution were found to

be significantly and reciprocally related when the task involved finding causes accounting for

failure; (c) Self – concept was statistically and predominantly causally related to academic

achievement, but not vice versa; and (d) aptitude and self – concept accounted for academic

achievement, although the effect of self – concept was predominant. These results suggest that in

adolescence, cognitive – affective variables become crucial in accounting for academic.

Shoukat et al ;( 2013), on their study of factors contributing to students’ academic performance:

A case study of Islamia University sub-campus, designed a linear model of graduate student

performance. Graduate student academic performance was taken as a dependent variable and

gender, status, residential area, medium of schooling, tuition, study hour and accommodation as

an independent variables. The data were collected from 100 students through separated structured


13

questionnaire from different department of Islamia University of Bahawalpur Rahim Yar Khan

Campus. Simple random sampling technique was employed in the selecting of the sample from

the targeted population. For the analysis, linear regression model, correlation analysis and

descriptive analysis were used. The finding revealed that age, father/guardian social economic

status and daily study hours significantly contribute the academic performance of graduate

students. A linear model was also proposed that will help to improve the academic performance

of graduate students at university level.

In a different study, Diaz (2003), establish a relationships between personal, family and academic

factors that account for school failures, as well as determine how these factors influence each

other. The sample composed of a total of 1178 students from four secondary schools in Almeria

city (Spain) including the four years of Mandatory Secondary Education. In order to collect the

data two measuring instruments were used: an adaptation of the TAMAI (Test Autoevaluativo

multifactorial de Adaptacion Infantil) questionnaire and measurement of school failure. The

hypotheses were fulfilled differentially showing the selective predictive power of the different

contextual variables (family and school related) in accounting for school failure in students of

Secondary Education. Such results offer us very relevant information for better understanding and

for decision – making with an aim towards prevention of school failure during this educational

stage. The results of this survey make clear the direct influence of variables such as parents’

academic level, gender, motivation, relationships between peers and others.

Farooq et al., (2011), in their descriptive study to examine the effect of different factors on students

quality of academic achievement at the secondary school level in metropolitan city of Pakistan,

used a sample size of 600 (300 male and 300 female). The study was delimited to only

demographic factors such as students’ gender, parents’ education, parents’ occupation and socio

economic status. The level of the academic performance was measured by their achievement

scores of the 9th grade annual examination. Standard t-test and ANOVA were applied to


14

investigate the effect of different factors on students’ achievement. The result revealed that socio-

economic status and parents’ education have a significant effect on students’ overall academic

achievement as well as achievement in the subjects of Mathematics and English. The high and

average socioeconomic level affects the performance more than the lower level.

Rubin (1977), in his work ‘Socioeconomic and Academic Factors Influencing College

Achievement and Business Majors’, focused on socioeconomic variables. He included other

independent variables like the education of the parents, hours per week studied (excluding time

spent in class), students’ earnings, family size and the number of times families moved. His

estimated regression model did not produce a good fit. Some of the assumptions he stated did not

hold, for example, the assumption that the education is positively correlated with their child’s

academic success did not hold for either parent. The assumption that students who worked outside

the school they attend make lower grades, perhaps because their study time was more limited, did

not also hold.

Yusif et al., (2011), used binary logit model to investigate the determinant of students’

performance in the final high school examination. Respondents’ background information was

merged with the results of West Africa Senior Secondary School Certificate Examination. A large

number of potential covariates for students, father and mother characteristics was obtained and

therefore exploratory factor analysis was used for data reduction.

To examine the factors influencing students’ performance in the senior high school final

examination, binary dependent variable taking the value 1 if the individual obtained aggregate 24

or less and 0 otherwise. Three equations were estimated, which was of the form;

1 2i i iY X

where Yi is an indicator that is 1 if candidates i had aggregate 24 or better and 0 otherwise. Xi is

a vector of individual students and parent characteristics, it is the error term and 1 is the


15

intercept. The coefficient vector 2 provides an estimate of the impact of students and parents

characteristics on the likelihood of performance in the senior high school examination.

It was found out that 55.3% qualified for post-secondary education. Empirical results revealed

that academic ability and type of school attended are the most important predictors of performance

in the final senior high school examination.

Sumankuro (2015), in his work to investigate into academic performance of students in second

cycle (Safdar Rehman Ghazi, 2013) (Safdar Rehman Ghazi, 2013) institutions in Northern Ghana

revealed that, instructional strategies, demographic factors as well as individual study factors were

found to be significant determinant of students’ performance at WASSCE. Systematic sampling

procedure was employed in choosing 300 respondent for the study. Qualitative and quantitative

methods were employed for data triangulation.

A study aimed at using panel data on student test score to determine the factors influencing

academic performance of Bolgatanga Polytechnic students was conducted by (Luguterah and

Apam, 2013). Data on grade point average (GPA), demographic and socio - economic features

from 131 female and 271 male students were used. The Generalised Linear Model (GLM) was

employed to study the effect of determinant on the differences among students’ academic

performance. The results revealed significant contribution of the predictors to the explanatory

power of the mean GPA score with the exception of semester 3 and the Department of Civil

Engineering. Thus the performance of students in polytechnics improves with decreasing age and

decreasing number of credits hours registered in a given semester. Though students admitted on

the basis of decisive factor and through the Matured Entrance Examination negatively affected

students’ academic performance, departmental affiliation has a positive impact on the

performance of students academically.

Frempong (2007), used multiple regression in his analysis of academic performance of Potsin T.

I Ahmadiyya Secondary School Students and revealed that sex and religious affiliation did not


16

significantly explain students’ academic performance. However, elective subjects, Business and

Home Economics related subjects significantly determine academic performance. In addition the

study revealed that elective subjects accounts for most of the variation in academic performance

than core subjects. Students’ performance in elective subjects was better than performance in core

subjects. He finally developed a regression model which explains 85% variation in students’

academic performance.

Mwinkume in 2007, conducted a study to compare the performance of schools and also find out

whether gender play a major role in performance in the Senior Secondary School Certificate

Examination (SSSCE) results. Six schools in the Cape Coast municipality made up of two co-

education schools and four single- sex schools (two girls schools and two boys schools were

considered). A sample of 6164 candidates was used in the study. All candidates who wrote the

SSSCE from 2003 to 2005 in the selected schools were considered. Multivariate Analysis of

Variance (MANOVA) was used for the analysis and the results revealed that there was general

improvement of results in 2004 and a decreased in performance in 2005 in all the four core subjects

(Mathematics, English Language, Integrated Science and Social studies. Generally it was

observed that the co-education schools performed below the single-sex schools in all disciplines.

The boys were ahead of the female counterparts. On the other hand girls put up a better

performance than boys in the single –sex schools. The best and the least performing schools were

from the single- sex and co- education schools respectively.

2.3 Factor Analysis

Its modern beginning lie in the early-20th century attempts of Karl Pearson, Charles Spearman and

others to define and measure intelligence. Because of this early association with constructs such

as intelligence, factor analysis was nurtured and developed primarily by scientists interested in

psychometrics (Johnson & W.Wichern, 2007) .


17

Argument over the psychological interpretations of several early studies and the lack of powerful

computing facilities impeded its initial development as a statistical method. The advent of high-

speed computers has generated a renewed interest in the theoretical and computational aspects of

factor analysis. Most of the original techniques have been abandoned and early controversies

resolved in the wake of recent development. It is still true, however that, each application of the

technique must be examined on its own merits to determine its success.

Giri (2004), defined factor analysis as multivariate technique which attempts to account for the

correlation pattern present in the distribution of an observable random vector X = (X1; . . . ; Xp)

in terms of a minimal number of unobservable random variables, called factors. In this approach

each component Xi is examined to see if it could be generated by a linear function involving a

minimum number of unobservable random variables, called common factor variates, and a single

variable, called the specific factor variate. The common factors will generate the covariance struc-

ture of X where the specific factor will account for the variance of the component Xi. Though, in

principle, the concept of latent factors seems to have been suggested by Galton (1888) in (Giri,

2004) , the formulation and early development of factor analysis have their genesis in psychology

and are generally attributed to Spearman (1904). He first hypothesized that the correlations among

a set of intelligence test scores could be generated by linear functions of a single latent factor of

general intellectual ability and a second set of specific factors representing the unique character-

istics of individual tests (Giri, 2004). Thurston (1945) extended Spearman’s model to include

many latent factors and proposed a method, known as the centroid method, for estimating the

coefficients of different factors (usually called factor loadings) in the linear model from a given

correlation matrix (Giri, 2004). Lawley (1940) in (Giri, 2004) assuming normal distribution for

the random vector X, estimated these factor loadings by using the method of maximum likelihood.


18

Factor analysis models are widely used in behavioural and social sciences. It is considered as

extension of principal component analysis. Both can be viewed as attempts to approximate covar-

iance matrix. However, the approximation based on the factor analysis is more elaborate (Johnson

& W.Wichern, 2007). The primary question in factor analysis is whether the data is consistent

with a prescribed structure.

Also, number of variables per component is somewhat important. Monte Carlo study by

Guadagnoli and Velicer (1988) according to Harris (2001) recommended the following:

a. Component with four or more loadings above 0.60 in absolute value are reliable regardless

of sample same.

b. Components with about 10 or more low (0.40) loadings are reliable as long sa sample size

is greater than about 150.

c. Components with only a few low loadings should not be interpreted unless sample size is

at 300.

2.4 Factor score

Following an exploratory factor analysis, factor score may be computed and used in subsequent

analyses. Factor scores are composite variables which provide information about an individual’s

placement on factor(s).

Once a study has used Exploratory Factor Analysis (EFA) and has identified the number of factors

or components underlying a data set, he/she may wish to use the information about the factors in

subsequent analyses (Gorsuch, 1983). To use EFA information in follow-up studies, the researcher

must create scores to represent each individual’s placement on the factor(s) identified from the

EFA (DiStefano et al., 2009). These factor scores may then be used to investigate the research

question of interest.

Kawashima and Shiomi (2007) in (DiStefano et al., 2009) used EFA with a thinking disposition

scale. The analyses uncovered four factors related to high school students’ attitude towards critical


19

thinking. Using students’ factor scores, Analysis of Variance was conducted by factor to

investigate student differences in attitude by scale level and gender.

Again, (Bell et al., 2003) in their cognitive elements underlying reading adopted Exploratory

Factor Analysis (DiStefano et al., 2009). After the factor solution was determined, factor scores

were calculated for each factor and were computed for each factor and were used in the follow-up

multiple regression analyses to investigate the capability of factors in predicting selected reading

and writing skills.

2.5 Logistic Regression

Logistic regression is an extension of linear regression that allows us to predict categorical

outcomes based on one or more predictor variables. Basically there are two models for which

logistic regression is applied; which Binary logistic regression and Multinomial logistic

regression. The Binary logistic regression is typically used when the dependent variable is

dichotomous and independent variables are either continuous or categorical variables. But in the

situation where the dependent/response variable is not dichotomous and can take two or more

cases a multinomial logistic regression is employed. This often produces similar result to the

binary case. The dichotomous response variable in logistic is often labelled “success” and

“failure” of which the probability of success is of great concern to us. Unlike linear regression

model which predict a numerical estimate for the response variable, logistic regression model

predicts the probability of event occurring. It can be applied to model a wide variety of real life

problem.

For instance, Aromolaran et al., (2013), in their empirical survey study used a data collected from

six hundred (600) students across different department and class study using a 28 item structured

questionnaires administered by quota sampling method, a non – probability sampling technique


20

in Yaba College of Technology, Yaba , Lagos. Pearson correlation test of existence of linear rela-

tionship between variable of study, Chi Square test for association of factors, and a four predictors

binary logistic regression was fitted to the data. The students’ academic performance was meas-

ured using GPA/CGPA categorised into two “poor” (GPA/CGPA between 0 and 2.49) and good

(GPA/CGPA between 2.50 and 4.00). Four factors; mothers’ education level, living togetherness

of parents, student class and weekly income/allowance; are found to influence students’ academic

performance. The four factors were fitted into a predictive binary regression model for log-odds

in favour of poor performance as Loge { 𝜋

1−𝜋} = 0.122 - 0.092𝑋1 + 0.479𝑋2 – 0.383𝑋3 – 0.411𝑋4.

Where 𝑋1 is weekly income/allowance, 𝑋2 represents parents living together, 𝑋3 is the mother’s

education level and 𝑋4 represents year.

In summary there has been a lot of research into factors affecting student academic performance.

Most of these researches use regression analysis, multivariate analysis of variance and others in

their analysis. The multivariate methods involving factors analysis used to identify the latent

variables affecting student academic performance in second cycle institutions before a model is

fitted with respect to their academic performance demonstrate the uniqueness of this work. This

work looks to add to the body of evidence and provide literature in Ghanaian context.


21

CHAPTER THREE

METHODOLOGY

3.0 Introduction

This chapter outlines the research methodology employed to achieve the objectives of the study

which were set out in chapter one. The chapter discusses the study design, followed by the study

population, sample size estimation and sampling technique, method of data collection, data explo-

rations (preliminary analysis) and the tools used for the data analysis.

3.1 Research Design

The study design adopted in this work was quantitative. In this approach, a sample of the popula-

tion was selected and an information was gathered on them. Hence, the information gathered from

the respondents was used to make generalizations which cover the entire population from which

the participants were taken. The information on the sample was collected through questionnaire

administration.

The study choose quantitative design because the outcome of the study would be used to general-

ised to cover the entire student population

3.2 Study Population

Nsawam – Adoagyiri Municipality is located in the Eastern part of Ghana. Its capital is Nsawam

and has two Government Assisted Senior High School. Namely St. Martin’s Senior High School

(Smarts) and Nsawam Senior High School (Nsasco). St. Martin’s SHS has a student population

of two thousand two hundred and thirty nine (2239) comprising of one thousand, one hundred and

forty- four (1144) males and one thousand and ninety-five (1095) females. Out of that, there are

six hundred and ninety-four (694) final year students of which 374 are males and 320 are females.

Nsawam SHS on the other hand has a student population of one thousand and eleven (1011) of

which 579 are males and 432 are females. The final year students of Nsawam SHS are 280 com-

prising 147 males and 133 females. St. Martin’s SHS offer five different programmes i.e. General


22

Arts, General Science, Home Economics, Agriculture Science and Business while Nsawam SHS

does Visual Arts with four of the above programme with exception of Business. The target sample

were all final year students from the schools populations.

3.3 Determination of Sample Size

Ascertaining the sample size for the study was very crucial and there was no mysterious way that

will help us obtain a perfect sample size for this study. According to Tabachnick and Fidell (1996),

correlation tend to be less reliable when estimated from small samples. Therefore it is important

that the sample size be large enough that correlation are reliably estimated. The required sample

size also depends on the magnitude of the population correlation and the number of factors.

The study will employ factor analysis as a statistical tool for the analysis of data. In factor analy-

sis, much attention has been given to the issue of sample. It is an accepted fact that the use of

larger samples in application of factor analysis tends to provide results such that sample factor

loadings are more precise estimates of population loadings and are also more stable; or less vari-

able, across repeated sampling (MacCallum et al., 1999). Despite general agreement on this mat-

ter, there is considerable divergence of opinion and evidence about the question of how large the

sample is should be to adequately achieve these objective. Recommendation and finding about

this issue are diverse and often contradictory.

A wide range of recommendation regarding sample size in factor analysis has been proposed.

These guidelines are stated in terms of either sample size N or the minimum ratio of N to the

number of variables p. Gorsuch (1983) recommended that N should be at least 100. Comrey and

Lee (1992) offered a rough rating scale for adequate sample size in factor analysis. They stated

that 100 = poor, 200 = fair, 300 = good, 500 = very good and 1000 or more = excellent. They

proposed that researchers should obtain 500 or more observations whenever possible in factor

analysis. Cattell (1978), claimed the minimum desirable N for factor analysis should be 250 or

more. And Cattell (1978), again recommended that the ratio of N:p for factor analysis should in


23

the range of three to six. Based on the recommendation from the literatures reviewed, a sample

size of 800 is used and according to Camrey and Lee (1992), it is “very good”.

3.4 Source of Data

The study used only final year students of both schools. The reason being that the study aims at

fitting a statistical model of factors affecting students’ academic performance at second cycle

institution and at that level students’ continuous cumulative assessment marks is only available

when students get to the final year. Because of this reason, students in Senior High School One

and Two (SHS 1and 2) were exempted from the study.

3.5 Sampling Procedure

The sampling procedure used in getting the sample for this study is the Mixed Methods (MM)

Sampling strategies. It involves selection of units or cases for a research study using both

probability sampling and purposive sampling (Teddlie and Yu, 2007).

Cluster sampling was initially used to group all SHS in the country (Ghana) into blocks (based on

the District in which the school is located). Purposive sampling, which involves taking a random

sample of a small number of units from a larger target population (Kemper et al.,2003) was used

to select all SHS in Nsawam- Adoagyiri Municipality block. The block was purposely selected to

focus on one district due to time constraints and cost involved in traveling from one district to the

other. Stratified sampling was finally used to divide the schools population into different

subpopulation. Thus; (SHS1, SHS2 and SHS3) and the entire subpopulation from SHS3 were used

for the study.


24

3.6 Data Collection

The study made use of both primary and secondary data. The secondary data included data on the

academic performance of students whereas primary data was collected through questionnaire ad-

ministration.

The questionnaires were responded to by only students in their final year of study as indicated

earlier of which the majority were General Art’s students and they responded very well.

The questionnaire was designed in four parts (from Part A to Part D) the least number of questions

in a part was ten, the longest part had twenty-six questions and on the average there were eighteen

questions in a part. See Appendix I for questionnaire. Part A and Part B of the questionnaire had

both types of items which are open and closed ended questions. The Part C and Part D asked the

respondents to indicate the degree of agreement or disagreement using a five-point Likert Scale.

The form of administration was self – administration. This form was used because it was a Senior

High School community and again students in their final year were used and it was therefore

presumed that students would understand the questions and answer accordingly without the

researcher’s assistance and the second reason was time constraint.

In all eight hundred (800) questionnaires were distributed in the two Senior High Schools in the

Municipality, Fifty-seven (57) of them were discarded because respondents did not provide

answers to some questions or their answers were not properly recorded. In all seven hundred and

forty-three (743) were valid for analysis. The mean response which is considered neutral value

was substituted for the missing responses of the questionnaires that were retained. Naresh (2004),

argued that the mean remains unchanged and other statistics such as correlation are not affected

much.


25

3.7 Method of Data Analysis

This section entails description of the data, procedures for the data analysis and discussion of the

underlying theories.

3.7.1 Description of Data

Tables were basically used to present the descriptive statistics of the data, frequencies were mainly

used and a few cross tabulations in describing the nature of the data. The tables depicted more

characteristics (total number of respondents, and cumulative percentages) of the data as compared

to charts.

3.7.2 Test of Reliability

When you are selecting scales to include in your study it is important to find scales that are reliable.

The internal consistency of the items in Part C and Part D of the questionnaire were checked using

Cronbach’s alpha coefficient. Reliability comes to the forefront when variables developed from

summated scales are used as predictor components in objective model. Since summated scales are

an assembly of interrelated items designed to measure underlying constructs, it is very important

to know whether the same set of items would elicit the same responses if recast and re-

administered to the same respondents. When items are used to form a scale they need to have

internal consistency. The items should all measure the same thing so they should be correlated

with one another. Ideally, the Cronbach alpha coefficient of a scale (rating scale; 1=poor,

5=excellent) should be a score of 0.7 or higher (Briggs and Cheek, 1986).

The reliability of a scale can vary depending on the sample. It is therefore necessary to check that

each of your scales is reliable with your sample.

3.7.3 Data Analysis

Two different statistical tools were used to analyse the data. Firstly, factor analysis was used to

reduce the variables to a number of smaller factors. And binary logistic regression was used to fit


26

a model; using student academic performance as dependent variable and the factor scores (from

factors extracted using the factor analysis) as predictors.

3.7.3.1 Factor Analysis

Hair et al.,( 2006), stated that, for the past decade factor analysis has experienced a massive usage

in all field of business related research and that as the number of variables to be considered

increases, so does the need for increased knowledge of the structure and interrelationship of the

variables. Factor analysis has numerous application. For example;

1. It can be employed in market segmentation for identifying the underlying variables on

which customers can be grouped.

2. Factor analysis can be used to determine the brand attributes that influence consumer

choice.

3. Factor analysis can be used in advertising industry to understand the media consumption

habits of the target market.

The study uses factor analysis because of its ability to examine the underlying patterns or rela-

tionships for a large number of variables and to determine whether the information can be sum-

marized in a smaller set of factors or components. A large number of variables are used for the

study and hence the need to be reduced and summarized for further analysis.

Factor analysis is a multivariate technique use to examine how underlying factors influence the

response on a measured variables (Decoster, 1998). It is the general name denoting a class of

procedure primarily used for data reduction and summarization. The intent of factor analysis is to

determine the number of specific factors that accounts for the variation and covariation among set

of observed measures, commonly called indicators.

According to (Johnson and Wichern, 2007), the factor model is motivated by the following

argument: Suppose variables can be grouped by their correlation. That is suppose all variables

within a particular group are highly correlated among themselves but have relatively small


27

correlation with variables in a different group. Then it is conceivable that each group of variables

represent a single underlying construct or factors that is responsible for the observed correlation.

Factor analysis is helpful in achieving the following:

- To identify underlying dimension or factors, that explains the correlations among a set of

variables.

- To identify a new, smaller set of uncorrelated variables in subsequent multivariate analysis.

3.7.3.1.1 MODEL DEFINITION AND ASSUMPTIONS

According to (Hardle and Simar, 2007), the aim of factors analysis is to explain the outcome of 𝑝

variables in the data matrix Χ using fewer variables, the so – called factors. Ideally all the

information in Χ can be reproduced by a smaller number of factors. These factors are interpreted

as latent (observed) common characteristics of the 𝑥𝜖𝑅𝑃. The case described occurs when every

observed x = (𝑥1, … 𝑥𝑝)T can be written as;

,

1

k

j jl l j

l

X q f

𝑗 = 1, … , 𝑝 (1)

where 𝑓𝑙 for 𝑙 = 1, … , 𝑘 denotes the factors.

The number of factors k, should always be much smaller then p. For instance, in psychology x

may represent p results of a test measuring intelligence scores. One common latent factor

explaining 𝑥𝜖𝑅𝑝 could be the overall level of intelligence. In marketing studies, x may consist of

p answers to a survey on the levels of satisfaction of the customers. These p measures could be

explained by common latent factors like the attraction level of the product or the image of the

brand, and so on. These p measures could be explained by common latent factors (Hardle and

Simar, 2007).


28

Consider a p-dimensional random vector X with mean 𝜇 and covariance matrix 𝑣𝑎𝑟(𝑥) = Σ.

A model can be written for X in matrix notation as;

X F (2)

where F is the k- dimensional vector of the k factor. The factor model (2), assumes that the factors

F are centered, uncorrelated and standardized: 𝐸(𝐹) = 0 𝑎𝑛𝑑 𝑣𝑎𝑟(𝐹) = 𝐼𝑘.

It is established practice in factor analysis to split the influences of the factors into common and

specific ones. There are, for instance, highly informative factors that are common to all of the

components X and factors that are specific to certain component. The factor analysis model used

in praxis is generalisation of (2):

X F (3)

where λ is a (p × k) matrix of the (non-random) loadings of the common factors and 𝜀 is a (p × 1)

matrix of the (random) specific factors. It is assumed that the factor variables F are uncorrelated

random vectors and that the specific factors uncorrelated and have zero covariance with the

common factors.

According to Johnson & Wichern (2007), model (3) assumes the following:

( ) 0E F ( ) ( )Cov F E FF I ( ) 0E

( ) ( )Cov E

1

2

0 . . . 0

0 . . . 0

. . .

. . .

. . .

0 .

p

and that F and 𝜀 are independent so

( , ) ( , ) 0Cov F E F


29

These assumptions and the generalized factor model (3) constitutes the orthogonal factor model.

Model (3) implies for the components of 1( ,... )T

PX X X that

1

k

J jl l j j

l

X q f

, 𝑗 = 1, … , 𝑝 (4)

where 𝑢𝑗 = mean of the variable j, 𝜀𝑗 = jth specific factor, 𝐹𝑙= 𝑙th common factor and 𝑞𝑗𝑙 = loading

of the jth variable on the 𝑙th factor.

Using Model (4) we can deduce that; 2

1

( )k

xjxj j jl jj

l

Var X q

The quantity 22

1

k

j jll

qh

is called communality and Ψ𝑗𝑗 the specific variance. Thus the

covariance of X can be written as;

( )( )TE X X

( )( )TE F F

( ) ( )T T TE FF E

( ) ( )TVar F Var

T (5) Thus

Variance = communality + specific variance

The jth communality is the sum of squares of the loadings of the jth variable on the common

factors.

In sense, Hardle & Simar (2007) stated that, the factor model explains the variations of X for the

most part by a small number of latent factors F common to its p components and entirely explains

all the correlation structure between its components, plus the error 𝜀 which allows specific

variations of each component to enter. The specific factors adjust to capture the individual

variance of each component.


30

Factor analysis relies on the assumptions presented above and if the assumptions are not met, the

analysis may not be genuine. The objective of factor analysis is to find the loadings 𝜆 and the

specific variance Ψ.

3.7.3.1.2 Method of Estimating Factor Loadings

Given the observations 𝑥1, 𝑥2, … 𝑥𝑝 on p, generally correlated, variables factor analysis seeks to

answer the question, ‘Does the factor model; 𝑋 − 𝜇 = 𝜆 𝐹 + 𝜀, with a small number of factors

adequately fit the data? In essence, we tackle this statistical model-building problem by trying to

verify the covariance relationship in 𝑋 − 𝜇 = 𝜆 𝐹 + 𝜀 (Johnson &Wichern, 2007).

The sample covariance matrices S is an estimator of the unknown population covariance matrix

∑. If the off – diagonal elements of S are small or those sample correlation matrix R essentially

zero, the variables are not related, and a factor analysis will prove useful. In these, situation, the

specific factors play the dominant role, whereas the major aim of factors analysis is to determine

a few important factors (Johnson &Wichern, 2007).

(Johnson &Wichern, 2007), however stated that, if ∑ appears to definite significantly from a

diagonal matrix, then a factor model can be considered, and the initial problem is one of estimating

the factor loadings 𝜆 and specific variance Ψ.

Factor extraction involves determining the smallest number of factors that can be used to best

represent the interrelations among the best set of variables. There are variety of approaches that

can be used to identify (extract) the number of underlying factors or dimensions. Some of the most

commonly available extraction technique are; principal component, maximum likelihood,

unweighted least square and generalised least square, principal axis method, etc.

The principal component method is used in this study because, the study has a lot of variables and

needed to be reduced to fewer variables such that the manipulation of the data becomes easier.

And primary concern of principal component is to determine the minimum number of factors that

will account for maximum variance in the data for use in subsequent analysis such as regression


31

model and the study will make use of regression model. Again it was chosen because it does not

make strong distributional assumptions. Normality is important only to the extent that skewness

or outliers affect the observed correlations or if significance tests are performed, it is based on

correlations. Independent sampling is required and the variables should be related to each other

(in pairs) in a linear fashion. Finally many of the variables should be correlated at a moderate level

(Leech, Barrett and Morgan, 2005).

3.7.3.1.3 Principal Component Method

From a random sample 𝑥1,. . . 𝑥𝑝, we obtain the sample covariance matrix S and then attempt to

find and estimator �̂� that will approximate the fundamental expression in (2) with S in place of

∑:

ˆ ˆS (6)

In principal component approach, we neglect �̂� and factor S into 𝑆 = 𝜆�̂�. In order to factor S, we

use spectral decomposition,

S LDL (7)

where L is an orthogonal matrix constructed with normalised eigenvector (𝑙1 1 𝑙𝑖 = 1) of S columns

and D is a diagonal matrix with the eigenvalues 𝜃1, 𝜃2, … 𝜃𝑝 of S on the diagonal:

D =

1

2

0 . . . 0

0 . . . 0

. . .

. . .

. . .

0 .

p

To finish factoring LDL in S LDL into ˆ ˆ we observe that since the eigenvalues 𝜃𝑖 of the

positive semi definite matrix S are all positive or zero, we can factor D into;

1 1

2 2D D D (8)


32

Where 𝐷1

2⁄ =

1

2

0 . . . 0

0 . . . 0

. . .

. . .

. . .

0 .

p

With this factoring of D, in expression (7) becomes:

1 1 12 2 2S LDL LD D L

1 12 2( )( )LD LD

This is of the form ˆ ˆS , but we do not define �̂� to be 𝐿𝐷1

2⁄ because 𝐿𝐷1

2⁄ is k×k, and we are

seeking a �̂�, that is p×k with k ˂ p. We therefore define D1 = 𝑑𝑖𝑎𝑔 (𝜃1, 𝜃2, … 𝜃𝑝) with k the largest

eigenvalues 𝜃1 ˃ 𝜃2 ˃ … ˃𝜃𝑝 and 𝐿1 = ( 𝑙1, 𝑙2, … 𝑙𝑝) containing the corresponding eigenvectors.

We then estimate 𝜆 by the first k columns of 𝐿𝐷1

2⁄ :

�̂� = 𝐶1𝐷1

12⁄ = (√𝜃1 𝑙1,√𝜃2 𝑙2, … √𝜃𝑝 ) (9)

where �̂� is p x k, 𝐶1 is k x p and 𝐷1

12⁄ is k x k.

The jth diagonal element of �̂��̂� is the sum of squares of the jth row of �̂� or2ˆ ˆ

k

j j jl

l

q .

Hence to complete the approximation of S in expression (6), we define

2ˆ ˆ

k

jj jl

l

S q (10)

and write ˆS (11)

where Ψ = 𝑑𝑎𝑔(Ψ1, Ψ2, … Ψ𝑝). Thus in (10) the variances on the diagonal of S are modelled

exactly, but the off-diagonal covariances are only approximate. From the equation


33

ℎ𝑗 2 = ∑ 𝑞𝑘

𝑙=1 𝑗𝑙

2 (12)

which is the sum of squares of the jth row of 𝜆 ̂.The sum of squares of the lth column of 𝜆 ̂is the

lth eigenvalue of S:

2 2

1

ˆ ( )p p

jl l jl

j j

q l

2

1

p

l jl

j

L

l (13)

By expression (8) and (9), the variance of jth variable is partitioned into a part due to the factors

and a part due to the variables:

2 ˆ

jj j jS h (14).

Thus the jth factor contributes 𝜆𝑗𝑙2 to 𝑆𝑗𝑗. The contribution of the lth factor to the total sample

variance 𝑡𝑟 (𝑆) = 𝑆11 + 𝑆22 + ⋯ + 𝑆𝑃𝑃 is therefore,

Variance due to jth factor 2 2 2 2

1 2

1

ˆ ˆ ˆ ˆ...p

jl l l pl

j

q q q q

(15),

which is the sum of squares of loadings in the jth column of ̂ . By (13), this is equal to the lth

eigenvalue, 𝜃𝑙. The proportion of total sample variance due to the lth factor is therefore,

2

1

( ) ( )

p

jl

j l

q

tr s tr s

(16)

Rencher (2002), stated that, if the variables are not commensurate, we can use standardized

variables and work with the correlation matrix R. The eigenvalues and eigenvectors of R are then

used in place of S in (9) to obtain estimates of the loadings. Since the emphasis in factor analysis

is on reproducing the covariances or correlations rather than the variances, use of the correlation


34

matrix R is more appropriate. In applications, R often gives better results than S. If we are

factoring R, the proportion corresponding to (16) is

2

1

ˆ

( )

p

jl

j l

q

tr R p

(17)

where p is the number of variables.

We can assess the fit of the factor analysis model by comparing the left and right sides of (11).

The error matrix comparing the left and right sides of ˆ ˆ ˆ( )E S has zeros on the diagonal

but nonzero off-diagonal elements. If the eigenvalues are small, the residuals in the error matrix

are small and the fit is good (Rencher, 2002).

3.7.3.1.4 Measures of Appropriateness of Factor Analysis

For appropriateness of factor analysis, the variables must be correlated. If the correlations between

all the variables are small, factor analysis may not be appropriate. Also, to decide whether or not

the data are appropriate for factor analysis, a number of measures are used for this purpose.

1. Correlation matrix: A correlation matrix is a lower triangle matrix showing the simple

correlation, r, between all possible pairs of variables included in the analysis. The diagonal

elements, which are 1 are usually omitted. High correlations among the variables indicate

that the variables can be grouped into homogeneous sets of variables such that each set of

variables measure the same underlying factors. On the other hand low correlations among

the variables signify that the variables are a group of heterogeneous variables.

2. Bartlett’s test of Sphericity: It is used to examine the hypothesis that the variables are

uncorrelated in a population. Thus all diagonal elements are 1 and all off- diagonal elements

are 0. If the significant value for the test is less than our alpha level, we reject the null

hypothesis that the population matrix is an identity matrix. The significant value for the


35

analysis leads to rejection of the null hypothesis and conclude that there correlation in the data

set that are appropriate for factor analysis. The test statistic is given by;

𝜒2 = −2 {1 −1

6𝑝𝑛(2𝑝2 + 𝑝 + 2)} 𝐼𝑛 Λ (18) Where

1

1

Geometric meanΛ

Arithmetic mean 1

n

2pn

j2

j j

p

jj

jp

(19) Where

𝜃𝑗 = (1,2, … 𝑝) are the eigenvalues of the component factors, p is the number of indicator

variables and n is the sample size. The test statistic has a chi-square distribution with degrees of

freedom equal to 1

2 (p -1) (p + 2). At an α–level of significance, a large value of 𝜒2 than the

corresponding table value of 𝜒𝛼, (𝑃−1)(𝑃+2)21

2 leads to the rejection of the null hypothesis. From

equation (18), it can be observed that the statistic is greatly dependent on the sample size (n). If n

is very large, the value of 𝐼𝑛Λ causes the statistic to be large. This makes results of the Bartlett’s

test of Sphericity highly dependent on the sample size.

3. Kaiser- Meyer- Olkin Measure of Sampling Adequacy: KMO Measure of Sampling Adequacy

is an index used to examine the appropriateness of factor analysis. High values (between 0.5 and

1.0) indicates factor analysis is appropriate and values below 0.5 imply that factor analysis may

not be appropriate. Interpretive adjective for KMO Measure of Sampling Adequacy are: in the

0.90 and above as marvellous, in the 0.80’s are meritorious, in the 0.70’s are middling, in the

0.60’s are mediocre, in the 0.50’s as miserable and below 0.50 as unacceptable. Kaiser and Rice

(1974) suggested that the overall KMO measure should exceed 0.8 although a measure of above

0.6 is acceptable. Again, Kaiser (1970) proposed a measure of sampling adequacy (MSA). This

measure is given by:

MSA =∑ 𝑟2

𝑗≠𝑙

∑ 𝑟2+∑𝑡𝑗𝑙2

𝑗≠𝑙 (20)


36

where 𝑟𝑖𝑗2 is the square of an element from R and 𝑡𝑗𝑙

2 is the square of an element from

𝑇 = 𝐷𝑅−1𝐷, with 𝐷 = [(𝑑𝑖𝑎𝑔 𝑅−1)1

2⁄ ]-1. As 𝑅−1 approaches a diagonal matrix, MSA

approaches one.

In summary, there are many data sets to which factor analysis should not be applied. If the

scree plot does not have a pronounced bend or the eigenvalues do not show a large gap around

one, then R is likely to be unsuitable for factoring. In addition, the communality estimates after

factoring should be fairly large.

3.7.3.1.5 Choosing Number of Factors to Retain

There is always the question of, ‘how many factors to retain?’ There is no definitive answer to

this question. There are various techniques that can be used to assist in the decision concerning

the number of factors to retain. However, this study will consider three (3) of this techniques as

proposed by Hardle & Simar (2007); (a) we choose p equal the number of factors necessary for

the variance accounted for to achieve a predetermined percentage of the total variance tr(S) or

tr(R). This approach is particularly applied in the PC method. By expression (16), the proportion

of total sample variance (variance accounted for) due to lth factor from S is

2

1

( )

p

jl

j

q

tr s

.

The corresponding proportion from R is 2

1

ˆp

jl

j

q

p

as in equation (17). The contribution of all p

factors to tr(S) or p is therefore 2

1 1

ˆpk

jl

j l

q

, which is the sum of square of all elements in �̂�. This

sum of square is equal to the sum of the first p eigenvalues or the sum of all k communalities.

Thus we choose p sufficiently large so that the sum of communalities or the eigenvalues

constitutes or relatively large portion of tr(S) or k. (b) The second method we will consider is

Kaiser’s criterion or eigenvalue rule – using this rule, we retain only factors with eigenvalue equal


37

or greater than one for further investigation. In essence, this is like saying that, unless a factor

extracts at least as much as the equivalent of one original variable, we drop it. This criterion was

proposed by Kaiser (1970), and is probably the most widely used. However Naresh (2004),

observed that, if the number of variables is less than 20, this approach will results in a conservative

number of factors. (c) The last technique employed by this study is Catell’s scree test. This is a

graphical method first proposed by Catell (1966). With the eigenvalue ordered from the largest to

the smallest a scree plot is a plot of 𝑞𝑗 versus 𝑗 – the magnitude of an eigenvalue versus its number.

To determine the appropriate number of components, we look for an elbow (bend) in a scree plot.

Catell recommend retaining all factors above the elbow in the plot, as these factors contribute the

most to the explanation of the variance in the data set.

When the data set is successfully fitted by factor analysis, all the three techniques will almost

always yield the same value of k, and there will be a little question as to what this value should

be.

3.7.3.1.6 Factor Rotation

Although the initial or unrotated factor matrix indicates the relationship between the factors and

individual variables, it seldom results in factors that can be interpreted, because the factors are

correlated with many variables. Therefore, through rotation the factor matrix is transformed into

a simpler one that is easier to interpret.

In rotating the factors, we would like each factor to have nonzero, or significant, loadings or

coefficients for only some of the variables. Likewise, we would like each variable to have nonzero

or significant loadings with only a few factors, if possible with only one.

The estimated loading matrix �̂� can be rotated to obtain

ˆ* M (21)

where M is orthogonal, since MM I .

The rotated loadings provide the same estimate of the covariance matrix as before:


38

ˆ ˆ* *

ˆ

ˆ ˆ ˆ (22)

S

MM

The equation (22), indicates that the residual matrix, ˆ ˆ ˆnS remains unchanged. Moreover,

the specific variance Ψ𝑖,the communalities2ˆlh ,are unaltered.

If a rotation in which every point is close to an axis can be achieved, then each variable loads

highly on the factor corresponding to the axis and has small loadings on the remaining factors.

Consequently, mere observations are made on which variables are associated with each other is

named accordingly.

To achieve the aims of factor rotation, two different forms are considered; thus oblique and

orthogonal rotation. The rotation is called oblique rotation when the axes are not maintained at

right angles, and the factors are correlated. Sometimes, allowing for correlations among factors

can simplify the factor pattern matrix. Oblique rotation should be used when factors in the

population are likely to be strongly correlated.

The rotation is called orthogonal rotation if the axes are maintained at right angles. The rotation

in (22) involving an orthogonal matrix is orthogonal rotation. The original perpendicular axes are

rotated rigidly and remain perpendicular. In orthogonal rotation, angles and distances are

preserved, communalities are unchanged, and the basic configuration of the points remains the

same. There are different types of orthogonal rotation; these include Varimax, Quartimax,

Equamax, etc. but the method of orthogonal rotation used is the Varimax method. The most

commonly used method for rotation is the varimax procedure. This is an orthogonal method of

rotation that minimizes the number of variables with high loadings on a factor, thereby enhancing

the interpretability of the factors. This is achieved by maximizing the variance of the squared


39

loading across variables, subject to the constraint that the communality of each variable is

unchanged. That is for any factor

2 2

1

( )p

jl l

j

l

q q

Xp

4 2

1 1

2

( )p p

jl jl

j j

p q q

p

(23)

Where Xl is the variance of the communalities of the variables within factor 𝑙 and 𝑞𝑙2 is the average

squared loading for factor 𝑙. The total variance for all factors is given by:

1

k

l

l

X X

2

4 2

1 1

21

p p

k ij jlj j

l

p

p

q q

=

2

4 2

1 11 1

2

pkpk

jljll jl j

p p

q l

(24),

since the number remains the same, maximizing equation (24) becomes:

2

4 1

1 1

pk

pk jlj l

ijl j

pXp

qq

(25)

In words 1

(var ( ) )K

J

X ianceof the squareof scaled loading for lth factor

.

Effectively, maximising X corresponds to “spreading out” the squares of the loadings on each as

much as possible.


40

3.7.3.1.7 Factor Scores

Factor scores are composite scores estimated of each respondent on the derived factors. These

quantities are often used for diagnostic purposes, as well as inputs to a subsequent analysis. The

goal of this study is to reduce the original set of variables to a smaller set of factors for the use of

further analysis and it is therefore useful to compute factor scores for each respondent.

Conceptually, the factor score represent the degree to which each respondent scored high on the

group of items with high factor loadings. Thus, high values on the variables with high loadings on

a factor will result in a higher factor score (Hair et al., 2006).

According to (DiStefano et al., 2009), there are two main classes of factor score computation

methods: refined and non-refined.

Non-refined methods are relatively simple, cumulative procedures to provide information about

individuals’ placement on the factor distribution. The simplicity lends itself to some attractive

features, that is, non-refined methods are both easy to compute and easy to interpret. Refined

computation methods create factor scores using more sophisticated and technical approaches.

They are more exact and complex than non-refined methods and provide estimates that are stand-

ardized scores (DiStefano et al., 2009).

The study will employ the Refined Method to compute the factor scores for the further analysis.

This procedures may be applied when both principal components and common factor extraction

methods are used with exploratory factor analysis. DiStefano et al.,( 2009) stated that resulting

factor scores are linear combinations of the observed variables which consider what is shared

between the item and the factor (i.e., shared variance) and what is not measured (i.e., the unique-

ness or error term variance) (Gorsuch, 1983).The most common refined methods use standardized

information to create factor scores, producing standardized scores similar to a Z-score metric,

where values range from approximately -3.0 to +3.0. However, instead of unit standard deviation,

the exact value can vary. Methods in this category aim to maximize validity by producing factor


41

scores that are highly correlated with a given factor and to obtain unbiased estimates of the true

factor scores (DiStefano et al., 2009). Furthermore, these methods attempt to retain the relation-

ships between factors.

The factor scores for the jth factor may be estimated as follows:

𝐹𝐽 = 𝑊𝐽1𝑋1 + 𝑊𝐽2𝑋2 + ⋯ + 𝑊𝐽𝑃𝑋𝑃 (26)

Where FJ = estimate of jth factor

Wj = Weight or factor score coefficient

Xj = jth standardized variable or the mean correlated value and

p = the number of variables.

The factor score coefficient, used to combine the standardized variables are obtained from the

factor score coefficient matrix. There are several means of estimating the factor scores by the

refined method but the study uses the regression approach.

The expression in (26), can be written in matrix form as:

�̂� = 𝑋�̂� (27)

Where �̂� is an n×m of m factor scores for the n individual, X is an n ×p matrix of observed variables

and �̂� is a p×m matrix of estimated factor score coefficient.

For standardised variables:

𝐹 ̂= 𝑍�̂� (28)

Equation (28) can be written as:

1

𝑛𝑧1�̂� =

1

𝑛 𝑧1𝑧�̂� (29)


42

Or 𝛽 = 𝑅�̂� as 1

𝑛(𝑧1𝑧) = 𝑅 and

1

𝑛𝑧1�̂� = 𝛽

Therefore the estimated factor score coefficient matrix is given by

�̂� = 𝑅−1𝛽 (30)

And the estimated factor score is also of the form:

�̂�= 𝑍𝑅−1𝛽 (31).

3.7.3.2 Regression Analysis

Regression analysis is used for explaining or modelling the relationship between a single variable

Y, called the response, output or dependent variable: and one or more predictor, input, independent

or explanatory variables; 𝑋1,…,𝑋𝑝. When p = 1, it is called simple regression but when p˃1 it is

called multiple regression or sometimes multivariate regression. When there is more than one Y,

then it is called multivariate multiple regression. But where the response variable (Y) of interest

has only two possible qualitative outcome, and therefore can be represented by a binary indicator

variables taking on values 0 and 1 is referred to as binary logistic regression. The use of simple,

multiple or multivariate regression cannot be used a hence binary logistic regression is employed

in such cases. The study make use of binary logistic regression to establish a relationship between

student academic performance (coded as Li =0, if grade point is between 0 – 49 and Li =1, if the

grade point is 50 – 100) and number of predictors (factors extracted using PCFA) since the re-

sponse variable is dichotomous labelled; “good” and “poor”.

3.7.3.2.1 Binary Logistic Regression model Assumptions

Consider a multiple linear model of the form;

𝐿𝑖 = 𝛽0 + 𝛽1𝑋𝑖1 + ⋯ + 𝛽𝑘𝑋𝑖𝑘 + 𝜀𝑖; (32)

where 𝐿𝑖 = 0,1; 𝑖 = 1,2, … , 𝑛


43

Since Li is 0 or 1 the ( )iE L for each iX becomes the proportion of the observations at iX for

which Li=1. This can be expressed as;

𝐸(𝐿𝑖) = 𝑃(𝐿𝑖 = 1) = Δ𝑖

1 − 𝐸(𝐿𝑖) = 𝑃(𝐿𝑖 = 0) = 1 − Δ𝑖 (33) The distribution

𝑃(𝐿𝑖 = 0) = 1 − Δ𝑖 𝑎𝑛𝑑 𝑃(𝐿𝑖 = 1) = Δ𝑖

The expression (32), is known as the Bernoulli distribution (Rencher and Schaalje, 2008).

Let 0 1( , ,..., )k and 1 2(1, , ,..., )i i i ikX X X X . By expression (32) and (33), we can deduce

that

( )i iE L X (34)

With variance 2

( ) ( )i i iVar L E L E L

= Δ𝑖(1 − Δ𝑖) (35)

From expression (33) and (34), we can now write variance as;

1( ) (1 )Var L X X

The expression (32), can be written in matrix notation form as:

iX (36)

The multiple logistic regression function is given as:

exp

( )1 exp( )

XE L

X

(37)

And that is extended as:

1

( ) 1 exp( )E L X

(38)


44

The logit transformation: 1

In

(39). And that leads to logit response, or linear pre-

dictor:

X (40)

The multiple logistic regression model can therefore be stated as follows;

Li are independent Bernoulli random variables with expected values 𝐸(𝐿𝑖) = Δ𝑖 where

exp

( )1 exp

i

i i

i

XE L

X

(41)

The 𝑋 observations are considered to be known constant. Also, the predictor variables may be

quantitative, or they may be qualitative and represented by indicator variables.

The following assumptions are adhere to when using binary logistic regression.

1. It does not need a linear relationship between response variable and explanatory variables.

2. Normality of the predictor variables and the error term (residuals) are not need under this model.

3. A large sample size is need when considering a binary logistic regression to yield a consistent

estimates and better predictors.

4. Homosciedacity assumption is not needed under binary logistic regression model.

5. Independence of the explanatory variables, so as to avoid multicolinearity is observed.

3.7.3.2.2 The odds and odds ratio

In logistic regression analysis, the odds refer to the ratio the probability of an event occurring to

the probability of the same event not occurring. Thus is;

( 1/ )( 1)

( 0 / )

P L X xodds L

P L X x

(42)


45

Where “odds” (L=1) is the odds of good academic performance

P (L=0/x) is the probability that a student performs poorly given a set of explanatory variables.

P (L=1/x) is the probability of good performance given set of explanatory variables.

From the Binomial logistic regression, we let ( 1)p L and ( 0) 1p L hence the odds

is given by;

Odds 1

As already stated

1

iIn X

exp1

iX

(43)

Equation (43) is the model for the odds, and we can see from the odds model that odds increase

multiplicatively with x .

If the odds of poor academic performance is greater than one it implies that, the probability of

poor performance is greater compare to good academic performance. A value less than one indi-

cates a higher probability of good academic performance than that of poor academic performance.

The odds ratio on the other hand is a measure of effect size describing the strength of association

or non-independence between two binary data values. The odds ratio treats the two variables being

compared symmetrically, and can be estimated using some of non-random sample.

The odds ratio is the ratio of the two odds, defined as;

Odds ratio 1

2

odd

odd


46

So the odds of event occurring 1 to the odds of the event not occurring 0 is given by

Odds ratio

1

1

0

0

1

1

(44)

the odds ratio for a variable in logistic regression represents how the odds change with a one unit

increase in that variable, holding all variables constant.

In fitting the model, we shall utilize the method of maximum likelihood to estimate the parameters

of the multiple logistic response function in (41), where the parameters in this study is the factors

extracted using the PCFA.

The log-likelihood function for multiple logistic regression is:

1 1

1 expn n

i i i

i i

InL L X In X

(45)

Numerical search procedure would be used to find the values of 𝛽0, 𝛽1, … , 𝛽𝑘 that maxim-

ise 𝐼𝑛 𝐿(𝛽). These maximum likelihood estimates will be denoted by 𝑏0, 𝑏1, … , 𝑏𝑘.

The fitted logistic response function and fitted values according to, Kutner et al. (2005) can then

be expressed as follows;

1exp

ˆ 1 exp( )1 exp( )

X bX b

X b

(46)

1exp

ˆ 1 exp( )1 exp( )

i

i i

i

X bX b

X b

(47)

Where

X′𝑏 = 𝑏0 + 𝑏1𝑋1 + ⋯ + 𝑏𝑘𝑋𝑘

𝑋𝑖′𝑏 = 𝑏0 + 𝑏1𝑋𝑖1 + ⋯ + 𝑏𝑘𝑋𝑖𝑘


47

The study shall rely on standard statistical package for logistic regression to conduct the numerical

search procedures for obtaining maximum likelihood estimates.

After fitting the model, the study will want to examine the contribution of individual predictors.

Thus examine the regression coefficient. In logistic regression, the regression coefficients repre-

sent the change in the logit for each unit change in the predictor. There are several different tests

designed to assess the significance of an individual predictors but the study will employ Wald

Statistics and the likelihood ratio test

3.7.3.2.3 Wald Statistics

The Wald statistics (WS) is used to assess the significance of individual coefficient in the model

by testing the null hypothesis;

0ˆ: 0H ( jX is not related to the response)

It is the ratio of the square of the regression coefficient to the square of the standard error of the

coefficient and is asymptotically distributed (Menard, 2002). Its test statistics is given as:

𝑍𝑘 =𝑏𝑘

𝑠[𝑏𝑘] (48)

where Z is the standard normal random variable and s(bk) is the estimated approximate standard

deviation of bk. The WS follows a chi-square with one degree of freedom and has its limitations;

thus, when regression coefficient is large, the standard error of the regression coefficient also tends

to be large increasing the probability of the Type –II error. Again, the WS tends to be biased when

data are sparse (Cohen et al., 2002).

3.7.3.2.4 Likelihood Ratio Test

The likelihood ratio test for a particular parameter compares the likelihood of obtaining the data

when the parameter is zero (𝐿0) with the likelihood (𝐿1) of obtaining the data evaluated at the

MLE of the parameter. The test statistics is calculated as follows:


48

00 1

1

2 ( ) 2 2L

In LR In InL InLL

(49)

The test statistics is compared with a 𝜒2 distribution with 1 degree of freedom. The change in

−2𝑙𝑜𝑔 − 𝑙𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 is generally more reliable than the Wald statistics. If the two disagree as to

whether the predictor is useful to the model trust the change in−2𝑙𝑜𝑔 − 𝑙𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑.

3.7.3.2.5 Test for Goodness of Fit

The appropriateness of the fitted logistic regression will be examined. Goodness of fit test provide

an overall measure of the fit of the model, and are usually not sensitive when the fit is poor for a

few cases (Kutner et al., 2005).

The Hosmer – Lemeshow (HL) Test will be used to measure the appropriateness of the fitted

model. The HL test uses a test statistic that asymptotically follows a 𝜒2 distribution to assess

whether or not the observed event rates match expected events rates in subgroups of the model

population. It allows any number of predictor variables, which may be categorical or continuous.

The HL test specifically identifies subgroup as deciles of fitted factor value.

The test statistics of Hosmer –Lemeshow is given by:

2

11

O En i iHL

N P Pi i i

(50)

where 𝑂𝑖, 𝐸𝑖 , 𝑁𝑖, 𝑃𝑖 denote the observed events, expected events, observations predicted factor for

the ith factor decile group, and n is the number of groups.

The number of factor groups may be adjusted depending on how many fitted factor are determined

by the model. This helps to avoid singular deciles groups. The HL statistics indicates a poor fit if

the significant value is less than 0.05


49

3.7.3.2.6 Pseudo R-Square

Pseudo R2 provides further statistics that may be used to measure the usefulness of the model

similar to the coefficient of determination (R2) in linear regression. The Cox and Snell and the

Nagelkerke R2 are two such statistics. The Nagelkerke is an adjusted version of the Cox and Snell,

R2 covers the full range from 0 to 1, and therefore it is often preferred. The R2 statistics indicates

effect size; thus how useful the explanatory variables are in predicting the response. The statistics

is mostly useful when comparing models. The test statistic is given by

2

tan

1 ,full

cons t

LLPseudoR

LL (51)

Where

fullLL : Log likelihood of the full model (chosen)

tancons tLL : Log likelihood of the model with constant only


50

CHAPTER FOUR

RESULTS OF DATA ANALYSIS

4.0 Introduction

This study used primary data solicited from SHS final year students of Nsawam-Adoagyiri

Municipality, in assessing factors affecting academic performance of students in the second cycle

institutions and fitting a statistical model that differentiates a poor academic performance and

good academic performance. Statistical tools such Cronbach Alpha, factor analysis (was used for

data reduction and summarisation) and binary logistic regression (was used for the statistical

model in favour of poor academic performance). This chapter is in three sections, the first section

presents the results of preliminary analysis, and the second presents the main analysis followed

by the last section which discusses the results of both analysis.

4.1 Preliminary Analysis

This section entails the results of the descriptive statistics of the data, frequency tables were mainly

used to depict percentages of respondent under various variables.

4.1.1 Demographic description

This subsection shows the summary of the following variables; Gender, age, religious affiliation,

region of birth, locality of residence, region of JHS, location of JHS, ownership of JHS and BECE

aggregate.

4.1.1.1 Responses on Gender

As displayed in the table below, out of 743 respondents used for the study, 375 representing 50.5%

were males and 368 representing 49.5% were females.

Table 4.1.1.1 Gender of Respondents

Sex Frequency Percent Cumulative Percent

Male 375 50.5 50.5

Female 368 49.5 100.0

Total 743 100.0

Source: Field data, 2015


51

4.1.1.2 Age of Respondents

None of the respondents were below 14years of age. Almost all of the respondents are aged 14 to

19 years. Thus 642 (86.4%) are aged 14 to 19 years while only 101 (13.6) are aged 20 years and

above.

Table 4.1.1.2 Age of Respondents

Age Frequency Percent Cumulative Percent

14-19 642 86.4 86.4

20+ 101 13.6 100.0

Total 743 100.0


4.1.1.3 Religion of Respondents

Majority of the respondents for this study were Christians. As depicted in the table 4.1.1.3, 93.8%

thus 697 of the respondents are Christians and 44 students constituting 5.9% are Muslims. Two

(2) respondents are affiliated to other religious bodies.

Table 4.1.1.3 Religion of Respondents

Religion

Frequency Percent Cumulative Percent

Christian 697 93.8 93.8

Muslim 44 5.9 99.7

Others 2 .3 100.0

Total 743 100.0


4.1.1.4 Region of Birth and Region of J.H.S of Respondents

The distribution in the various regions indicates that most of the respondents were born in Eastern

Region (46%) followed by Greater- Accra Region which forms 31.8% of the total population. The

region with the least respondents was Upper West Region with only 2 students. In addition Upper

East and Northern Region had the same number (7) of respondents, given 0.9% each. Four (4)

constituting 0.5% of the students were born outside the country as shown in the Table 4.1.1.4.


52

Table 4.1.1.4 Respondent’s Region of Birth and Region of J.H.S

Region

Birth J.H.S

Frequency Percent Frequency Percent

Ashanti 32 4.3 10 1.3

Brong-Ahafo 11 1.5 6 .8

Central 41 5.5 18 2.4

Eastern 342 46.0 384 51.7

Greater-Accra 236 31.8 303 40.8

Northern

Upper East

Upper West

Volta

Western

Others

7

7

2

39

22

4

.9

.9

.3

5.2

3.0

.5

1

3

0

9

9

0

.1

.4

.0

1.2

1.2

0

Total 743 100 743 100


From Table 4.1.1.4, majority of the respondents attended J.H.S in the Eastern region followed by

Greater-Accra region with a student population of 303 forming 40.8%. Again, 32 respondents

given 4.3 percent were born in Ashanti region while 1.3 percent of the respondents attended JHS

in Ashanti region.

Furthermore, Central and Western Regions were moderately represented with 41 and 22

respondents respectively having been born in those regions. Out of 743 students 18 and 9 of the

students had their JHS education in Central and Western regions respectively. Brong Ahafo and

the three Northern Regions were least represented in the study with Upper West recording zero

(0) with respect to respondents who had their JHS in that region. Brong Ahafo had six (6)

representing 0.8% of the total population who had their JHS education in the region and eleven

(11) of the respondents were born in the region.

The four (4) respondents who were born outside the ten regions had their JHS education in Ghana.


53

4.1.1.5 Responses on Locality of Residence and Location of J.H.S

Out of 743 respondents used for this research, 478 representing 64.1% resided in urban areas, 178

forming 24% resided in rural areas and 89 students constituting 12% permanently stay in Regional

capitals as delineated in table 4.1.1.5

Table 4.1.1.5 Responses on Locality of Residence and Location of JHS

Location

Residence JHS


Urban 476 64.1 272 36.6

Rural 178 24.0 344 46.3

Regional Capital

Total

89

743

12.0

100

127

743

17.1

100


As shown in Table 4.1.1.5, although 24% reside in rural areas, a small proportion 17.1% (127

respondents) out of the entire population had their JHS located in the rural areas. Additionally,

344 respondents constituting 46.3% have their JHS located in the urban areas (thus recording the

highest figure in terms of location of JHS).

Moreover, Regional capitals were moderately represented with 36.6% (272 students), haven their

JHS located in those areas. From the above one can conclude that minority of the respondents had

their JHS in the so called deprived schools since 17.1% out of the total percentage of respondents

had their JHS located in rural areas.

4.1.1.6 Responses on Ownership of JHS

Out of 743 respondents, 392 constituting 52.8% of the population used for the study attended

Public JHS and 351 which is little below half forming 47.2% had their JHS education in Private

institutions as indicated in the table 4.1.1.6.

Table 4.1.1.6 Responses on Ownership of JHS

Ownership Frequency Percent Cumulative Percent

Public 392 52.8 52.8


54

Private 351 47.2 100.0

Total 743 100.0

4.1.1.7 Responses opinion’s on BECE Aggregate

It is shown in table 4.1.1.7 that, 4.0% of the respondents had an aggregate 15 to 19. With 191 of

the respondents fallen in the grade range 30 and above given us a 25.7% while little below that

had 25 to 29 given a percentage of 25.3.

It was evident in table 4.1.1.7 that 106 respondents had aggregate 10 to 14 forming 14.3% and as

few as 82 respondents which is 11.0% had 6 to 9. It is only a small proportion thus is 19.7% that

had 20 to 24.

Table 4.1.1.7 Responses opinion’s on BECE Aggregate.

Aggregates Frequency Percent Cumulative Percent

6-9 82 11.0 11.0

10-14 106 14.3 25.3

15-19 30 4.0 29.3

20-24 146 19.7 49.0

25-29 188 25.3 74.3

30+ 191 25.7 100.0

Total 743 100.0


4.1.2 Educational, Social and Economic description

This items shows the educational, social and economic status of the respondents.

4.1.2.1 Responses on Current School

With reference to the table 4.1.2.1, majority of the respondents (544) representing 73.2% attended

St. Martin’s SHS while the rest of the population are students from Nsawam SHS.

Table 4.1.2.1 Current School Name

School Frequency Percent Cumulative Percent

St.Martin's

SHS 544 73.2 73.2

Nsawam SHS 199 26.8 100.0

Total 743 100.0


4.1.2.2 Responses on Course of study


55

As shown in Table 4.1.2.2, 355 (47.8%) of students offered General Arts which was the highest

course offered by the respondents. This was followed by Home Economics with a student’s

population of 114 representing 15.3% while a small percentage (3.5%) of the respondents read

Visual Arts. General Science and Business were fairly represented with 113 and 93 respondents

respectively.

Table 4.1.2.2 Course of Study

Courses of study Frequency Percent Cumulative Percent

General Science 113 15.2 15.2

General Arts 355 47.8 63.0

Agricultural

Science 42 5.7 68.6

Home Economics 114 15.3 84.0

Business 93 12.5 96.5

Visual Arts 26 3.5 100.0

Total 743 100.0


4.1.2.3. Responses on Mode of Residence

The distribution of respondents mode of residence as portray by Table 4.1.2.3 indicates that more

than half of the respondents, thus 435(58.5%) are boarders with small proportion (5.1%) been in

hostels. It was seen that 270 respondents given 36.3% were day students.

Table 4.1.2.3 Mode of Residence

Residence Frequency Percent Cumulative Percent

Boarding 435 58.5 58.5

Hostel 38 5.1 63.7

Day 270 36.3 100.0

Total 743 100.0


4.1.2.4 Responses on participation in Sporting activity and Affiliation to Societies/Clubs

The distribution of respondent’s opinion on participation in sporting activity and affiliation to

societies/clubs is displayed in Table 4.1.2.4. As delineated in Table 4.1.2.4 a chunk of the

respondents (thus 479 out 743) representing 64.5% do not participate in any sporting activity while

majority of the respondents 63.2 percent are affiliated to clubs/societies. The other 35.5% of the

students participate in various sports whilst 36.8 percent are not affiliated to any club or society.


56

Table 4.1.2.4 Participation in Sporting activity and Affiliation to Societies/Clubs

Responses

Affiliation to Societies/Clubs Sporting Activities


Yes

463 62.3 264 35.5

No

280 37.7 479 64.5

Total

743 100 743 100


4.1.2.5 Hours spend on clubs/Societies and Sporting Activities

With reference to table 4.1.2.5, almost all of the respondents (83.8%) spend at most 2 hours on

their affiliated clubs or societies in a week. It was only 2 respondents who spend 9 to 11 hours in

week on clubs and societies while approximately 13% spends 3 to 5 hours in a week on clubs.

Table 4.1.2.5. Hours spend on the clubs/societies and sporting activities

Hours

Affiliation to clubs/societies Sporting Activities


0-2 623 83.8 641 86.3

3-5 94 12.7 74 10.0

6-8 19 .3 17 2.3

9-11 2 .2 8 1.1

12+ 4 .5 3 .4

Missing 1 .1

Total 743 100 743 100


Four (4) respondents spent 12+ hours on clubs in a week which is highest hours spent on clubs

or societies in this study while 19 respondents’ uses 6 to 8 hours in week as shown in Table 4.1.2.5.

Again, it can be observed that, as low as 0.4% of the respondents spend 12+ hours in week on

sports and as many as 641 forming 86.3% spends at most 2 hours in a week on any sporting

activity. This indicates that aside 479 respondents who do not participate in any sporting activity

162 of the total respondents who participate in sporting activity uses at most 2 hours in week of

their time on sporting activity. Furthermore, 17 (2.3%) and 8(1.1%) of the students spends (6 to


57

8) and (9 to 11) hours respectively on sporting activities while 10.0% were with the opinion that

they spend about 3 to 5 hours on sports.

4.1.2.6 Use of mobile phone and Access to internet

As captured in table 4.1.2.6, a chunk (89.0%) of the respondents use mobile phone and

approximately 90% of them have access to internet as at the time of the survey. Only 82

respondents were with the opinion that, they do not use mobile phone while 71 of them do not

have access to internet.

Table 4.1.2.6 Use of mobile phone and Access to internet

Responses

Use of Mobile Phone Access to Internet


Yes

661 89.0 672 90.4

No

82 11.0 71 9.6

Total

743 100 743 100


4.1.2.7 Device use when on social media and Minutes spend on social media

From Table 4.1.2.7, three-thirds of the respondents (518 out of the 743) use mobile phone when

on social media while 20.1% of the students are of the view that, they use computer when on social

media. A very small proportion 1.2% of the respondents uses other devices when on social media

and 67 forming 9.0% refused to indicate the device use when accessing social media.

Table 4.1.2.7 Minutes spend on social media

Minutes Frequency Percent Cumulative Percent

0-200 364 49.0 49.0

201-400 174 23.4 72.4

401-600 133 17.9 90.3

601-800 24 3.2 93.5

801-1000 17 2.3 95.8

1001-1200 7 .9 96.8

1201-1400 9 1.2 98.0

1401-1600 4 .5 98.5

1601-1800 2 .3 98.8


58

1801-2000 4 .5 99.3

2001+ 5 .7 100.0

Total 743 100.0


As portrayed by Table 4.1.2.7, majority of respondents 49.0% spend 0 to 200 minutes on social

media while as low as 0.3% and 0.5% spend 1601 to 1800 and 1801 to 2000 minutes in a week

respectively. Second in majority was 201 to 400 minutes in week which had 23.4% followed by

401 to 600 minutes in week with 133 respondents.

Moreover, from 601 to 800 minutes in a week was represented by 24 students and 2.3% were with

the opinion that, they spend 801 to 1000 minutes in a week. Again, only seven (7) respondents

spent 1001 to 1200 minutes in a week while 1.2% of the total respondents spends 1201 to 1400

minutes in a week. Furthermore, 5 students uses 2001+ minutes in week on social media.

4.1.2.8 Hours spend on Television

Table 4.2.1.8, depicts the fact that many students, thus 212 out of 743 (constituting 28.5%) spend

at most 4 hours in week on television while only one(1) student spend (30 to 34) hours in week

on television. Moreover, 175(23.6%) respondents spend 5 to 9 hours in week on television and

140(18.8%) spend 10 to 14 hours on television. On the other hand, 11.4% of the respondents spend

15 to 19 hours in week on television and 90 (12.1%) of the students spend 20 to 24 hours in week.

However, 5.2% of the students spend 25 to 29 hours in a week on a television.

Table4.1.2.8 Hours spend on television

Hours Frequency Percent Cumulative Percent

0-4 212 28.5 28.5

5-9 175 23.6 52.1

10-14 140 18.8 70.9

15-19 85 11.4 82.4

20-24 90 12.1 94.5

25-29 39 5.2 99.7

30-34 1 .1 99.9

35+ 1 .1 100.0

Total 743 100.0


4.1.2.9 Responses on Mother’s and Father’s Age


59

The most represented mothers age distribution was 35 to 39years which forms 25.8%, with that

of the fathers age distribution been 55 to 59years representing 26.4% of the total number of

students enumerated as delineated in Table 4.1.2.9 The second highest from both fathers and

mothers age categories was 50 to 54 and that constituted 23.7% and 23.4% respectively.

The least represented age categories from the mothers side were 75 to 79 and 80+ years which

were represented by 0.1% each while 80+years was the least represented on the fathers age

category forming 0.9%. The third and fourth highest were 40 to 49 and 55 to 59 years and they

represented 20.9% and 16.2% respectively from the mothers age category. On the other hand, 60

to 64years and 40 to 49years were the third and fourth highest from the father category constituting

16.2% and 13.1% respectively.

Moreover, one (1) student did not indicate the mothers age while seven (7) of them refused to

indicate the ages of their fathers. As shown in table 4.1.2.9, 65 to 69years was fairly represented

in both mothers and fathers age distribution with 14 and 58 respondents respectively. A small

proportion (0.4%) of the respondents indicated that their father’s age were 30 to 34 years while

31 of them indicated that their mothers were 60 to 64 years. Again, as low as 1.1% and 3.9%

represented the age distribution 70 to 79years on mother and father age category respectively.


60

Table 4.1.2.9 Responses on Mother’s and Father’s Ages

Age Categories

Mothers Fathers


30-34 46 6.2 3 .4

35-39 192 25.8 43 5.8

40-49

50-54

55-59

60-64

155

174

120

31

20.9

23.4

16.2

4.2

97

176

196

120

13.1

23.7

26.4

16.2

65-69

70-74

75-79

14

8

1

1.9

1.1

.1

58

29

12

7.8

3.9

1.6

80+

Missing

Total

1

1

743

.1

.1

100

2

7

743

.3

.9

100


4.1.2.10 Responses on number of siblings

It can be deduced from Table 4.1.2.10 that majority of the respondents had 4 to 6 siblings. This

was followed by 0 to 3 siblings which had 202 respondents and that forms 27.2%. 174(23.4%) of

the respondents had 7 to 9 siblings at the time of the survey. The category with the least represen-

tation of siblings was 10+ which was represented by 46 students given as 6.2%.

Table 4.1.2.10 Responses on number of siblings

Number of

siblings


0-3 202 27.2 27.2

4-6 321 43.2 70.4

7-9 174 23.4 93.8

10+ 46 6.2 100.0

Total 743 100.0


4.1.2.11 Respondent’s Position of birth in the family

Considering the respondents position of birth in the family, more than half of the respondents,

391(52.6%) are in the 1st to 3rd position. The 4th to 6th position had 242 respondents representing


61

32.6% followed by 7th to 9th position with 92 students. The remaining 18(2.4%) were in the 10th

+ category as displayed by Table 4.1.2.11.

Table 4.1.2.11 Respondent’s Position of birth

Position of

birth


1-3 391 52.6 52.6

4-6 242 32.6 85.2

7-9 92 12.4 97.6

10+ 18 2.4 100.0

Total 743 100.0


4.1.2.12 Respondent’s Parents living together

With evidence from Table 4.1.2.12, a chunk of the respondents, thus 471 constituting 63.4% of

the total students enumerated for the study had their parents living together while the remaining

portion at the time of the survey had their parents not living together.

Table 4.1.2.12 Respondent’s Parents living together

Status Frequency Percent Cumulative Percent

Yes 471 63.4 63.4

No 272 36.6 100.0

Total 743 100.0


4.1.2.13 Marital Status of Respondents’ Parents

It can be observed from Table 4.1.2.13 that 145 out of the parents who are not staying together

(see Table 4.1.2.10) had divorced and 123 of the respondents had their parents separated. Four (4)

of the students did not indicate their parents’ marriage status.

Table 4.1.2.13 Respondents parents’ marital status

Marriage Status Frequency Percent Cumulative Percent

Divorce 145 19.5 19.5

Separated 123 16.6 36.1

None 475 63.9 100

Total 743 100



62

4.1.2.14 Responses on whom respondents live with

From Table 4.1.2.14, it can be observed that 471(63.4%) out of 743 respondents live with both

parents at the time the study was conducted. Those living with their mothers only was the highest

recording 20.9% followed by other relative with 98 respondents forming 13.2%. Fifty (50) of the

students were with the opinion that, they live with their fathers only. None relatives has the

minimum representation of only 17(2.3%) students.

Table 4.1.2.14 Responses on whom respondents live with

Responses Frequency Percent Cumulative Percent

Both Parents 471 63.4 56.9

Mother only 107 20.9 77.8

Father only 50 6.7 84.5

Other

Relative 98 13.2 97.7

Non Relative 17 2.3 100.0

Total 743 100.0


4.1.2.15 Highest level of education of respondents Parents

As depicted in Table 4.1.2.15, the highest level of education for both parents was secondary

education which recorded 361(48.6%) and 328 (44.1%) respondents for mothers and fathers

respectively. Approximately 37% of respondents had their fathers attaining tertiary education

while 12.1% out of the population sampled, their mothers highest level of education was tertiary.

Basic education level had 275 for mothers and 127 for fathers. 2.3% of the respondents indicated

that their mothers had never attended any level of education while 1.1% of the respondents were

with the opinion that their fathers never attended school. Two (2) of the students did not specify

their fathers level of education, which forms 0.3%.


63

Table 4.1.2.15 Highest Level of respondent’s parents

Level of Education

Mothers Fathers


Basic 275 37.0 127 17.1

Secondary 361 48.6 328 44.1

Tertiary

90

12.1

278

37.4

None

17

2.3

10

1.4

Total

743

100

743

100


4.1.2.16 Mothers status of employment

As shown in Table 4.1.2.16, the highest mother’s status of employment was self-employed with-

out employee(s), recording 50.5% which was followed by employee with 138 respondents. The

least status of employment was contributing family worker with 2.7% of the total population. Self

–employed with employee(s) was the third highest with 116 respondent. The fourth and the fifth

mother’s status of employment was casual worker and domestic employee which recorded

48(6.5%) and 46(6.2%) respectively.

Table 4.1.2.16 Mothers status of employment

Status of employment Frequency Percent Cumulative Percent

Employee 138 18.6 18.6

Self-employed without

employee(s) 375 50.5 69.0

Self-employed with

employee(s) 116 15.6 84.7

Casual worker 48 6.5 91.1

Contributing family

worker 20 2.7 93.8

Domestic employee 46 6.2 100.0

Total 743 100.0


4.1.2.17 Fathers status of employment


64

With reference to Table 4.1.2.17, majority (289 out of 743) of the fathers were employees with

213 representing 28.7% been self-employed without employee(s). Self-employed with

employee(s) was fairly represented with 162 fathers while casual worker and domestic employees

were represented by 51 and 7 fathers respectively. The status with minimum record was

contributing family worker with only 7 respondent. Four (4) of the student could not indicate the

employment status of their fathers.

Table 4.1.2.17 Fathers status of employment

Employment status Frequency Percent Cumulative Percent

Employee 289 38.9 38.9

Self-employed without

employee(s) 213 28.7 67.6

Self-employed with

employee(s) 162 21.8

89.4

Casual worker 51 6.9 96.3

Contributing family

worker 7 .9 97.2

Domestic employee 17 2.3 99.5

None 4 .5 100

Total 743 100

4.1.2.18 Sponsors of respondent’s education

It can be observed that the main sponsor of most (86.1%) of the respondents education were their

parents as shown in Table 4.1.2.18. A few respondents (1.1%) had their education sponsored by

their non-relatives and 2.4% were self-sponsors. Twenty-one (21) of the respondents had their

main sponsorship from scholarship while 56(7.5%) of the respondents had their education spon-

sored by relatives.

Table 4.1.2.18 Sponsors of Respondent’s education

Sponsors Frequency Percent Valid

Percent

Cumulative

Percent

Self 18 2.4 2.4 2.4

Parent 640 86.1 86.1 88.6

Relative 56 7.5 7.5 96.1

Non-

Relative 8 1.1 1.1 97.2


65

Scholarship 21 2.8 2.8 100.0

Total 743 100.0 100.0


4.1.2.19 Respondent’s responses on number of textbooks in all subjects

As delineated in Table 4.1.2.19, 547 out of 743 of the respondents did not have textbooks in all

subjects while minority of the respondents 196 constituting 26.4% had textbooks in all subjects.

Table 4.1.2.19 Responses on number of textbooks


Yes 196 26.4 26.4

No 547 73.6 100.0

Total 743 100.0


4.1.2.20 Distributions of number of Textbooks

With regards to the distribution of number of textbooks respondents have, 31.4% had 7 to 8 text-

books and those with 2 and below textbooks had the minimum percentage (8.7%). A few of the

respondents (175) had 3 to 4 textbooks in all subjects while those with 5 to 6 textbooks recorded

the highest number of textbooks respondents had at the time of the study, representing 270 re-

spondents of the number enumerated for this research as seen from Table 4.1.2.20

Table 4.1.2.20 Distributions of number of textbooks

Number Frequency Percent Cumulative Percent

0-2 65 8.7 8.7

3-4 175 23.6 32.3

5-6 270 36.3 68.6

7+ 233 31.4 100.0

Total 743 100.0


4.1.2.21 Responses on extra classes

As portrayed in Table 4.1.2.21, it can be observed that majority (67.2%) of the respondents do not

offer any extra classes apart from the normal instructional hours. However, a good number (244)

of the respondents as at time of the study do extra classes.

Table 4.1.2.21 Responses on extra classes



66

Yes 244 32.8 32.8

No 499 67.2 100.0

Total 743 100.0


4.1.2.22 Number of Hours spend in week on extra classes

It can be seen from Table 4.1.2.22 that, only two (2) students spent at least 12 hours in a week on

extra classes while a chunk (80.9%) of the respondents spent at most three (3) hours on extra

classes in week. 4 to 7hours recorded 124 respondents of the population sampled and 2.2% of the

students spent 8 to 11hours in a week on extra classes.

Table 4.1.2.22 Hours spend on extra classes

Hours Frequency Percent Cumulative Percent

0-3 601 80.9 80.9

4-7 124 16.7 97.6

8-11 16 2.2 99.7

12+ 2 .3 100.0

Total 743 100.0


4.1.2 23 Responses on place of study

A little above half (51.7%) of the respondents do study in their bedrooms and few of the students

(32) representing 4.3% of the respondents do study in reading rooms in their homes. 186 (25.0%)

out of the 743 respondents indicated that, they do study in the halls of their homes while 141 of

them ‘prep’ at other places apart from the three places listed.

Table 4.1.2.23 Respondent’s opinions on place of study

Place of study Frequency Percent Cumulative Percent

Bedroom 384 51.7 51.7

Hall 186 25.0 76.7

Reading

Room 32 4.3 81.0

Others 141 19.0 100.0

Total 743 100.0


4.1.2.24 Responses on amount of money spend in a week


67

Analysis of respondents opinions on amount of money spent in week as display in Table 4.1.2.24,

depicts that, almost 61% of the respondents spent GH¢ 10 to GH¢ 24 in a week. On the other

hand, only 34 students used at least GH¢50 in a week at the time of the survey besides 130 (17.5%)

of the respondents spent GH¢25 to GH¢49 in a week. Finally, 17.2% of the students enumerated

spent at most GH¢9 in a week.

Table 4.1.2.24 Amount of money spend in a week

Amount in

GH¢


0-9 128 17.2 17.2

10-24 451 60.7 77.9

25-49 130 17.5 95.4

50+ 34 4.6 100.0

Total 743 100.0


4.2 Main Analysis

This section provides the results of the reliability of the scale, factor analysis and binary logistic

regression conducted.

4.2.1 Reliability of the scale

As indicated in section 3.7.2 the reliability of items in Part C and D of the questionnaire (see

appendix 1) was checked using Cronbach alpha. The Cronbach’s alpha coefficient in this case is


68

.775 which is above the recommended .70, so the scale can be considered reliable with the sample

size (743).

4.2.2 Factor Analysis

The exploratory techniques used in this sub-section include analysis based on KMO and Bartlett’s

test, analysis of the eigenvalues and analysis based on the scree plots. Again the sub-section will

look at techniques used to extract exact factors that influence students’ academic performance in

second cycle institutions. These techniques include factor extraction and rotation.

4.2.2.1 Analysis of the value of Kaiser-Meyer Olkin Measure of Sampling Adequacy

The KMO statistics varies between 0 and 1. An overall KMO measure of 0.706 for this data as

depicted in Table 4.2.1.2, indicates that the correlation matrix is appropriate for factor analysis.

Since the value is close to one, it suggests that patterns of correlation are relatively compact and

therefore factor analysis should yield distinct and reliable factors. Kaiser and Rice (1974),

suggested that KMO values should exceed 0.8 although, 0.6 is acceptable. They were with the

view that values below 0.5 are unacceptable and values greater than or equal to 0.9 are marvellous.

The value for these data falls into the range of being middling as indicated in section 3.7.3.1.4,

which means that factor analysis is appropriate for these data.

4.2.2.2 Analysing the value of the Bartlett’s test of Sphericity

As indicated in section 3.7.3.1.4, specifically equation 18 and 19, are test statistic used to calculate

the value of the Bartlett’s test of Sphericity. The sample size 𝑛 = 743, indicators variables 𝑝 =

36 and the eigenvalues of the components 𝜃𝑗 are given in the Table 4.2.1.3. The Bartlett’s test of

Sphericity obtained for the data was 4426 and p-value was 0.000 as shown in Table 4.2.1.2. This

shows that the Bartlett’s test of Sphericity is highly sufficient for these data.

Table 4.2.1.2 KMO and Bartlett's Test

Kaiser-Meyer-Olkin Measure of Sampling Adequacy. .706

Bartlett's Test of Sphericity Approx. Chi-Square 4426.137

Df 630


69

Sig. .000


4.2.2.3 Analysis of Eigenvalues

The eigenvalues represent the total variance explained by each factor. It explains the variance

associated with a particular linear component. Again, eigenvalues are variances of the components

extracted. It provides a lower bound for the number of factors present in the data. Table 4.2.2.3

shows the eigenvalues and corresponding percentage of variances associated with each of the 36

possible factors before extraction.

Table 4.2.2.3 Total Variance Explained

Component

Initial Eigenvalues Extraction Sums of Squared Loadings

Total % of Variance Cumulative % Total % of Variance Cumulative %

1 3.801 10.559 10.559 3.801 10.559 10.559

2 2.316 6.433 16.993 2.316 6.433 16.993

3 2.063 5.731 22.724 2.063 5.731 22.724

4 1.964 5.455 28.179 1.964 5.455 28.179

5 1.593 4.425 32.604 1.593 4.425 32.604

6 1.485 4.126 36.730 1.485 4.126 36.730

7 1.344 3.733 40.463 1.344 3.733 40.463

8 1.312 3.644 44.106 1.312 3.644 44.106

9 1.234 3.428 47.535 1.234 3.428 47.535

10 1.150 3.194 50.729 1.150 3.194 50.729

11 1.121 3.114 53.843 1.121 3.114 53.843

12 1.028 2.857 56.700 1.028 2.857 56.700

13 .995 2.763 59.463

14 .974 2.706 62.169

15 .952 2.645 64.814

16 .857 2.379 67.193

17 .837 2.325 69.518

18 .814 2.265 71.780

19 .783 2.174 73.954

20 .732 2.033 75.987

21 .721 2.003 77.990

22 .712 1.978 79.968

23 .672 1.868 81.836

24 .643 1.787 83.622

25 .635 1.764 85.386

26 .608 1.688 87.074

27 .589 1.636 88.710

28 .573 1.591 90.300

29 .551 1.529 91.830

30 .536 1.488 93.318

31 .495 1.375 94.692

32 .488 1.355 96.047

33 .474 1.316 97.363

34 ..408 1.132 98.495

35 .301 .837 99.332

36 .240 .668 100.000


70

Source: Field data,2015

In all thirty-six (36) factors were identified within the data set to affect students’ academic

performance before extraction. Based on eigenvalues greater than one rule, twelfth (12) factors

were extracted as listed in Table 4.2.2.3.

The first factor explains 10.559 percent of the total variance. It is obvious that the first few

factors explain relatively large amount of variance (especially factor 1) whereas the subsequent

factors explain only small amount of variance. From the number of factors extracted, this im-

plies that only 12 components are appropriate to estimate the correlation matrix. These twelfth

factors explain about 57 percent of the total variation in the data set. If the first twenty compo-

nents are selected to approximate the observed matrix, then the implication is that about 33%

of information would be lost.

4.2.2.4 Rotation Sums of Squared Loadings for the twelfth (12) factors

Based on the procedure described in chapter three (section 3.7.3.1.3) the 12 significant factors

that was extracted from the 36 variables explains approximately 57% of variation in the data.

The first factor which is supposed to be the most important factor has 2.8 percent factor loading

after rotation and explains 7.8% of the variation in the data. The second, third and fourth factors

explains approximately 6.3%, 6.0% and 5.1% of the variation in the data respectively while the

twelfth factor has 1.142 percent of the total loading after rotation and it explains the least var-

iations among the factors extracted, thus 3.173%. The rotated sums of squared loadings for the

twelve factors are depicted in Table 4.2.2.4.


71

Table 4.2.2.4 Rotation sums of Squared Loadings

Components Total % of Variance Cumulative %

1 2.810 7.805 7.805

2 2.250 6.251 14.056

3 2.169 6.024 20.080

4 1.834 5.095 25.175

5 1.722 4.783 29.958

6 1.560 4.334 34.292

7 1.538 4.273 38.565

8

9

10

11

12

1.417

1.410

1.382

1.178

1.142

3.937

3.916

3.838

3.271

3.173

42.502

46.418

50.255

53.527

56.700

2.2.5 Analysis based on Scree plot

More often than not, eigenvalues greater than one rule extracts too many factors, so it is always

important to employ the scree plot. If there is a change (or elbow) in the shape of the plots, then

we choose k equal to the number of factors before the straight line. Figure 1 shows, the plot of

the eigenvalues against the corresponding components. The eigenvalues and the corresponding

components used in the scree plot are given in Table 4.2.2.3 above.

A careful look at figure 1 indicates that the elbow appears to fall on the tenth (10) component.

The plot tends to show steep declines initially and then levels off, meaning first ten eigenval-

ues tend to have quite different numerical values while twenty-six eigenvalues tend to have


72

approximately equal values. .

Figure 1 Scree plot of indicator variables.

4.2.2.6 Determining the Number of Factors

Determining the number of factors to be used has been an issue since the onset of factor analysis.

This has always been a judgment call. Most of the commonly used technique for factor extraction

as reviewed in chapter three had been employed and different numerical factors were extracted.

The Kaiser criterion (eigenvalue greater than one rule) extracted twelve factors out of the a lot

whilst a careful look at the Cattell scree plot indicates that ten factors are significant.

This could imply that the number of factors k may be within the range space 10≤ 𝑘 ≤ 12. This

interval will serve as quite to the number to the most suitable choice of k.


73

Based on the percentage of variance explained by these factors as indicated in Table 4.2.2.1. It

can be seen that, selecting twelve factors, approximately 57 percent of correlation among indica-

tors is explained by the model. Opting for 11- factor model would imply that the model accounts

for approximately 54 percent of the variation in the data. The choice of 10- factor model would

also account for just 51 percent of the variation and more than 39 percent of the information will

be sacrificed. On that score, it was prudent to recommend 12-factor model since it accounts for a

higher variation compared with 10- factor and 11-factor.

4.2.2.7 Factor Rotation

Once the number of factors have been determined, the next step is to interpret these factors. To

assist in this process the factors were rotated using the Orthogonal Varimax factor rotation as

indicated in section 3.7.1.6. The varimax factor rotation encourages the detection of factors each

of which is related to a few variables. It discourages the detection of factors influencing all varia-

bles. Rotation reproduces a transformation matrix. The varimax transformation matrix of this data

set is shown in Appendix III

The values portray how much the axes were rotated to foster the axes to foster simple structure.

The values on the off- diagonal are cosines and the values on the off-diagonal are sines. It must

be noted that although this transformation fosters the interpretability of factor solution, it does not

alter the communality of the indicators.


74

Table 4.2.2.7 Rotated Component Matrix

Component

1 2 3 4 5 6 7 8 9 10 11 12

A1 .3664

A7 .838

A8 .780

B1 .828

B3 .843

B17 .616

B20 .783

B21 .796

B22 .558

B9 .521

B11 .883

B12 .887

B13 .742

B4 .710

B5 .711

B23 .730

C23 .340

C1 .659

C3 .718

C4 .658

C7 .560

C8 .636

C9 .670

C11 .439

C12 .554

C17 .740

C19 .707

C21 .594

C14 .785

C15 .775

D2 .708

D3 .724

D5 .421

D7 .631

D9 .692

D10 .589

4.2.2.8 Factors Interpretation

As indicated on the Questionnaire (see Appendix I), the first factor C1,C3,C4,C7,C8 and C9 sug-

gests that the underlying factor influencing student’s academic performance in second cycle insti-

tutions at Nsawam-Adoagyiri Municipality is Teacher instructional strategies factor. For students

to accomplish learning, teachers should provide meaningful and authentic learning activities to


75

enable students to construct their understanding and knowledge of the subject domain. This im-

plies that, if teachers do diligent work in various classrooms, there will be an improvement in

students’ academic performance in second cycle institutions in Ghana.

The indicator variables C11, C12, C17, C19, and C21 in the second factor talks about Students’ moti-

vation to learn factor related. The desire to learn or understand something unknown could be an

important factor in students’ academic achievement.

The third factor comprises the variable B11, B12 and B13 which is Parental age/ Family size factor.

This indicate that Age of parent’s and the size of a family as research has shown has a direct

relation with students’ academic performance.

An issue of Learning environment is the fourth factor that seems to affect students’ academic

performance in the second cycle institution. School context and its facilities could be an important

factor in student achievement. The indicator variables are B1, B3 and C23.

Furthermore, the fifth factor was represented by indicators (D7, D9 and D10) which is Individual

study habit factor. Generally, learning requires a deep understanding of the concepts therein, the

ability to make connections between them, and produce effective solutions to ill-structured do-

mains or concepts and this is an important factor that influence students’ academic performance.

The sixth factor C14, C15 and C16 is Examination related factor. Generally the state of the individual

at the period of examination affect his/her performance. How nervous or uneasy one feels during

examination truly affects one’s performance.

Moreover, A1, D2, D3 and D5 comprises the seventh factor and that is Gender/Students’ indiscipline

as a lot of study have shown, this factor have diverse influence on academic performance of stu-

dents at second cycle institutions. Again the eighth factor is Junior High School attended factor

related. Indicator variables A7 and A8 and A9 constitutes the eighth factor.


76

In addition, the ninth factor, B4 and B5 is extra- curricular activity related factor while the tenth

factor (B20 and B21) is based on Parental employment status. Studies repeatedly discovered that

the parents’ annual level of income is correlated with students’ achievement scores.

Again, B9, B10 and B23 constitutes the eleventh factor and is an issue of Course materials/Media

study habit factor and that could be an obstacle to good academic achievement. The variables that

constitutes the twelfth factor are B17 and B22. Thus is Guardian/Sponsorship factor related.

In summary, factor rotation has helped in the interpretation of the twelve factors affecting stu-

dents’ academic performance in the second cycle institutions in Nsawam – Adoagyiri Municipal-

ity, Ghana. Accordingly, some of these factors are teacher instructional strategies factor, students’

motivation to learn, gender/students’ indiscipline, extra-curricular activities, parental age/ family

size factor, parental employment status factor, just to mention a few.

4.2.2.9 Calculating the factor score

Factor scores which are composite scores estimated of each respondent on the derived factors was

computed. The procedure for calculating the factor score is provided in section 3.7.3.1.7. Subse-

quent binary logistic regression will be carried out in the next section using the factor scores com-

puted for the twelve factors extracted and Cumulative Continuous Assessment Marks (CCAM) of

respondents in individual Core Subjects.

4.2.2.10 Summary of Results from the Factor Analysis

The 36 items of presumed factors affecting students’ academic performance were subjected to

factor analysis with principal component analysis (PCA). Prior to performing PCA the suitability

of the data for factor analysis was assessed. Inspection of the correlation matrix revealed the pres-

ence of many coefficient of .3 and above. The Kaiser-Meyer-Oklin value was 0.706 exceeding the

recommended value of .6 (Kaiser, 1970) and the Bartlett’s Test of Sphericity reached statistical

significance, supporting the factorability of the correlation matrix.


77

Principal component analysis revealed the presence of twelve (12) component with eigenvalues

exceeding one rule explaining approximately 57 percent of the total variance. An inspection of

the scree plot revealed a break after the ten component. Using eigenvalue greater than one rule

and comparing the variances explained by the tenth, eleventh and the twelfth components, we

decided to retain twelfth components for further investigation. To aid in the interpretation of these

twelfth component, Varimax rotation was performed. The rotated solution revealed the presence

of simple structure with all components showing a number of fairly strong loadings and all varia-

bles loading substantially on only a component. The factor scores of the twelfth components was

calculated using regression method as stated in section 3.7.3.1.7

4.2.3 Analysis on Binary Logistic Regression

This section throws light on how the binary logistic regression was performed. The section

comprises, summary and descriptive analysis of the respondents’ academic performance and

model building using binary logistic regression for all the core subjects in both schools.

4.2.3.1 Summary of Students’ Academic Performance

This subsection summaries the academic performance of respondents from both schools.

4.2.3.1.1 Respondents Performance in Core Subjects (Nsawam Senior High School)

From Table 4.2.3.1.1, out of the 199 respondents of Nsawam Senior High School, used for the

study, approximately, Fifty- one percent (51%) were classified as having poor academic

performance and a little above 49 percent had good academic performance with respect to Core

Mathematics. On the other hand, English Language had more than half of the students being in

good academic performance category; thus 51.8% of the total respondents while 48.2% of the

respondents were in poor academic performance category.

Moreover, Ninety-one (91), out of 199 respondents were classified as having poor academic

performance while as many as 108 respondents fell in good academic performance category with

reference to Integrated Science. Lastly, Social Studies had only 66 (33.2%) respondents classified


78

as having poor academic performance while good academic performance had 66.8 percent of the

total respondents.

Table 4.2.3.1.1 Respondents Performance in Core Subjects (Nsawam Senior High School)

Subjects Poor Performance Good Performance


Mathematics

101

50.8

98

49.2

Integrated Science

English Language

Social Studies

91

96

66

45.7

48.2

33.2

108

103

133

54.3

51.8

66.8

4.3.3.1.2 Respondents Performance in Core Subjects (St. Martin’s Senior High School)

As shown in Table 4.3.3.2, Social Studies recorded the lowest number of respondents that were

classified as poor academic performance category with 102 respondents representing 18.8 percent.

That was followed by English Language with 25.0 percent. Integrated Science and Core

Mathematics recorded 154 (28.3%) and 202 (37.1%) respondents classified as poor academic

performance respectively.

Again, the Table 4.3.3.2 depicts that, Core Mathematics had the least respondents with good

academic performance with 62.9 percent of the total respondents. The core subject with the highest

good academic performance was Social Studies with 441 respondents representing 81.3%. English

Language and Integrated Science recorded 75.0 percent and 71.7 percent in good academic

performance category respectively.


79

Table 4.2.3.1.2 Respondents Performance in Core Subjects (St. Martin’s SHS)s

Subjects Poor Performance Good Performance


Mathematics

202 37.1 342 62.9

Integrated Science

English Language

Social Studies

154

136

105

28.3

25.0

18.8

390

408

439

71.7

75.0

80.7

4.2.3.2 Descriptive Statistics of Students’ Academic Performance

This subsection talks about the descriptive statistics of respondent’s academic performance of

both schools.

4.2.3.2.1 Descriptive Statistics of St. Martin’s Senior High School

The descriptive statistics conducted for respondents academic performance in St. Martin’s SHS

as delineated in Table 4.2.3.2.1, shows that, the mean of students’ academic performance in

Mathematics (Core) was 56.2721, was the least among the four subjects, with Social Studies

recording the highest mean mark with 66.6710 followed by English Language and Integrated

Science having 58.5662 and 58.0037 respectively.

The lowest standard deviation as depicted by Table 4.2.3.2.1 was recorded by English Language

with 10.68923 while Mathematics had the highest standard deviation of 13.10123 With Integrated

Science following with 12.28108 whilst Social Studies had a mean of 12.85892.

The skewness of the respondents’ academic performance was also analysed and it was shown

that, Mathematics had 0.715, Integrated Science recorded 0.206, English Language had -0.294

and Social Studies had a standard deviation of -0.756. The standard error of skewness for all the

four subjects was 0.105.


80

4.2.3.2.1 Descriptive Statistics of St. Martin’s Senior High School

Academic

Performance

Total

Number

Mean Std. Deviation Skewness

Statistic Std. Error

Students’

performance in

Social Studies

544 66.6710 12.85892 -.756 .105

Students’

performance in

English Language

544 58.5662 10.68928 -.294 .105

Students’

performance in

Mathematics

544 56.2721 13.10123 .715 .105

Students’

performance in

Integrated Science

544 58.0037 12.28108 .206 .105

4.2.3.2.2 Descriptive Statistics of Nsawam Senior High School

With reference to Table 4.2.3.2.2, the mean performance mark of students in Core Mathematics

was 54.8794 with Social Studies recording the highest mean mark of 60.4623. Integrated Science

and English Language recorded mean of 57.3065 and 56.2764 respectively. The standard

deviation of all the four subjects were also computed with Social Studies having a standard

deviation of 12.84755 while Mathematics, English Language and Integrated Science recording

14.72322, 12.84755 and 13.85646 respectively.

Again from Table 4.2.3.2.2, the skewness of students’ academic performance of Nsasco shows

that Mathematics recorded 0.449 with English Language recording 0.536 while Integrated Science

and Social Studies recorded .618 and 0.127 respectively. The standard error of skewness for all

the four subjects was seen as illustrated in Table 4.2.3.2.2 as 0.172.


81

4.2.3.2.2 Descriptive Statistics of Nsawam Senior High School

Academic Performance Total

Number

Mean Std. Deviation Skewness

Statistic Std. Error

Students’ performance in

Mathematics 199 54.8794 14.72322 .449 .172


Integrated Science 199 57.3065 13.85646 .618 .172


English Language 199 56.2764 12.84755 .536 .172


Social Studies 199 60.4623 12.56849 .127 .172

In summary, comparing the mean mark of the two schools in all the core subjects we can conclude

that the mean mark of respondents’ performance from St. Martin’s Senior High School in all the

core subjects was greater than the mean mark of respondent’s performance in all the core subjects

in Nsawam Senior High School. Which implies that St. Martin’s SHS students perform better than

Nsawam SHS respondents in all core subjects.

4.2.3.3 The Model Building

Prior to the models building, multicollinearity is checked to satisfy the assumptions of binary

logistic regression. The correlations between the independent variables and the dependent

variables shows some relationship of at least .30. Again, the correlation between each of the

predictors is not too high (is below 0.7).

The students’ academic performance was categorised into ‘poor’ and ‘good’. Those students

whose marks ranges between 0 – 49, are categorised as being poor, while those marks range

between 50 -100 are categorised as ‘good’. The descriptive statistics of each subjects is given in

section 4.2.3.2. The logistic model was built for each core subject in each school. Students’

academic performance (categorical) was the dependent variable while the twelve (12) factors

extracted from the thirty-six (36) variables were used as the predictor variables.


82

4.2.3.3.1 Model building for Core Mathematics (St. Martin’s Senior High School)

Table 4.2.3.3.1 shows only the constant included, before any coefficients are entered into the

equation. Logistic regression compares this model with a model including all the predictors to

determine whether the latter model is more appropriate. The classification table (Table 4.2.3.3.1a)

suggests that if we knew nothing about our variables and guessed that a person would performance

poorly in core mathematics at St. Martin’s SHS, we would be 58.7% correct of the time. The

second classification table, Table 4.2.3.3.1b, presents the results when the predictors are included.

This second classification table (Table 4.2.3.3.1b) shows how the classification error rate has

changed from the original 58.7% to 64.9% after the predictors was added. So, by adding the

variables we can now predict with 64.9% accuracy. Meaning that adding variables to the model

improves its predictive accuracy of the results

Table 4.2.3.3.1a Classification Table

Observed Predicted

Performance of students in

Mathematics

Percentage

Correct

Poor Good


Mathematics

Poor 0 202 .0

Good 0 342 100.0

Overall Percentage

58.7

Table 4.2.3.3.1b Classification Table

Observed Predicted


Mathematics

Percentage

Correct

Poor Good


Mathematics

Poor 37 165 18.3

Good 26 316 92.4

Overall Percentage

64.9


83

The –2LLvalue from the Model Summary table below is 699.909 which is distributed as 𝜒12 with

a significant probability of p = 0.048˂0.05. Thus, the indication is that the model has a poor fit,

with the model containing only the constant indicating that the predictors do have a significant

effect on the response variable and create essentially a different model. So we need to look closely

at the predictors and determine which of them will be significant in the model.

Table 4.2.3.3.1c Model Summary

Step -2 Log likelihood Cox & Snell R

Square

Nagelkerke R

Square

1 699.909 .032 .044

Table 4.2.3.3.1d Omnibus Tests of Model Coefficients

Chi-square Df Sig.

Step 17.797 12 .048

Block 17.797 12 .048

Model 17.797 12 .048

Model Summary: Although there is no close analogous statistic in logistic regression to the

coefficient of determination 𝑅2, the Model Summary Table provides some approximations. Cox

and Snell’s R-Square attempts to imitate multiple R-Square based on ‘likelihood’, but its

maximum can be (and usually is) less than 1.0, making it difficult to interpret. The cox and Snell’s

R-square obtained is 0.032 indicating that 3.2% of the variation in the dependent variables is

explained by the logistic model. The Nagelkerke modification that does range from 0 to 1 is a

more reliable measure of the relationship. Nagelkerke’s 𝑅2will normally be higher than the Cox

and Snell measure. In our case it is 0.044, indicating a weak relationship of 4.4% between the

predictors and the response variable.

Hosmer Lemeshow statistic: A probability (p) value is computed from the chi-square distribution

with 8 degrees of freedom to test the fit of the logistic model.

𝐻0: There is no difference between the observed and predicted values

𝐻1: There is a difference between the observed and predicted values

Since the p-value (0.05) for the Hosmer-Lemeshow goodness-of-fit test statistic is less than the

significance value of 0.618, we fail to reject the null hypothesis that there is no difference between


84

observed and model-predicted values, implying that the model’s estimates fit the data at an

acceptable level.

Table 4.2.3.3.1e Hosmer and

Lemeshow Test

Step Chi-square Df Sig.

1 6.265 8 .618

Table 4.2.3.3.1g Variables in the Equation

Predictors B S.E. Wald Df Sig. Exp(B)

Factor one .157 .095 2.721 1 .017 1.138

Factor two -.063 .100 .399 1 .187 .873

Factor three .166 .098 2.906 1 .048 .923

Factor four .028 .170 .027 1 .018 1.128

Factor five -.025 .091 .079 1 .854 .984

Factor six .133 .093 2.053 1 .227 .899

Factor seven -.038 .093 .162 1 .007 .893

Factor eight -.048 .091 .282 1 .023 .839

Factor nine -.195 .084 5.426 1 .009 .799

Factor ten -.139 .088 2.451 1 .888 1.012

Factor eleven .083 .093 .794 1 .019 .872

Factor twelve .038 .092 .167 1 .043 1.154

Constant .560 .131 18.175 1 .130 1.752

Variables in the equation: The simplest way to assess Wald is to take the significance values and

if it is less than 0.05 reject the null hypothesis and accept the alternative hypothesis. Where the

null and the alternate hypothesis are;

𝑯𝟎:𝜷𝒊 = 𝟎 i.e. Xi makes no significant contribution in the model

𝑯𝟏: 𝜷𝒊 ≠ 𝟎 i.e. Xi makes a significant contribution in the model

Table 4.2.3.3.1, shows the variables that are significant in the final model. The variables left after

the forward likelihood selection are factor one, factor three, factor four, factor seven, factor

eight, factor nine, factor eleven and factor twelve. The table has several important elements.

The Exp(B) is the exponential of the logistic coefficients. The Exp(B) column in Table presents

the extent to which raising the corresponding measure by one unit influences the odds ratio. If the

value of EXP(B) exceeds 1 then the odds of an outcome occurring increases while if the figure is


85

less than 1 then any increase in the predictor leads to a drop in the odds of the outcome occurring.

The ‘B’ values are the logistic coefficients that can be used to create a predictive equation (similar

to the beta values in linear regression).

The regression model for the log –odds in favour of poor performance is:

1 2 3 4 5 6 7 8log 0.560 0.157 0.166 0.028 0.038 0.048 0.195 0.085 0.0381

e X X X X X X X X

To estimate odds, the model exponentiated as;

1 2 3 4 5 6 7 8exp(0.560 0.157 0.166 0.028 0.038 0.048 0.195 0.085 0.038 )1

X X X X X X X X

The probability of poor performance (Core Mathematics) is obtained by applying the logistic

transformation;

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

exp(0.056 0.157 0.166 0.028 0.038 0.048 0.195 0.085 0.038

1 exp(0.560 0.157 0.166 0.028 0.038 0.048 0.195 0.085 0.038 )

X X X X X X X X

X X X X X X X X

Where 𝑋1= Factor one = Teacher instructional strategies

𝑋2= Factor three = Parental age/Family size

𝑋3 = Factor four = Learning Environment

𝑋4 = Factor seven = Gender/ Students’ indiscipline

𝑋5 = Factor eight = JHS attended factor

𝑋9 = Factor nine = Extra- curricular factor

𝑋11 = Factor eleven = Course materials/Media study habit

𝑋12 = Factor twelve = Guardian/Sponsorship factor


86

4.2.3.3.2 Model building for Integrated Science (St. Martin’s Senior High School)

Table 4.2.3.3.2a, suggests that we would have been 65.1 percent correct to assume that a student

from St. Martin’s Senior High School (Smarts) would perform poorly in Integrated Science, if we

knew nothing about our predictors. The second classification table, depicts results when the

variables are included. The classification error rate changed from 65.1 percent to 72.4 percent

when the predictors were added. This implies that we can now predict 72.4% accuracy which

signifies that including variables to the model improves its accuracy.


Observed Predicted


Integrated

Percentage

Correct

Poor Good


Integrated

Poor 0 154 .0

Good 0 390 100.0

Overall Percentage

65.1


Observed Predicted


Integrated

Percentage

Correct

Poor Good


Integrated

Poor 6 148 3.9

Good 2 388 99.5

Overall Percentage

72.4

The –2LLvalue from the Model Summary table (see appendix IV) is 628.278 which is distributed

as 𝜒12 with a significant probability of p = 0.041˂0.05. Thus, the indication is that the model has

a poor fit, with the model containing only the constant indicating that the predictors do have a

significant effect on the response variable and create essentially a different model.

Model Summary: The cox and Snell’s R-square obtained is 0.018 indicating that 1.8% of the

variation in the dependent variables is explained by the logistic model. Nagelkerke’s 𝑅2 in our


87

case is 0.026, indicating a weak relationship of 2.6% between the predictors and the response

variable.

Hosmer Lemeshow statistic: Since the p-value (0.05) for the Hosmer-Lemeshow goodness-of-fit

test statistic is less than the significance value of 0.439, implying that the model’s estimates fit the

data at an acceptable level.

Table 4.2.3.3.2c Hosmer and

Lemeshow Test


1 7.940 8 .439

Table 4.2.3.3.2d Variables in the Equation


Factor one .068 .101 .451 1 .000 1.070

Factor two -.043 .107 .162 1 .013 .958

Factor three .153 .104 2.157 1 .100 1.165

Factor four .189 .181 1.086 1 .050 1.208

Factor five .043 .096 .204 1 .001 1.044

Factor six -.012 .099 .014 1 .724 .988

Factor seven .102 .101 1.010 1 .876 1.107

Factor eight .125 .102 1.504 1 .698 1.133

Factor nine .059 .092 .407 1 .641 1.060

Factor ten -.085 .092 .849 1 .485 .919

Factor eleven .021 .100 .042 1 .046 1.021

Factor twelve -.156 .097 2.586 1 .048 .855

Constant 1.053 .143 54.280 1 0.97 2.866

Variables in the equation: To determine the predictive efficiency model, the Wald chi- square

statistics in Table 4.2.3.3.1, is made use of out of the twelve (12) variables only six (6) were

significant. The variables left after the forward likelihood selection are factor one, factor two,

factor four, factor five, factor eleven and factor twelve.

Let 𝑋1= Factor one = Teacher instructional strategies

𝑋2 = Factor two = Students’ motivation to learn

𝑋3 = Factor four = Learning environment


88

𝑋4 = Factor five = Individual study habit


𝑋6 = Factor twelve = Guardian/Sponsorship factor

The regression model for the log –odds in favour of poor performance is;

1 2 3 4 5 6log 1.053 0.68 0.043 0.189 0.043 0.021 0.1561

e X X X X X X


1 2 3 4 5 6exp(1.053 0.68 0.043 0.189 0.043 0.021 0.156 )1

X X X X X X

The probability of poor performance (Integrated Science) is obtained by applying the logistic

transformation; 1 2 3 4 5 6

1 2 3 4 5 6

exp(1.053 0.68 0.043 0.189 0.043 0.021 0.156 )

1 exp(1.053 0.68 0.043 0.189 0.043 0.021 0.156 )

X X X X X X

X X X X X X

4.2.3.3.3 Model building for English Language (St. Martin’s SHS)

As indicated in classification table (Table 4.3.2.2.3a) before, the predictor variables were added,

one could have guessed that students from St. Martin’s SHS would performed poorly in English

Language at 70 percent. But the inclusion of the predictors changed the classification error rate

from 70 percent to 76.2 percent. This indicates that, we can now predict 76.2 percent accuracy

which implies that including variables to the model improves its accuracy.


Observed Predicted


English Language

Percentage

Correct

Poor Good


English Language

Poor 0 136 .0

Good 0 408 100.0

Overall Percentage

70.0


89


Observed Predicted

Performance of students in English

Language

Percentage

Correct

Poor Good


English Language

Poor 3 133 2.22.

Good 1 407 99.8

Overall Percentage 76.2

The –2LL recorded a value of 595.232 which has a significant probability of p = 0.048˂0.05.

Thus, the indication is that the model has a poor fit, with the model containing only the constant

indicating that the predictors do have a significant effect on the response variable and create

essentially a different model.


variation in the dependent variables is explained by the logistic model. Nagelkerke’s 𝑅2 had

0.044, indicating a strong relationship of 4.4% between the predictors and the response variable

(see appendix IV).


test statistic is less than the significance value of 0.416, it implies that the model’s estimates fit

the data at an acceptable level.

Table4.2.3.3.3c Hosmer and

Lemeshow Test


1 16.071 8 .410


90



Factor one -.216 .109 3.890 1 .049 .813

Factor two -.049 .115 .183 1 .037 .947

Factor three -.023 .114 .046 1 .470 .888

Factor four -.117 .107 .395 1 .503 1.076

Factor five .096 .187 .941 1 .265 1.115

Factor six -.034 .099 .107 1 .039 1.048

Factor seven .030 .105 .084 1 .050 1.062

Factor eight .194 .109 3.171 1 .022 .895

Factor nine -.033 .092 .131 1 .957 .995

Factor ten .042 .101 .175 1 .019 .906

Factor eleven .263 .104 6.343 1 .012 .999

Factor twelve -.152 .101 2.285 1 .979 .997

Constant 1.054 .143 6.116 1 .013 2.868


statistics in Table 4.2.3.3.1,is made use of, out of the twelve(12) variables, seven (7) were signif-

icant. These variables are factor one, factor two, factor six, factor seven, factor eight, factor

ten and factor eleven.


𝑋2 = Factor two = Students’ motivational to learn

𝑋3 = Factor six = Examination factor related

𝑋4 = Factor seven = Gender/Students’ indiscipline


𝑋6 = Factor ten = Parental employment status

𝑋7 = Factor eleven = Course materials/Media study factor

The regression model for the log –odds in favour of poor performance (English Language) is;

1 2 3 4 5 6 71.054 0.216 0.049 0.034 0.304 0.194 0.042 0.263

1eLog X X X X X X X


91


1 2 3 4 5 6 7exp(1.054 0.216 0.049 0.034 0.304 0.194 0.042 0.263 )1

X X X X X X X

The probability of poor performance (English Language) is obtained by applying the logistic

transformation;

1 2 3 4 5 6 7

1 2 3 4 5 6 7

exp(1.054 0.216 0.049 0.034 0.304 0.194 0.042 0.263 )

1 exp(1.054 0.216 0.049 0.034 0.304 0.194 0.042 0.263 )

X X X X X X X

X X X X X X X

4.2.3.3.4 Model building for Social Studies (St. Martin’s SHS)

As shown in the classification table 4.2.3.3.4a, we would have been 74.7 percent correct to assume

that a student from St. Martin’s SHS would perform poorly in Social Studies, if we knew nothing

about our variables. The second classification table, depicts results when predictors are added.

The classification error rate changed from 74.7% to 81.3% when the predictors were added.


Observed Predicted

Performance of students in Social

Studies

Percentage

Correct

Poor Good


Social Studies

Poor 0 105 .0

Good 0 439 100.0

Overall Percentage

74.7


Observed Predicted


Studies

Percentage

Correct

Fail Pass


Social Studies

Poor 3 102 .0

Good 0 439 100.0

Overall Percentage

81.3

The –2LL recorded a value of 513.318 (see appendix IV) which has a significant probability of p

= 0.044˂0.05 Thus, the indication is that the model has a poor fit, with the model containing only


92

the constant indicating that the predictors do have a significant effect on the response variable and

create essentially a different model.



0.055, indicating a weak relationship of 3.1% between the predictors and the response variable.

(See appendix IV)

Hosmer Lemeshow statistic: The p-value (0.05) for the Hosmer-Lemeshow goodness-of-fit test

statistic is less than the significance value of 0.668 that indicates that the model’s estimates fit the

data at an acceptable level.

Table 4.2.3.3.4c Hosmer and

Lemeshow Test


1 3.167 8 .668



Factor one -.113 .118 .922 1 .035 .948

Factor two .020 .124 .025 1 .043 1.121

Factor three -.297 .116 6.522 1 .011 1.210

Factor four -.066 .206 .102 1 .047 .811

Factor five .085 .109 .601 1 .050 1.007

Factor six .155 .114 1.848 1 .762 .968

Factor seven .061 .116 .277. 1 .182 1.168

Factor eight .040 .113 .124 1 .034 1.057

Factor nine -.056 .101 .306 1 .003 .974

Factor ten .004 .109 .001 1 .024 1.040

Factor eleven -.065 .116 .313 1 .281 1.163

Factor twelve

Constant

-.113

1.454

.111

.159

1.044

2.825

1

1

.054

.093

.719

4.279


statistics in Table 4.2.3.3.1, is made use of out of the twelve (12) variables only eight (8) were

significant. The variables left after the forward likelihood selection are factor one, factor two,

factor three, factor four, factor five, factor eight, factor nine , factor ten and factor twelve.


93

Let 𝑋1= Factor one = Teacher instructional strategies,


𝑋3 = Factor three = Parental age/family size




𝑋7 = Factor nine = Extra - curricular factor


The probability of poor performance (Social Studies) is obtained by applying the logistic

transformation;

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

exp(1.454 0.113 0.0204 0.0297 0.066 0.08545 0.040 0.056 0.0048 )

1 exp(1.454 0.113 0.0204 0.0297 0.066 0.08545 0.040 0.056 0.0048 )

X X X X X X X X

X X X X X X X X

4.2.3.3.5 Model building for Core Mathematics (Nsawam Senior High School)

As indicated in classification table in (appendix IV) before, the variables were added, one could

have predicted that students from Nsawam SHS would performed poorly in Core Mathematics at

50.8 percent. But the inclusion of the predictors changed the classification error rate from 50.8

percent to 64.8 percent. This indicates that, we can now predict 64.8 percent accuracy which

implies that including variables to the model improves its accuracy.


Observed Predicted


Mathematics

Percentage

Correct

Poor Good


Mathematics

Poor 66 36 64.0

Good 39 58 59.8

Overall Percentage

64.8


94

The –2LL recorded a value of 260.006 (see appendix IV) which has a significant probability of p

= 0.045˂0.05. Thus, the indication is that the model has a poor fit, with the model containing only

the constant indicating that the predictors do have a significant effect on the response variable and




0.102, indicating a relationship of 10.2% between the predictors and the response variable (See

appendix IV).

Hosmer Lemeshow statistic:

Since the p-value (0.05) for the Hosmer-Lemeshow goodness-of-fit test statistic is less than the

significance value of 0.222, implying that the model’s estimates fit the data at an acceptable level.

Table 4.2.3.3.5b Hosmer and

Lemeshow Test


1 10.649 8 .222

Table 4.2.3.3.5c Variables in the Equation


Factor one .139 .158 .776 1 .378 1.14901

Factor two .024 .129 .035 1 .050 1.02481

Factor three .179 .137 1.715 1 .020 1.19651

Factor four .096 .387 .061 1 .028 1.10085

Factor five -.210 .172 1.483 1 .404 .8119

Factor six .177 .153 1.340 1 .592 1.19406

Factor seven -.236 .155 2.329 1 .992 .7892

Factor eight .276 .157 3.089 1 .040 1.31858

Factor nine .343 .226 2.298 1 .000 1.40922

Factor ten -.004 .167 .001 1 .046 .9966

Factor eleven .143 .153 .0876 1 .010 1.15467

Factor twelve -.074 .153 .233 1 .695 1.07644

Constant -.056 .591 .009 1 .924 .945

Variables in the equation: The Wald chi –square statistics in Table 4.2.3.3 is used to determine

the predictive efficiency model, out of the twelve (12) variables, seven (7) were significant. The


95

variables left after the forward likelihood selection are factor two, factor three, factor four

factor eight, factor nine, factor ten and factor eleven.

Let 𝑋1= Factor two = Students’ motivation to learn

𝑋2 = Factor three = Parental age/ family size


𝑋4= Factor eight = JHS attended factor related

𝑋5 = Factor nine = Extra-curricular activity factor


𝑋7 = Factor eleven = Course materials/ Media study habit

The regression model for the log –odds in favour of poor performance (Core Mathematics) is;

The probability of poor performance (Core Mathematics) is obtained by applying the logistic

transformation and that yields;

1 2 3 4 5 6 7

1 2 3 4 5 6 7

exp( 0.056 0.024 0.179 0.096 0.276 0.343 0.004 0.143 )

1 exp( 0.056 0.024 0.179 0.096 0.276 0.343 0.004 0.143 )

X X X X X X X

X X X X X X X

4.2.3.3.6 Model building for Integrated Science (Nsawam Senior High School)

As shown in the classification table in (appendix IV) we would have been 54.3 percent correct to

assume that a student from St. Martin’s SHS would perform poorly in Social Studies, if we knew

nothing about our variables. The second classification table, depicts results when predictors are

added. The classification error rate changed from 54.3% to 67.0% when the predictors were added.


96


Observed Predicted


Integrated Science

Percentage

Correct

Poor Good


Integrated Science

Poor 54 38 60.0

Good 29 78 72.9

Overall Percentage

67.0

The –2LL recorded a value of 251.535(see appendix IV) which has a significant probability of p

= 0.029˂0.05. The indication is that the model has a poor fit, with the model containing only the

constant indicating that the predictors do have a significant effect on the response variable and





appendix IV).

Hosmer Lemeshow statistic: Table 4.2.3.3.6b depicts that Hosmer – Lemeshow goodness- test

statistic with it significance (0.110) greater than p-value of 0.05, implying that the model’s

estimates fit the data at an acceptable level


Lemeshow Test

Step Chi-square df Sig.

1 14.377. 8 .110


97



Factor one .126 .158 .635 1 .026 1.134

Factor two .-108 .130 .697 1 .004 .897

Factor three -.056 .138 .164 1 .031 .946

Factor four -.584 .395 2.182 1 .034 .558

Factor five -.055 .178 .095 1 .035 .946

Factor six .211 .155 1.844 1 .024 1.234

Factor seven -.254 .158 2.578 1 .708 .776

Factor eight .373 .169 4.884 1 .361 1.452

Factor nine .247 .228 1.174 1 .794 1.280

Factor ten .193 .170 1.298 1 .017 1.213

Factor eleven .330 .159 4.325 1 .038 1.391

Factor twelve -.002 .156 .000 1 .089 .998

Constant 1.003 .605 2.742 1 0.98 2.725


the predictive efficiency model, out of the twelve (12) variables, eight (8) were significant. The

variables left after the forward likelihood selection are factor one, factor two, factor three,

factor four, factor five, factor six, factor ten and factor eleven.



𝑋3 = Factor three = Parental age/family size

𝑋4= Factor four = Learning environment


𝑋6 = Factor six = Examination factor




98

The probability of poor performance (Integrated Science) is obtained by applying the logistic

transformation which results into;

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

exp(1.003 0.126 0.018 0.056 0.584 0.55 0.211 0.193 0.330 )

1 exp(1.003 0.126 0.018 0.056 0.584 0.55 0.211 0.193 0.330 )

X X X X X X X X

X X X X X X X X

4.2.3.3.7 Model building for English Language (Nsawam Senior High School)

The classification table in (appendix IV) suggests that we would have been 51.8 percent correct

to assume that a student from Nsawam SHS (Nsasco) would perform poorly in English Language,

if we knew nothing about our predictors. The second classification table, depicts results when the

variables are included. The classification error rate changed from 51.8 (see appendix IV) percent

to 60.8 percent when the predictors were added. This implies that we can now predict 60.8%

accuracy which signifies that including variables to the model improves its accuracy.


Observed Predicted


Language

Percentage

Correct

Poor Good


English Language

Poor 53 43 56.4

Good 32 71 68.9

Overall Percentage

60.8

The value of -2LL is 254.748 (see appendix IV) which has a significant probability of p =

0.049˂0.05. This portrays that the model has a poor fit, with the model containing only the






99

0.133, indicating a relationship of 13.3% between the predictors and the response variable. (See

appendix IV)

Hosmer Lemeshow statistic: With a p-value of (0.05) for the Hosmer-Lemeshow goodness-of-

fit test statistic being less than the significance value of 0.314, implies that the model’s estimates

fit the data at an acceptable level.


Lemeshow Test


1 9..351 8 .314


the predictive efficiency model, out of the twelve (12) variables, eight (8) were significant. The


factor four, factor six, factor eight, factor ten and factor eleven.



Factor one .0.73 .159 .212 1 .045 1.076

Factor two .136 .131 1.069 1 .001 1.45

Factor three .177 .141 1.587 1 .008 1.194

Factor four -.036 .395 .008 1 .050 .965

Factor five -.120 .179 .449 1 .857 .887

Factor six .213 .158 1.829 1 .013 1.237

Factor seven -.113 .158 .510 1 .814 .893

Factor eight .428 .182 5.510 1 .019 1.534

Factor nine .112 .228 .239 1 .684 1.118.

Factor ten .276 .173 2.530 1 .012 1.318

Factor eleven .447 .161 7.725 1 .005 1.564

Factor twelve -.011 .156 .005 1 .830 .989

Constant .373 .604 .380 1 .537 1.451

The probability of poor performance (English Language) is obtained by applying the logistic

transformation resulting into;


100

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

exp(0.373 0.73 0.136 0.177 0.036 0.213 0.428 0.276 0.447 )

1 exp(0.373 0.73 0.136 0.177 0.036 0.213 0.428 0.276 0.447 )

X X X X X X X X

X X X X X X X X

Where 𝑋1= Factor one = Teacher instructional strategies


𝑋3= Factor three = Parental age/family size


𝑋5 = Factor six = Examination factor related

𝑋6 = Factor eight = Gender/Students’ indiscipline


𝑋8 = Factor eleven = Course materials/Media study habit.

4.2.3.3.8 Model building for Social Studies (Nsawam Senior High School)

The classification table in (appendix IV) presents with only the constant included, before any

coefficients are entered into the equation. Logistic regression compares this model with a model

including all the predictors to determine whether the latter model is more appropriate. The

classification table in (appendix IV) suggests that if we knew nothing about our variables and

guessed that a person would performance poorly in Social Studies at Nsawam SHS, we would be

62.0% correct of the time. This classification table below shows how the classification error rate

has changed from the original 62.0% to 69.5% after the predictors was added. So, by adding the

variables we can now predict with 69.5% accuracy. Meaning that adding variables to the model

improves its predictive accuracy.


101


Observed Predicted


Studies

Percentage

Correct

Poor Good


Social Studies

Poor 24 43 33.8

Good 17 115 87.1

Overall Percentage

69.5

The value of -2LL is 234.807 (see appendix IV) which has a significant probability of p =

0.036˂0.05. This indicates that the model has a poor fit, with the model containing only the






appendix IV).


test statistic is less than the significance value of 0.509, we fail to reject the null hypothesis that

there is no difference between observed and model-predicted values, implying that the model’s

estimates fit the data at an acceptable level.


Lemeshow Test

Step Chi-square df Sig.

1 7.259 8 .509

Variables in the equation: The Wald chi –square statistics in Table 4.2.3.3.8c is used to determine

the predictive efficiency model, out of the twelve (12) variables, six (6) were significant. The


factor seven, factor eleven and factor twelve (See Appendix IV).


102



𝑋3 = Factor three= Parental age/family size

𝑋4= Factor seven = Gender/Students’ indiscipline

𝑋5 = Factor eleven = Course materials/ gender study habit and

𝑋6 = Factor twelve = Guardian/sponsorship factor.

The probability of poor performance (Social Studies) is obtained by applying the logistic

transformation;

1 2 3 4 5 6

1 2 3 4 5 6

exp(1.199 0.052 0.212 0.52 0.166 0.479 0.206 )

1 exp(1.199 0.052 0.212 0.52 0.166 0.479 0.206 )

X X X X X X

X X X X X X


103

CHAPTER FIVE

5.0 SUMMARY, CONCLUSION AND RECOMMENDATION

This chapter presents summary of the findings from the study, and recommends rational measures

for stakeholders, educationist and investors. The chapter provides the concluding statements of

the research based on empirical evidences from the research results to guide policy formulation

and future research.

5.1 Summary

The main purpose of this research was to investigate and model factors that are capable of

influencing students’ academic performance at the second cycle institutions in Nsawam-

Adoagyiri Municipality, Ghana. The study considered two different statistical tools namely;

Factor Analysis and Binary Logistic Regression.

The factor analysis using the principal component analysis (PCA) was used to summarised and

reduced the covariates of academic performance from sixty- three (63) to twelve (12) constructs

(factors) based on the correlation that exist between the presumed variables.

Prior to performing PCA the suitability of the data for factor analysis was assessed. Inspection of

the correlation matrix revealed the presence of many coefficient of 0.3 and above. The Kaiser-

Meyer-Oklin value was 0 .706 exceeding the recommended value of 0.6 (Kaiser, 1970) and the

Bartlett’s Test of Sphericity reached statistical significance, supporting the factorability of the

correlation matrix.

Principal component analysis revealed the presence of twelve (12) component with eigenvalues

exceeding one rule explaining approximately 57 percent of the total variance. An inspection of

the scree plot revealed a break after the tenth component. Using eigenvalue greater than one rule

and comparing the variances explained by the tenth, eleventh and the twelfth components, we

decided to retain twelfth components for further investigation. To aid in the interpretation of these

twelfth component, Varimax rotation was performed. The rotated solution revealed the presence


104

of simple structure with all components showing a number of fairly strong loadings and all varia-

bles loading substantially on only a component. The factor scores of the twelve components were

calculated using Refined method specifically regression method.

Based on the factor scores of the twelve factors, a binary logistic regression was developed using

the students’ academic performance as response variables (categories into two; 0-49% as poor

academic performance and 50-100% as good academic performance) and the factors extracted

were used as explanatory variables.

Prior to the building of the model, multicolinearity which is an assumption under binary logistic

regression was checked. In all eight models were built, thus models were developed for all core

subjects in the two schools. To test the overall fit or significance of the binary logistic regressions,

we used the Hosmer and Lemeshow Test (Hosmer and Lemeshow, 2000) to test the capability of

all explanatory variables in the model to predict the dependent variables. The Wald chi-square

statistic was used to determine the predictive efficiency model at a significance level of 0.05.

5.2 Discussion of Results

The results from the factor analysis suggests that, the main factor influencing academic

performance at Nsawam- Adoagyiri Municipality, Ghana is teacher instructional strategies. The

influential factors in decreasing order are; teacher instructional strategies, students’ motivation to

learn, parental age/family size, learning environment, individual study habit, examination factor

related, gender/students’ indiscipline, junior high school attended factor related, extra-curricular

activity factor, parental employment status, course materials/media study habit and

guardian/sponsorship factor.

To determine the predictive efficiency of the model, the Wald chi-square statistic is made use of.

The model for poor academic performance in core mathematics for St. Martin’s SHS as displayed

in chapter four depicts that out of the twelve predictors, eight (8) were very significant at p-value


105

of 0.05. These predictors are; teacher instructional strategies, parental age/ family size, learning

environment, gender/students indiscipline, JHS attended factor, extra – curricular activity factor,

course materials/media study habit and guardian/sponsorship factor. Likewise, teacher

instructional strategies, parental age/ family size, learning environment, junior high school

attended factor, extra – curricular activity factor, parental employment status and course

materials/media study habit are the predictors that are very significant with reference to poor

academic performance in Core Mathematics at Nsawam SHS. Again, at p – value of 0.05, using

the Wald statistic, teacher instructional strategies, students’ motivation to learn, learning

environment, individual study habit, educational materials/media study habit factor, are the six (6)

out of twelve (12) predictors that are very significant to poor academic performance in Integrated

science at St. Martin’s SHS. On the other hand, eight (8) explanatory variables out of the twelve

(12) are very significant to poor Integrated science performance at Nsawam SHS. These variables

are; teacher instructional strategies, students’ motivation to learn, parental age/family size,

learning environment, individual study habit, examination factor, parental employment status and

course materials/media study habit.

Moreover, out of twelve (12) factors extracted that are presumed to affect students’ academic

performance in English Language at St. Martin’s SHS only seven (7) were significant at p- value

of 0.05 using the Wald chi-square statistic. These are; teacher instructional strategies, students’

motivation to learn, examination factor, gender/students’ indiscipline, junior high school attended

factor, parental employment status and course materials/ media study habit. Eight predictor

variables are very significant to poor academic performance in English Language at Nsawam SHS

out of the twelve factors extracted. These are; teacher instructional strategies, students’ motivation

to learn, parental age/family size, learning environment, examination factor, junior high school

attended factor, parental employment status and course materials/ media study habit.


106

Lastly, with regards to poor performance in social studies at St. Martin’s SHS eight explanatory

variables are significant at p-value of 0.05 while six out of the twelve predictors are significant at

the same p-value.

These factors are in line with the literatures reviewed in chapter two with the exception of Pandey

(2008). According to him academic achievement of students were not affected by employment

status of parents. The study was conducted, on 92 higher secondary students of Mizoram tribes.

5.4 Conclusions

The results from the factor analysis suggest that the main factor that influence academic

performance at second cycle institutions at Nsawam-Adoagyiri Municipality, Ghana is Teacher

instructional strategies factor related.

Again, based on the mean mark the two schools recorded (as shown in chapter four) in all the core

subjects, the study conclude that St. Martin Senior High School performance is relatively better

than Nsawam Senior High School.

The mathematical relation that came out of this model fitted in favour of poor academic

performance for all the core subjects to enabled us make a forecast are;

The probability of poor performance (Core Mathematics) in St. Martin’s SHS is given by;

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

exp(0.056 0.157 0.166 0.028 0.038 0.048 0.195 0.085 0.038

1 exp(0.560 0.157 0.166 0.028 0.038 0.048 0.195 0.085 0.038 )

X X X X X X X X

X X X X X X X X

The probability of poor performance (Core Mathematics) in Nsawam SHS is;

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

exp(1.454 0.113 0.0204 0.0297 0.066 0.08545 0.040 0.056 0.0048 )

1 exp(1.454 0.113 0.0204 0.0297 0.066 0.08545 0.040 0.056 0.0048 )

X X X X X X X X

X X X X X X X X

The probability of poor performance (Integrated Science) in St. Martin’s SHS is given by;

1 2 3 4 5 6

1 2 3 4 5 6

exp(1.053 0.68 0.043 0.189 0.043 0.021 0.156 )

1 exp(1.053 0.68 0.043 0.189 0.043 0.021 0.156 )

X X X X X X

X X X X X X

The probability of poor performance (Integrated Science) of Nsawam SHS is;


107

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

exp(1.003 0.126 0.018 0.056 0.584 0.55 0.211 0.193 0.330 )

1 exp(1.003 0.126 0.018 0.056 0.584 0.55 0.211 0.193 0.330 )

X X X X X X X X

X X X X X X X X

The probability of poor performance (English Language) in St. Martin’s SHS is as follows;

1 2 3 4 5 6 7

1 2 3 4 5 6 7

exp(1.054 0.216 0.049 0.034 0.304 0.194 0.042 0.263 )

1 exp(1.054 0.216 0.049 0.034 0.304 0.194 0.042 0.263 )

X X X X X X X

X X X X X X X

The probability of poor performance (English Language) in Nsawam SHS is;

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

exp(0.373 0.73 0.136 0.177 0.036 0.213 0.428 0.276 0.447 )

1 exp(0.373 0.73 0.136 0.177 0.036 0.213 0.428 0.276 0.447 )

X X X X X X X X

X X X X X X X X

The probability of poor performance (Social Studies) in St. Martin’s SHS is given by;

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

exp(1.454 0.113 0.0204 0.0297 0.066 0.08545 0.040 0.056 0.0048 )

1 exp(1.454 0.113 0.0204 0.0297 0.066 0.08545 0.040 0.056 0.0048 )

X X X X X X X X

X X X X X X X X

The probability of poor performance (Social Studies) in Nsawam SHS is;

1 2 3 4 5 6

1 2 3 4 5 6

exp(1.199 0.052 0.212 0.52 0.166 0.479 0.206 )

1 exp(1.199 0.052 0.212 0.52 0.166 0.479 0.206 )

X X X X X X

X X X X X X

Where 𝑋𝑖 = 1,2, … ,8 are defined in chapter four.

5.3 Recommendation

Factor scores from PCA have proven to be good explanatory variables for predicting a categorical

(dependent variables) data in a binary logistic regression modelling. We can therefore employ this

model to other areas. Based on the findings, the study suggests the following recommendation;

1. In order to improve students’ academic performance parents are encouraged to have family size

they can adequately cater for, while government among other things is encouraged to provide

schools with adequate learning materials.

2. The students’ should be oriented on the possible factors that may impede their success in

academic pursuit.

3. In-service training and seminars should be organised for both newly recruit and the old-hands

in the teaching profession.


108

4. School counsellors are advised to provide the necessary assistance and psychological support

for students so as to overcome their emotional problems especially during examination.


109

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APPENDICES

Appendix I

Questionnaire to ascertain Factors Affecting Academic Performance of Students in Second

Cycle Institutions: A case study of Nsawam-Adoagyiri Municipality.

This questionnaire is designed for academic purpose to seek information from final year students in

Nsawam–Adoagyiri Senior High Schools on factors affecting their academic performance. We promise

that any information provided on this questionnaire will be held in utmost confidence.

Part A: Demographic Information

(Please tick only one option for each question)

A1. What is your sex? 1. Male [ ] 2. Female [ ]

A2. What is your age? …………..

A3. What is your religious affiliation?

1. Christian [ ] 2. Muslim [ ] 3. Others [ ]. If others state……..

A4. What is your region of birth? ………..

A5. What is your district of birth? ………

A6. What locality do you permanently reside in? Urban [ ] Rural [ ] Regional Capital [

A7. In what region is your JHS? ………

A8. Where is the JHS you attended located? Regional Capital [ ] Urban [ ] Rural [ ]

A9. What is the ownership of your JHS? Public [ ] Private [

A10. What was your aggregate in BECE? …… …


117

Part B: Social and Economic Information

(Please tick one appropriate option for each question)

B1. Your Current School Name ……………………………

B2. Course of study……………………………………………………………………..

B3. What is your mode of residence? 1. Boarding [ ] 2. Hostel [ ] 3. Day [ ]

B4. Do you participate in any sporting activity? 1. Yes [ ] 2. No [ ]. If Yes in your own esti-

mation how many hours do you spend in week on this sport? ...........

B5. Do you belong to any club or society in school? 1. Yes [ ] 2. No [ ]. If Yes in your estimation

how many hours do you spend in week on this society? ………….

B6. Do you own a mobile phone(s)? 1. Yes [ ] 2. No [ ]

B7. Do you have access to internet? 1. Yes [ ] 2. No [ ]

B8. Which device do you use when on social media? ……………..

B9. In your estimation, how many minutes do you spend on social media networks in a week?

……………… Minutes

B10. In your estimation how many hours per a week do you spend watching television? ……….. .

B11. Mother’s age? ..........

B12. Father’s age? ………..

B13. How many siblings do your parents have? ............

B14. What is your position of birth in the family? ………

B15. Are your parents living together? 1. Yes [ ] 2. No [ ]. If No go to B16 and Yes go to B17.

B16 Why are parents not living together 1. Divorce [ ] 2. Separated [ ] 3. Loose union [ ]


118

B17. Whom do you live with? 1. Both Parents [ ] 2.Mother only [ ] 3. Father only [ ]

4. Other relative [ ] 5. Non relative [ ]

B18. What is your mother’s highest level of education? 1. Basic [ ] 2. Secondary [ ] 3.Tertiary

B19. What is your father’s highest level of education? 1. Basic [ ] 2. Secondary [ ] 3. Tertiary [ ]

B20. What is your mother’s status of employment?

1. Employee [ ]

2. Self-employed without employee(s) [ ]

3. Self-employed with employee [ ]

4. Casual worker [ ]

5. Contributing family worker [ ]

6. Apprentice [ ]

7. Domestic employee [ ]

B21. What is your father’s status of employment?

1. Employee [ ]

2. Self-employed without employee(s) [ ]

3. Self-employed with employee [ ]

4. Casual worker [ ]

5. Contributing family worker [ ]

6. Apprentice [ ]

7. Domestic employee [ ]

B22. Who sponsors your education? 1. Self [ ] 2. Parent [ ] 3. Relative [ ] 4. Non-relative [ ]

5. Scholarship [ ]

B23. Do you have textbooks in all the subject areas? Yes [ ] No [ ].If No how many do you have?

B24. Apart from the regular class period do you do any extra classes? ……. If Yes how many hours

in a week?

B25. Where do you study at home? ........ What distracts your study at your place of study …………


119

B26. In your own estimation, how much money do you spend in a week? ……..

PART C: Teacher and Self - Motivation

Please tick one appropriate option for each question.

Reasons

Str

on

gly

dis

agre

e

Dis

agre

e

Un

dec

ided

Ag

ree

Str

on

gly

agre

e

1. Teachers monitor students’ performance and provide constructive feedback as

needed.

2. Teachers give and mark homework.

3. The teachers are available to consult with students about problem.

4. The teachers reward and reinforce actual achievement.

5. Teachers provide approximately equal opportunity to respond and become

involved in instructions.

6. The teachers start lessons on time and continue without interruptions.

7. The teacher’s explanations and directions are clear and understandable.

8. The teachers spend sufficient time presenting, demonstrating and explaining

new content and skills to the whole group of students in the classroom.

9. The teachers provide adequate opportunity for students to practice and

reinforce newly acquired skills and content where help is available.

10. Teachers support academic focus of the school by spending most of the day on

instructional activities.

11. Compared with other students in this class I expect to do well.

12. I am certain I can understand the idea taught in class.

13. Even when I do poorly on a test I try to learn from my mistake.

14. I am nervous during a test that I cannot remember facts I have learned.

15. I have an uneasy, upset feeling when I take a test.

16. When I study for a test, I try to put together the information from class and

from books.

17. When I study, I try to remember as much as I can.


120

18. I use what I have learned from old assignment and textbooks to do new

assignment.

19. I ask myself questions to make sure I know the material I have been studying.

20. When work is hard I either give up or study the easy part.

21. Before I begin studying I think about the things I will need to do to learn.

22. I work hard to get good grades even when I don’t like the subject.

23. Students expect to and actually master academic work?

Part D: Students Behaviour

Please tick one appropriate option for each question

Reasons

Str

on

gly

dis

agre

e

Dis

agre

e

Un

dec

ided

Ag

ree

Str

on

gly

agre

e

1. I pay particular attention during teaching.

2. I find myself sleeping during teaching.

3. Chatting with one another during teaching.

4. Always on time to the classroom.

5. Coming to classroom habitually late.

6. Start answering questions before the question finishes.

7. Always listen to questions carefully before answering them.

8. Challenging teachers on certain concept.

9. I seek for explanations on concepts I do not understand.

10. I always follow teacher’s instructions.

11. Ignoring teacher’s direction.

C. Student Index Number ………………


118

Appendix II

Descriptive summary of the variables on the Likert scale

Teachers monitor students' performance and provide constructive feedback

Responses Frequency Percent Valid Percent Cumulative

Percent

Strongly disagree 96 12.9 12.9 12.9

Disagree 94 12.7 12.7 25.6

Undecided 60 8.1 8.1 33.6

Agree 348 46.8 46.8 80.5

Strongly agree 145 19.5 19.5 100.0

Total 743 100.0 100.0


Teachers are available to consult with student about problem


Percent


Disagree 108 14.5 14.5 26.4

Undecided 68 9.2 9.2 35.5

Agree 333 44.8 44.8 80.3

Strongly agree 146 19.7 19.7 100.0

Total 743 100.0 100.0



Teacher's start lessons on time and continue without interruptions


Percent


Disagree 224 30.1 30.1 47.2

Teachers reward and reinforce actual achievement


Percent


Disagree 171 23.0 23.0 36.9

Undecided 96 12.9 12.9 49.8

Agree 294 39.6 39.6 89.4

Strongly agree 79 10.6 10.6 100.0

Total 743 100.0 100.0


119

Undecided 67 9.0 9.0 56.3

Agree 228 30.7 30.7 86.9

Strongly agree 97 13.1 13.1 100.0

Total 743 100.0 100.0


Teachers spend sufficient time presenting, demonstrating and explaining new content

and skills to the whole group of students


Percent


Disagree 126 17.0 17.0 28.7

Undecided 77 10.4 10.4 39.0

Agree 310 41.7 41.7 80.8

Strongly agree 143 19.2 19.2 100.0

Total 743 100.0 100.0


Teachers support academic focus of the school by spending most of the day on

instructional activities


Percent


Disagree 137 18.4 18.4 33.1

Undecided 114 15.3 15.3 48.5

Agree 268 36.1 36.1 84.5

Strongly agree 115 15.5 15.5 100.0

Total 743 100.0 100.0


I am certain I can understand the idea taught in class


Percent


Disagree 73 9.8 9.8 13.9

Undecided 79 10.6 10.6 24.5

Agree 345 46.4 46.4 70.9

Strongly agree 216 29.1 29.1 100.0

Total 743 100.0 100.0



120

I am nervous during a test that I cannot remember facts I have learned


Percent


Disagree 131 17.6 17.6 37.0

Undecided 57 7.7 7.7 44.7

Agree 241 32.4 32.4 77.1

Strongly agree 170 22.9 22.9 100.0

Total 743 100.0 100.0


Even when I do poorly on a test I try to learn from my mistake


Percent


Disagree 20 2.7 2.7 6.9

Undecided 37 5.0 5.0 11.8

Agree 303 40.8 40.8 52.6

Strongly agree 352 47.4 47.4 100.0

Total 743 100.0 100.0


I have an uneasy, upset feeling when I take a test


Percent


Disagree 177 23.8 23.8 45.0

Undecided 80 10.8 10.8 55.7

Agree 224 30.1 30.1 85.9

Strongly agree 105 14.1 14.1 100.0

Total 743 100.0 100.0



121

When I study for a test, I try to put together the information from class and from

books


Percent


Disagree 47 6.3 6.3 10.0

Undecided 49 6.6 6.6 16.6

Agree 341 45.9 45.9 62.4

Strongly agree 279 37.6 37.6 100.0

Total 743 100.0 100.0


Before I begin studying I think about the things I will need to do to learn.


Percent


Disagree 64 8.6 8.6 13.5

Undecided 67 9.0 9.0 22.5

Agree 340 45.8 45.8 68.2

Strongly agree 236 31.8 31.8 100.0

Total 743 100.0 100.0


Students expect to and actually master academic work.


Percent


Disagree 43 5.8 5.8 10.0

Undecided 104 14.0 14.0 24.0

Agree 331 44.5 44.5 68.5

Strongly agree 234 31.5 31.5 100.0

Total 743 100.0 100.0



122

I work hard to get good grades even when I don't like the subject.


Percent


Disagree 47 6.3 6.3 9.7

Undecided 37 5.0 5.0 14.7

Agree 303 40.8 40.8 55.5

Strongly agree 331 44.5 44.5 100.0

Total 743 100.0 100.0


Students expect to and actually master academic work.


Percent


Disagree 43 5.8 5.8 10.0

Undecided 104 14.0 14.0 24.0

Agree 331 44.5 44.5 68.5

Strongly agree 234 31.5 31.5 100.0

Total 743 100.0 100.0


I pay particular attention during teaching


Percent


Disagree 42 5.7 5.7 9.7

Undecided 28 3.8 3.8 13.5

Agree 326 43.9 43.9 57.3

Strongly agree 317 42.7 42.7 100.0

Total 743 100.0 100.0

I find myself sleeping during teaching


Percent


Disagree 234 31.5 31.5 66.9

Undecided 73 9.8 9.8 76.7

Agree 122 16.4 16.4 93.1

Strongly agree 51 6.9 6.9 100.0

Total 743 100.0 100.0


123

Always on time to the classroom


Percent


Disagree 77 10.4 10.4 16.6

Undecided 42 5.7 5.7 22.2

Agree 272 36.6 36.6 58.8

Strongly agree 306 41.2 41.2 100.0

Total 743 100.0 100.0


Coming to classroom habitually late


Percent


Disagree 180 24.2 24.2 87.5

Undecided 29 3.9 3.9 91.4

Agree 39 5.2 5.2 96.6


Total 743 100.0 100.0


Always listen to questions carefully before answering them


Percent


Disagree 41 5.5 5.5 8.5

Undecided 41 5.5 5.5 14.0

Agree 332 44.7 44.7 58.7

Strongly agree 307 41.3 41.3 100.0

Total 743 100.0 100.0


Challenging teachers on certain concept.


Percent


Disagree 231 31.1 31.1 52.6


124

Undecided 87 11.7 11.7 64.3

Agree 177 23.8 23.8 88.2

Strongly agree 88 11.8 11.8 100.0

Total 743 100.0 100.0


I seek for explanations on concept I do not understand.


Percent


Disagree 66 8.9 8.9 12.5

Undecided 37 5.0 5.0 17.5

Agree 323 43.5 43.5 61.0

Strongly agree 290 39.0 39.0 100.0

Total 743 100.0 100.0


I always follow teacher's instructions.


Percent


Disagree 34 4.6 4.6 6.5

Undecided 47 6.3 6.3 12.8

Agree 308 41.5 41.5 54.2

Strongly agree 340 45.8 45.8 100.0

Total 743 100.0 100.0


Ignoring teacher's direction.


Percent


Disagree 190 25.6 25.6 88.8

Undecided 34 4.6 4.6 93.4

Agree 32 4.3 4.3 97.7


Total 743 100.0 100.0



125

Appendix IV

Result from Binary Logistic Regression

(A)

Variables in the Equation

B S.E. Wald df Sig. Exp(B)

Constant .527 .049 15.208 1 .124 1.993

Model Summary

-2 Log

likelihood

Cox & Snell R

Square

Nagelkerke R

Square

1 692.378 .045 .062

Omnibus Tests of Model Coefficients

Chi-square Df Sig.

Step 25.328 17 .048

Block 25.328 17 .048

Model 25.328 17 .048

Appendix IV (B)


B S.E. Wald Df Sig. Exp(B)

Constant .929 .095 95.323 1 .124 2.532

Model Summary

Step -2 Log

likelihood

Cox & Snell R

Square

Nagelkerke R

Square

1 628.278 .018 .026


Chi-square Df Sig.

Step 1

Step 20.003 17 .041

Block 20.003 17 .041

Model 20.003 17 .041


126

Appendix IV (C)



Constant 1.099 .099 123.109 1 .102 3.000

Model Summary

Step -2 Log

likelihood

Cox & Snell R

Square

Nagelkerke R

Square

1 595.232 .030 .044


Chi-square Df Sig.

Step 1

Step 14.337 17 .048

Block 14.337 17 .048

Model 14.337 17 .048

Appendix IV (D)

Classification Table

Observed Predicted


Studies

Percentage

Correct

Poor Good

Step 1


Social Studies

Poor 0 105 .0

Good 0 439 100.0

Overall Percentage

80.7



Step 0 Constant 1.466 .110 178.193 1 .142 7.31

Model Summary

Step -2 Log

likelihood

Cox & Snell R

Square

Nagelkerke R

Square

1 513.318 .021 .031


Chi-square Df Sig.

Step 1

Step 18.726 17 .044

Block 18.726 17 .044

Model 18.726 17 .044


127

Appendix IV (E)


Observed Predicted


Mathematics

Percentage

Correct

Poor Good


Mathematics

Poor 102 0 100.0

Good 97 0 .0

Overall Percentage

50.8



Constant -.030 .143 .046 1 .831 .970

Model Summary

Step -2 Log

likelihood

Cox & Snell R

Square

Nagelkerke R

Square

1 260.006 .076 .102


Chi-square df Sig.

Step 25.441 17 .045

Block 25.441 17 .045

Model 25.441 17 .045

Appendix IV (F)


Observed Predicted


Integrated Science

Percentage

Correct

Poor Good


Integrated Science

Poor 0 92 .0

Good 0 107 100.0

Overall Percentage

54.3



Constant .173 .143 1.463 1 .226 1.189


128

Model Summary

Step -2 Log

likelihood

Cox & Snell R

Square

Nagelkerke R

Square

1 251.535 .0.109 .145


Chi-square df Sig.

Step 26.490 17 .046

Block 26.490 17 .046

Model 26.490 17 .046

Appendix IV (G)


Observed Predicted


Language

Percentage

Correct

Poor Good


English Language

Poor 0 96 .0

Good 0 103 100.0

Overall Percentage

51.8



Step 0 Constant .091 .143 .411 1 .522 1.096

Model Summary

Step -2 Log

likelihood

Cox & Snell R

Square

Nagelkerke R

Square

1 254.748 .100 .133


Chi-square df Sig.

Step 21.726 17 .049

Block 21.726 17 .049

Model 21.726 17 .049

Appendix IV (H)


129


Observed Predicted


Studies

Percentage

Correct

Poor Good


Social Studies

Poor 0 67 .0

Good 0 132 100.0

Overall Percentage

62.0



Constant .708 .152 21.857 1 .060 2.031

Model Summary

Step -2 Log

likelihood

Cox & Snell R

Square

Nagelkerke R

Square

1 234.807 .087 .121


Chi-square df Sig.

Step 28.837 17 .036

Block 28.837 17 .036

Model 28.837 17 .036



Factor one .052 .180 .031 1 .002 1.032

Factor two .212 .141 4.673 1 .012 1.358

Factor three .52 .388 3.204 1 .043 .499

Factor four .029 .154 .036 1 .849 1.030

Factor five .039 .178 .047 1 .828 1.040

Factor six .395 .209 3.565 1 .072 1.485

Factor seven -.166 .182 .003 1 .047 1.010

Factor eight .074 .171 .186 1 .666 1.076

Factor nine -.012 .195 .004 1 .949 .988

Factor ten -.158 .244 2.146 1 .043 .699

Factor eleven .479 .154 .166 1 .033 .939

Factor twelve -.206 .156 1.112 1 .012 .848

Constant 1.199 .589 9.691 1 0.53 6.254


130


statistical modelling of factors affecting students

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