ABSTRACT
In this project entitled statistical analysis on education trust fund
allocation to tertiary institutions in six geo-political
zones of Nigeria, the average allocation to zones, method of distributions,
extraction of principal components, classification of the components into
factors and to test if there is any significant difference in the allocation
among the zones was carried out using principal components analysis, factor
analysis, normality test just to mention but a few. The average allocation to
all the zones within the period under review was #14,605,429,76. The allocation
to zones was normally distributed indicating unbiasedness in the allocations.
University allocation is the principal factor component in the ETF allocation
among the institutions revealing high contribution of university with 0.201 in
the first component, followed by monotechnics, polytechnics and colleges of
education. With little difference in the allocations among polytechnics,
monotechnics and colleges of education, they were grouped into one factor and
university in another factor. Based on the results obtained; no zone is more
favored and their distribution is unbiased.
CHAPTER ONE
1.0 INTRODUCTION
1.1 BACKGROUND OF STUDY
In
Principal Components Analysis (PCA) and Factor Analysis (FA) one wishes to
extract from a set of P variables a reduced set of M components or factors that
accounts for most of the variance in a P variables in other words, we wish to
reduce a set of P variables to a set of M underlying super ordinate dimensions.
These
underlying factors are inferred from the correlations among the P variables.
Each factor is estimated as a weighted sum of the P variables. The factor is
thus;
F1
= W1X1 + Wi2X2 + W1pXp+ K.
One may
also express each of the P variables as a linear combination of the M factors,
Xj
= Aij F1 + A2j F2 + Amj Fm + k+ Uj
Where
Uj is the variance that is unique to variable j, variance that
cannot be explained by any of the common factors. Principal component analysis
is a variable reduction procedure which provides
guidelines regarding the necessary sample size and number of items per
component. It also shows how
to determine the number of components to retain, interpret the rotated
solution, create factor scores and summarize the results.
It is
appropriate when you have obtained measures on a number of observed variables
and wish to develop a smaller number of artificial variables called Principal
Components that will account for most of the variance in the observed variables.
The principal components may then be used as predictor variables in subsequent
analysis.
Principal
component is defined as a linear combination of optimally weighted observed
variables. The “linear combination” here refers to the fact that scores on a
component are created by adding together scores on the observed variables being
analyzed and “optimally weighted” refers to the fact that the observed
variables are weighted in such a way that the resulting components account for
a maximal amount of variance in the data set.
Factor
analysis is a mathematical tool which can be used to examine a wide range of
data sets. It is the most familiar multivariate procedure used in the
behavioral sciences; it includes both component analysis and common factor
analysis. In factor analysis, you need only the correlation or covariance
matrix not the actual scores. The purpose of factor is to discover simple
patterns in the patterns of relationship among the variables. In particular, it
seeks to discover if the observed variable can be explained largely or entirely
in terms of a much smaller number of variable called factors.
Onyeagu
(2003) explained the difference between factor analysis and principal component
analysis. Factor analysis is covariance (or correlation) oriented. In principal
component analysis, all components are needed to produce an inter-correlation
(covariance) exactly. In factor analysis, a few factors will reproduce the
inter-correlations (covariance) exactly.
Wang (2007)
differentiate the principal component analysis and factor analysis as in
principal component analysis the major objective is to select a number of
component that will express as much of the total variance in the data as
possible.
However,
the factors formed in the factor analysis are generated to identify the latent
variables that are contributing
to the common variance in the data. A factor analysis attempts to exclude
unique variance from the analysis; whereas a principal component analysis does
not differentiate common and unique variance. PCA analyzes variance while FA
analyses covariance.
The PCA
and FA have some similarities such as their measurement scale is interval or
ratio level, linear relationship between observed variables, normal
distribution for each observed variables. Each pair of observed variables has a
bivariate normal distribution and lastly PCA and FA are both variable reduction
techniques. If communalities are large, close to 1.00, results could be similar.
1.2
SOME FACTS ABOUT NIGERIA EDUCATION
The
literacy and educational characteristic of population aged 6 years and above
were enumerated in 1991 population census. The literacy was 60% for males and
40% for females. The literacy level in the country appears to have improved
over years, while the sex differential on literacy among persons in the age
group 35-39 was almost twice as high for male (68.3%) and female (35.8%). In
contrast, the age group
10-14, literacy rate among male (76.6%) is higher than the corresponding rates
for females (74.7%) by barely 2%. This pattern did not vary among the States,
which indicates that there was increase awareness in all the States, that
education of the female child is desirable as that of a male child even for
heads of households.
Among the
population aged 15 years and above literacy rate was found to be 44.3% at the
national level. Adult literacy rate was lowest in Lagos State (19.8%) and River
State (20.3%) and highest Yobe State (68.6%). Very high adult literacy rates
were recorded also in Niger State (61.8%), Taraba (64.4%), Sokoto (64.5%),
Kebbi (66.1%) and in all 46% have no education. Such high illiteracy rate has
serious implication for schools, social and economic development. Similarly
more males than females attained either primary, secondary or tertiary level of
education and these situations may have resulted from long neglect of women’s
education needs and lack of funds to our educational system.
The education trust fund
(ETF) was established under Acts No7 of 1993 and amended by the act No 40 of
1998 with project management to improve the quality of education in
Nigeria.
To enable the ETF achieve the above objective, Act No 7 of 1993 as amended
imposes a two percent (2%) education tax on the assessable profit of all
registered companies in Nigeria. The Federal Inland Revenue Service (FIRS) is
empowered by the Act to access and collect the education tax. The fund
administers the tax imposed by the Act, and disburses the amount to educational
institution at Federal, State and Local Government levels. It also monitors the
projects executed with the funds allocated to the beneficiaries for effective
and efficient realization of mandate, implementation of its function and
general organization of work, the fund is structured into two segments below:-
1.
The Board of Trustees, and
2.
The Secretariat.
The
Board of Trustees
The funds
are managed by eleven member board of trustees headed by Chief (Mrs.) Olutoyin
Olakunri, OFR, with members drawn from the six geo-political zones of the
country as well as representatives of the Federal Ministry of Education,
Federal Ministry of Finance and Federal Inland
Monitor
and ensure collection of tax by the Federal Inland Revenues Service and ensure
transfer of the collected funds; Disburse the tax to appropriate ministries
responsible for collection of the tax; Receive requests, approve admitable
project after due consideration; Ensure disbursement to various level and
categories of education; Update the federal government on its activities and
progress through annual audited reports; review Progress and Suggest
improvement within the provision of the acts; Invest funds in appropriate and
state securities.
The
Secretariat
The
secretariat is headed by the chief executive Secretary, who is the chief executive
and accounting officer of the funds. Director and Heads of Department and unit,
assist him in the day to day running of the offices of the fund. The
departments are:
1.
Administration and procurement;
2.
Finance and Account ;
4.
Planning Research and Assessments;
5.
The Specializations Units;
6.
Information and Communication
Technology, Inter Audits;
7.
Legal services and board
secretariat servicom. Education Trust Fund has developed a culture of
accountability and
transparency in its operations over the years. These qualities are very
entrenched in all its policies and programmes in the areas of intervention in
the sector. The Education Trust Fund in promoting the twin qualities of
transparency and accountability ensures that education tax collection by the
Federal Inland Revenue Services are monitored and reconciled periodically. The
board also ensures that disbursement of funds to the beneficiary educational
institutions are use for the restoration, rehabilitation and consolidation of
education in the country.
Education
Trust Funds intervention in educational sector in Nigeria covers Federal
ministry of education, its agencies and parastatals, unity and technical
schools. Thirty six States plus FCT Primary Education Boards, and thirty six States
plus FCT ministries of education for secondary school education.
All
National and State Libraries;
All
Federal and State Universities;
All
Federal and State Polytechnic, Monotechnics; All Federal and State Colleges of
Education;
The main activities undertaken by Education Trust Funds
includes:-
1.
Liaising with Federal Inland
Revenue Service to monitor the collection of education tax;
2.
Providing pro-active support for
education tax collection by federal Inland Revenue Service;
3.
Embarking on periodic tax tour to
mobilize education tax;
4.
Embarking on joint reconciliation
visit to area offices of the Federal Inland Revenue Services;
5.
Receiving proposal on areas of
intervention from beneficiaries;
6.
Receiving proposal by
professionals to assess their relevance to improving the quality of teaching
and learning;
7.
Organizing periodic
workshops/seminars across the country
to enable stakeholders and beneficiaries make input into future intervention
policies.
The challenges before Education Trust Fund are as flows:-
1.
Boasting the confident of
stakeholders in funds by maintaining high standard of transparency as well as
efficient and effective operations;
2.
Ability to enhance and boast
teachers’ morale to such a high level and to positively rekindle interest in
teaching and learning in Nigeria schools;
3.
Ability to sufficiently sensitize
and collaborate effectively with the Federal Inland Revenue Service to expand
the funds revenue base;
4.
Encouragement of
information centre technology
to
enhance
teaching and learning in Nigeria schools. However, Education Trust Fund has the
following stated
goals:
1.
To continuously improve education
tax revenue by ensuring that all such taxes are collected and made available to
Education Trust Fund intervention.
2.
To promote cutting edge
technologies ideas and organization skills in education and ensure that
projects are forward-looking as well as responding to present needs;
3.
To ensure the prompt, effective
and successful completion of intervention projects in accordance with the most
pressing needs of beneficiary institution;
4.
To form a viable and enduring
partnership between the ETF and all bodies and institution interested in the
qualitative improvement of education in Nigeria;
5.
To create a cohesive and solid
organization characterized by commitment principles, loyalty to organization
and the nation, adequate capacity to accomplish set task with a learning
structured cooperation among the level of the organization and within each
levels, institutional periodic consultant among all levels and arms of the
organization;
6.
To manage education tax in a way
that is most beneficial to the Nigeria people;
7.
To deliver appropriate and
adequate intervention programmes to sensitize various groups and individuals in
the country.
1.3 STATEMENT OF PROBLEMS
The study
sought to examines the series of questions related to Education Trust Fund
funding to education. Is the funds normally distributed among the six
geo-political zones? Is any zone more favored? These with some other questions
about Education Trust Fund serve as the basis for which this research will be
carried out.
1.4 PURPOSE OF THE STUDY
The
purpose of this study is to examine how the Education Trust Fund disburses
funds to tertiary institution among the six geo-political zones in Nigeria.
1.5 SIGNIFICANCE OF THE STUDY
This study
is going to contribute significantly to educational development in Nigeria. It
will help statisticians in understanding the mechanism of Educational Trust
Last but not the least; it
will create an interest among the new researchers to employ such techniques in
their inter-disciplinary approach of research and literature review.
1.6 SCOPE OF THE STUDY
The study
will consider only the Educational Trust Fund funding to Tertiary Institution
in the six geo-political zones in Nigeria, from 1999-2007.
1.7 AIMS AND OBJECTIVES
The
specific aims and objective of this study are as follows:-
1.
To extract the first factor
principal component between the tertiary institution under study;
2.
To classify the components into
factors;
3.
To know if the distribution is
normally distributed;
4.
To know which of the zones is
favored by this distribution;
1.8 TEST OF HYPOTHESIS
Ho:
There is no significant difference in the allocation of ETF funding to tertiary
institution in the six geo-political zones. Hi: There is a significant
difference in the allocation of ETF funding to tertiary institution in the six
geo-political zones.
1.9 OPERATION KEY WORDS
Communality
– Denoted by h2. It is the proportion of the variance of an item
that is accounted for by the common factors in a factor analysis.
The
unique variance- of an item is given by 1− h2.
Eigen value - The
standardized variance associated with a particular factor. The sum of the
eigenvalues cannot exceed the number of items in the analysis, since each item
contributes one to the sum of variances.
Eigen vector are weights in a
linear transformation when computing principal components scores.
Factor: A
linear combination of items (in a regression sense, where the total test score
is the dependent variable and the items are the independent variables).
Principal Component- is a
linear combination of observed variables that explain a maximal amount of
variance in the data.
The factor
loading expresses the correlation of the item with the factor.
The square of this factor
loading indicates the proportion of variance shared by the item with the
factor.
Scree
plot: A plot of the obtained eigenvalue for each factor.
(A
paper by Diana D.S on Principal component Analysis Vs
Exploratory Factor Analysis.)
1.10
ABBREVIATIONS
P.A.
- Principal Analysis
F.A.
- Factor Analysis
C.O.E.
- College of Education
Univer
- University
Poly
- Polytechnic
Mono
- Monotechnic
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