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
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)
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
Revenue Service. The board of trustees has the following
responsibilities as stated in the Acts:
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 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
1. Administration and procurement;
2. Finance and Account ;
3. Operation ;
4. Planning Research and Assessments;
5. The Specializations Units;
6. Information and Communication Technology, Inter
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
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
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
4. Embarking on joint reconciliation visit to area offices of
the Federal Inland Revenue Services;
5. Receiving proposal on areas of intervention from
6. Receiving proposal by professionals to assess their
relevance to improving the quality of teaching and
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
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
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
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
Funds, funding to tertiary institution and its impact on
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
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
5. To know the distribution of ETF allocation to Tertiary
Institution in Nigeria.
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
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.