## DETERMINATION OF STUDENTS’ ACADEMIC PERFORMANCE USING CANONICAL CORRELATION AND FACTOR ANALYSES

TABLE OF CONTENT

Title Page
Abstract
Table of Content

CHAPTER ONE: General Introduction
1.1       Introduction
1.2       Statement of the Problem
1.3       Background to the Study
1.4       Aim and Objectives
1.5       Scope and Limitation of the Study
1.6       Definition of terms and Concept Used

CHAPTER TWO: Literature Review
2.1       The Concept of Academic Performance
2.2       Canonical Correlation Analysis of Students’ Performance
2.3       Factor Analysis of Students’ Performance
2.4       Other Statistical Analysis of Students’ Performance

CHAPTER THREE: Materials and Methodology
3.1       Data Collection
3.2       Mathematical Computation of Canonical Correlation Analysis
3.3       Mathematical Computation of Factor Analysis
3.3.1    Orthogonal Factor Model
3.3.2    Estimating Factor Scores
3.4       Method of Computation of Canonical Coefficient
3.5       Significant Test
3.5.1    Wilk’s Lambda Test
3.5.2    Bartlett’s Test
3.6       Interpretation
3.7       Statistical Package used for the Study

CHAPTER FOUR: Results and Discussion
4.1       Introduction
4.2       Results from the Analysis of the Data Used
4.3       Discussion on the Result of the Analysis from the Data Used

CHAPTER FIVE: Summary, Conclusion and Recommendations
5.0       Introduction
5.1       Summary from output of Canonical Correlation Analysis
5.2       Summary from output of Factor Analysis
5.3       Conclusion
5.4       Recommendation
5.5       Contribution to Knowledge
References

ABSTRACT

In this study, we tried to evaluatestudents’ academic performance through the use of the relationship between mathematical and less-mathematical subjects and also tried to verify the subjects that contribute significantly to the variation among them. Canonical correlation analysis was employed to analyse the relationship between mathematical and less-mathematical subjects and to also test the significance of canonical variate and the homogeneity of variance among the variables obtained with the use of Wilk’s Lambda and Bartlett’s test respectively. Factor analysis was used to investigate the variability among the subjects and find out the variables that contribute significantly to the percentage of variance obtained. The data used is the Senior Secondary Certificate Examination results of Command Secondary School, Kaduna, conducted by the National Examination Council in the year 2008, 2009 and 2010 respectively. The data consists of results of 90 students in eight subjects out of nine registered subjects by each student. Two sets were formed; set-1 which consists of Mathematics, Chemistry and Physics; was classified as the mathematical subjects, while set-2 which consists of Economics, English Language, Biology, Geography and Hausa Language; was classified as less-mathematical subjects. The data wasanalyzed and structured into mathematical and less-mathematical data using the NCSS 2007 package. The purpose of the structuring was that of gathering information needed to quantify elements which were considered in order to construct determinant factors and to as well check which of the variables contributed significantly to the variance.Our results showed that less-mathematical subjects have significant impact on determining students’ academic performance.Three canonical roots were obtained and two are statistically significant showing a strong correlation between the two sets. Four factors were considered and it shows that less-mathematical subjects contribute significantly to the variation among the variables.Mathematical subjects are directly related, so also less-mathematical subjects. However, mathematical subjects are inversely related to less-mathematical subjects, which means, an increase in the students’ performance in mathematical subjects will lower the performance in less-mathematical subjects.

CHAPTER ONE

General Introduction

1.1              Introduction

Multivariate Statistics is a useful set of methods for analyzing a large amount of

information in an integrated frame, focusing on the simplicity (Simon, 1969) and latent order (Wheatley, 1994) in seemingly complex array of variables. Benefits of using multivariate statistics include: Expanding sense of knowing, allowing rich and realistic research designs and having flexibility built on similar univariate methods.

Canonical correlation analysis is the most generalized member of the family of multivariate statistical techniques. It is directly related to several dependence methods, similar to regression; canonical correlation’s goal is to quantify the strength of the relationship, in this case between the two sets of variables. It also resembles discriminant analysis in its ability to determine independent dimension for each variable set, in this situation with the objective of producing the maximum correlation between the dimensions. Thus, canonical correlation identifies the optimum structure or the dimensionality of each variable set that maximizes the relationship between dependent and independent variable sets(Anastasi and Urbina, 1997; Harlow, 2005).

Numerous studies, such as those carried out by Fullana (1995) and Montero (1990)have sought to understand the factors which account for low or high achievements. Studies seeking to identify what determines academic failure or success frequently appear as a reaction to conditions of change, such as plans for educational reform, or in response to critical situations: the National Examination Council (NECO) result, 2010, shows that less than twenty percent of those who sat for the examination made their subject combinations that can guarantee them admission into the tertiary institutions....

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