Factor Analysis: Factors influencing the academic performance of students
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Transcript of Factor Analysis: Factors influencing the academic performance of students
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Introduction
1.1 IntroductionThere are a large number of higher learning institutions in Bangladesh that are governed by and
under supervision of Ministry of Education (MOE), Bangladesh. As to date, Bangladesh has 26
public universities (http://www.moedu.gov.bd) and University of Dhaka (DU) is the largest
university in Bangladesh, with a student population of over 115000.
Students are main assets of universities. The students performance (academic achievement)
plays an important role in producing the best quality graduates who will become great leader and
manpower for the country thus responsible for the countries economic and social development.
The performance of students in universities should be a concern not only to the administrators
and educators, but also to corporations in the labor market. Academic achievement is one of the
main factors considered by the employer in recruiting workers especially the fresh graduates.
Thus, students have to place the greatest effort in their study to obtain a good grade in order to
fulfill the employers demand. Students academic achievement is measured by the Cumulative
Grade Point Average (CGPA). CGPA shows the overall students academic performance where
it considers the average of all examinations grade for all semesters/years during the tenure in
university. Many factors could act as barrier and catalyst to students achieving a high CGPA that
reflects their overall academic performance.
There are several ways to determine student academic performance which are cumulative grade
point average (CGPA), grade point average (GPA), tests and others. In Bangladesh, researchers
evaluate the student academic performance based on CGPA. In addition, a study in the United
States by Nonis and Wright (2003) also evaluate student performance based on CGPA.
Most of the researches done in other countries used GPA as a measurement of academic
performance. They used GPA because they are studying the student performance for that
particular semester/year. Some other researcher used test results since they are studying
performance for the specific subject.
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1.2 Review of literature
Many studies have been developed concerning the factors influence studentsperformance such as demographic, active learning, student attendance, extracurricular
activities, peers influence and course assessment. Studies have shown that
demographic characteristics can influence academic excellence. Among these
characteristics are parents income, parents education and English results.
Hossain (1994) in his work A study of Factor Analysis and its Application" discussed
about its background, advantages limitations, uses factor model, method of analysis,
uses of SPSS for factor analysis. He also gave an example of motivation measures and
students attitude on the basis of his study.
Nasri and Ahmed (2007) in their study on business students (national students and
non-national students) in United Arab Emirates indicate that non-national students had
higher grade point average were more competent in English, which is reflected in
higher average for high school English.
Shamima Syeda Sultana (2003) in her work "Factor Analysis: An application to gross
domestic product data" discussed about the factors which have effects on the domestic
product from 1995-96 to 1999-2000 for 64 districts of Bangladesh. She also discussed
the division wise factors and comparison among the districts for the factors for that
period.
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1.3 Objectives of the study
The objectives of this study are
1. To collect primary data for the factor analysis.
2. To reduce the list of variables to few factors for modeling purposes.3. To fit a model with this factors to check the significance of the model. .
4. To find out the factors which influence the academic performance of the students.
5. To find out the association between these variables.
1.4 Sources of Data:
The data used in this study were collected from the students who live in the
Shahidullah hall (residential) of University of Dhaka.
1.5 Data processing:
After collecting data, the following computer application packages are used to process
the data:
1. SPSS 162. Microsoft Excel
1.6 Limitations of the study :
The limitations of this study are:
1. As primary data is used to analysis the data collecting procedure was not 100%
accurate.
2. In this report we only consider major 12 variables. Other less influential variables
have been ignored.
3. In our data collecting procedure the non residential students are ignored.
4. The data collecting procedure took a long time so that enough analysis could not be
done.
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Methods of Factor Analysis
2.1 Principal Component Analysis (PCA)
Principal component analysis (PCA) is a classical statistical method. It was first
derived by Karl Pearson (1901) and rediscovered by Hostelling in (1933). Principal
Components Analysis (PCA) is a multivariate procedure which rotates the data such
that maximum variabilities are projected onto the axes. Essentially, a set of correlated
variables are transformed into a set of uncorrelated variables which are ordered by
reducing variability. The uncorrelated variables are linear combinations of the original
variables, and the last of these variables can be removed with minimum loss of real
data. The main use of PCA is to reduce the dimensionality of a data set while retaining
as much information as is possible. It computes a compact and optimal description of
the data set. In communication theory, it is known as the Karhunen-Loeve transform.
This procedure performs Principal Component Analysis on the selected dataset. A
principal component analysis is concerned with explaining the variance covariance
structure of a high dimensional random vector through a few linear combinations of the
original component variables. Consider a p-dimensional random vector X = (Xi, X2...
Xp). k principal components ( k p ) of X are k (univariate) random variables YI,Y2,...,
Ykwhich are defined by the following formulae
Y1 = l1X = l11X1 +l12X2 + . . . + l1pXp
Y2 = l2X = l21X1 +l22X2 + . . . + l2PXp
.
.
.
Yk= lkX = lk1X1 +lk2X2 + . . . + lpkXp
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Where the coefficient vectors l1, l2 . . . etc are chosen such that they satisfy the
following conditions:
First Principal Component = Linear combination l1Xthat maximizes Var (l1X) and
|| l1|| =1
Second Principal Component = Linear combination l2Xand maximizes Var (l2X) and
|| l2||=1 and Cov (l1X, l2 X) = 0.
j th Principal Component = Linear combination ljX thatmaximizes Var(ljX) and ||lj||
=1 and Cov(lk'X,l'
jX) =0 for all k < j.
This says that the principal components are those linear combinations of the original
variables which maximize the variance of the linear combination and which have zero
covariance (and hence zero correlation) with the previous principal components.
It can be proved that there are exactly p such linear combinations. However, typically,
the first few of them explain most of the variance in the original data. So instead of
working with all the original variables X1, X2, . . . ,Xp you would typically first perform
PCA and then use only first two or three principal components, say Y1 and Y2, in
subsequent analysis.
2.2 Objectives of principal component analysis
1. To discover or to reduce the dimensionality of the data set.
2. To identify new meaningful underlying variables.
3. To derive a small number of linear combinations (principal components) of a set of
variables that retain as much of the information in the original variables as possible.
4. To reveal relationship that was not previously suspected and thereby allows
interpretation that would not ordinarily result.
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2.3 Properties of Principal Components
1. Transformation from z to y: The equation y = V'z represents a transformation, where
y is the transformed variable, z is the original standardized variable and V is thepremultiplier to go from z toy.
2. Orthogonal transformations simplify things: To produce a transformation vector for
y for which the elements are uncorrelated is the same as saying that we want V such
that Dy is a diagonal matrix. That is, all the off-diagonal elements of Dy must be zero.
This is called an orthogonalizing transformation.
3. Infinite number of values for V: There are an infinite number of values for V that
will produce a diagonal Dy for any correlation matrix R. Thus the mathematical
problem "find a unique V such that Dy is diagonal" cannot be solved as it stands. A
number of famous statisticians such as Karl Pearson and Harold Hotelling pondered
this problem and suggested a "variance maximizing" solution.
4. Principal components maximize variance of the transformed elements one by one:
Hotelling (1933) derived the "principal components" solution. It proceeds as follows:
for the first principal component, which will be the first element of y and be defined by
the coefficients in the first column of V, (denoted by V1), we want a solution such that
the variance of y1 will be maximized
5. Constrain v to generate a unique solution: The constraint on the numbers in V1is that
the sum of the squares of the coefficients equals 1. Expressed mathematically, we wish
to maximize
=
N
i
iyN 1
2
1
1
where y1i = v1' ziand v1'v1= 1 (this is called "normalizing v1).
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6. Computation of first principal component from R and v1, Substituting the middle
equation in the first yields
=
N
iiyN 1
2
1
1
= v1 Rv1
where R is the correlation matrix of Z, which, in turn, is the standardized matrix of X,
the original data matrix. Therefore, we want to maximize v1 Rv1 subject to v1'v1 = 1.
2.4 Procedure for Principal Component Analysis
Principal Components are particular linear combinations of the p random variables X1,
X2, . . . ,Xp
The first principal component is then the linear combination of the variables X1, X2, . . .
,Xp
Z1 = l11X1 + l12X2+ . . . + 11pXP = liX.
That varies as much as possible for the individuals, subject to the condition that li li =>
1211
+I
2'1p + . . .+1
21p =1 Thus the variance of Z, V(Z)is as large as possible given this
constraint on the constants 1ij.
The second principal component, Z2= l21X1 + 122X2+......... +12pXp =12 X is such that
V(Z2 ) is as large as possible subject to 1212=1=> 12
21+ 1222 +1
22p =1 and also to the
condition that Z1 and Z are uncorrected i.e. COV(Zl Z2)COV(l1 X,l'2X)= 0. Similarly
other principal components are defined in this way. If there are p variables, there can be
up to p principal components. The variance-covariance matrix is,
C=
pppp
p
p
CCC
CCC
CCC
...
............
...
...
21
22221
11211
Where the diagonal elements Cii are the variances of Xi' s and Cii' s are covariance's.
The variances of the principal components are the eigenvalues of the matrix C.
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Assuming that the eigenvalues are ordered as ip then ,0...21 corresponds to
the ith principal component
.11...11 '12121111 XXXXZ ipp =+++=
Now V(Zj) = i and the constants ipii 1...,11 ,2,1 . are the elements of eigenvector. An
important property of the eigenvalues ispppiccc +++= ...... 22111 .
It means that sum of the variances of principal components is equal to the sum of the
variance of the original data.
2.5 The Steps in a Principal Component Analysis
1. First code the variablesp
XXX ...,,2,1
to have zero means and unit variances.
2. Then calculate the nxp Data Matrix, Covariance Matrix, S or Correlation Matrix, R
3. Get eigenvalues ( pi ..,,,1 ) and eigenvectors ( pi aaa ,...,2, ), proportion of total
variation explained by the jth principal component is /j tr(S) and proportion of total
variation explained by the jth principal component is /j p.
4. Rescale principal components (aj*= ii a2/1
) and find correlation between ith variable
and jth principal component is aji*
5. Choose the number of principal components, Select a percentage of the total
variation that could be explained (70%-90%), Exclude principal components whose
eigenvalues are less than tr(S)/l (for R).
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2.6 Factor Analysis
Factor Analysis is a statistical approach that can be used to analyze interrelationships
among a large number of variables and to explain these variables in terms of their
common underlying dimensions (factors). Thousands of variables have been proposed
to explain or describe the complex variety and interconnections of social and
international relations. Perhaps an equal number of hypotheses and theories linking
these variables have been suggested.
Cureton and DAgostino (1983) described factor analysis as "a collection of procedures
for analyzing the relations among a set of random variables observed or counted or
measured for each individual of a group".
Bryman and Cramer (1990) broadly defined factor analysis as "a number of related
statistical techniques which help us to determine the characteristics which go together".
Hair et al. (1992) described factor analysis as "The statistical approach involving
finding a way of condensing the information contained in a number of original
variables into a smaller set of dimensions (factors) with a minimum loss of
information"
2.7 Types of factor analysis: Two main types:
1. Principal component analysis: - This method provides a unique solution, so that the
original data can be reconstructed from the results. It looks at the total variance among
the variables, so the solution generated will include as many factors as there are
variables, although it is unlikely that they will all meet the criteria for retention. There
is only one method for completing a principal components analysis; this is not true ofany of the other multidimensional methods described here.
2. Common factor analysis: - This is what people generally mean when they say "factor
analysis." This family of techniques uses an estimate of common variance among the
original variables to generate the factor solution. Because of this, the number of factors
will always be less than the number of original variables. So, choosing the number of
factors to keep for further analysis is more problematic using common factor analysis
than in principle components.
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2.8 Objectives of Factor analysis
1. To reduce a large number of variables to a smaller number of factors for modelingpurposes, where the large number of variables precludes modeling all the measures
individually. As such, factor analysis is integrated in structural equation modeling
(SEM), helping create the latent variables modeled by SEM. However, factor analysis
can be and is often used on a stand-alone basis for similar purposes.
2. To select a subset of variables from a larger set, based on which original variables
have the highest correlations with the principal component factors.
3. To create a set of factors to be treated as uncorrelated variables as one approach to
handling multi co-linearity in such procedures as multiple regression
4. To validate a scale or index by demonstrating that its constituent items load on the
same factor, and to drop proposed scale items which cross-load on more than one
factor.
5. To establish that multiple tests measure the same factor, thereby giving justification
for administering fewer tests.
6. To identify clusters of cases and/or outliers.
7. To determine network groups by determining which sets of people cluster together.
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2.9 Assumptions of Factor Analysis
1. Large enough sample to yield reliable estimates of the correlations among the
variables.
2. Statistical inference is improved if the variables are multivariate normal.
3. Relationships among the pairs of variables are linear.
4. Absence of outliers among the cases.
5. Some degree of co-linearity among the variables but not an extreme degree or
singularity among the variables.
6. Large ratio of N/k.
2.10 Procedure of Factor Analysis
Factor analysis has similar aim to principal component analysis. Here also, we reduce a
set of p variables to a few number of indices or factors and hence elucidate the
relationship between variables. Spearman proposed the idea that the test scores are all
of the form ,iii FX += where -X~ is the ith standardized test score with mean 0,
standard deviation 1. 1i is a constant. F is a factor value having mean 0 and standard
deviation =1 for all the individuals as a whole, c, is the part of X that is specific to ith
test. Also V(Xi)=l2i + V( i ) Since li is a constant, F and 6i are independent and V (F)
is assumed to be unity. But V(X,) is also unity, so that l2i+ V( i ) = 1. Hence the
constant li also called the factor loading, is such that its square is the proportion of the
variance of Xj that is accounted for by its factor.In the way the generalized factor
analysis model is -
ikikiii FFFX ++++= 1...11 2211
Where Xi is the ith response score (e.g. test score) with mean 0, variance 1, Ijj' s, (j =
1,2, . . . ,m), are factor loadings for the ith response variable. F1, ,F2, ... ,Fk are k
uncorrelated common factors, each with mean 0 and standard deviation I and is a
factor specific only to the ith response, ci's are uncorrelated with any of the common
factors and have zero means. In this model -
V (Xi) =1 = l211 V (F1) + l
211 V (F2) + . . .+ l
2ikV(Fk) + V ( i )=l
2i1+ . . . + l
2ik + V( i )
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where l2i1 + l
2i1 + . . . + l
2jk is called the communality. V( i )is called the specific
variance or uniqueness i.e., the part of variance that is unrelated to the common factors.
2.11 Steps in Factor Analysis
1. Collect data and compute an intercorrelation matrix. Compute the factorability of the
matrix.
2 .Extract an initial solution.
3. From the initial solution, determine the appropriate number of factors to be extracted
in the final solution
4. If necessary, rotate the factors to clarify the factor pattern in order to better interpretthe nature of the factors
5. Depending upon subsequent applications, compute a factor score for each subject on
each factor
2.12 The Factor Model
Let us assume that our Y variables are related to a number of functions operating
linearly.
That is,
Equation 1:
,12121111 ... mmFxFxFxY +++=
,22221212 ... mmFxFxFxY +++=
,32321313...
mmFxFxFxY +++=
K
K
K
,2211 ... mnmnnn FxFxFxY +++=
Where:
Y = a variable with known data
x= a constant
F = a function, f ( ) of some unknown variables.
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By application to the known data on the Y variables, factor analysis defines the
unknown F functions. The loadings emerging from a factor analysis are the constants.
The factors are the F functions. The size of each loading for each factor measures how
much that specific function is related to Y. For any of the Y variables of Equation 1 wemay write
Equation 2:
,...332211 xmFmFxFxFxY ++++=
With the F's representing factors and the it's representing loadings.
2.13 Methods of Estimation
A variety of methods have been developed to extract factors from an intercorrelation
matrix. SPSS offers the following methods i
1. Principle components method j
2. Maximum likelihood method (a commonly used method)
3. Principal axis method also know as common factor analysis
4. Unweighted least-squares method
5. Generalized least squares method
6. Alpha method
7. Image factoring
The most popular methods of estimation of parameters of factor analysis are the
principle component method and the maximum likelihood method. In this methods
principal component analysis transforms the correlation matrix into new, smaller sets
of linear combinations of independent (i.e., uncorrelated) principle components
(Zillmer and Vuz, 1995). Principal component analysis is a separate technique from the
ML method because it partitions the variance of the correlation matrix into new
principle components (Zillmer and Vuz, 1995).
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2.13.1 The Principal Component Method
Let the observable random vector X has covariance matrix . Let Z has eigenvalue -
eigenvector pairs (ii
,
) with
pi
...2,
) 0 Then
)1('...' .........................111 ppp ++=
We can write = LL
Allowing for the specific variance T we can write the equation
)2.(....................' += LL
2.14 Some Basic Terms Related to Factor Analysis
2.14.1 Factor- loading
A factor loading is the correlation between a variable and a factor that has been
extracted from the data .Factor loadings are the basis for imputing a label to the
different factors. The correlations between the variables and the two factors (or "new"
variables), as they are extracted by default; these correlations are called factor loadings.
Factor loading are those values, which explain how closely the variables are related to
each one of the factors discovered. They are also known as factor-variable correlation.
In fact, factor loading work as key to understanding what the factors mean. It is the
absolute size (rather than the signs, plus or minus) of the loading that is important in
the interpretation of a factor. In a word, correlation between the factor and a variable is
called factor-loading. The component matrix indicates the correlation of each variable
with each factor.
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2.14.2 Communality
The sum of the squared factor loadings for all factors for a given variable (row) is the
variance in that variable accounted for by all the factors, and this is called the
communality. Communality shows how much of each variable is accounted for by the
underlying factor taken together. A high value of communality means that not much of
the variable is left over after that ever the factors represent is taken into consideration.
It is worked out in respect of each variable as under:
Communality of the ith variable= (ith factor loading of factor A)2 + (ith factor loading
of factor B)2+ ...
2.14.3 Eigenvalue (or Latent Root) i
Eigenvalue is the amount of variance in variable set explained by the factor. When we
take the sum of squared values of factor loading relating to a factor, then such sum is
referred to as eigenvalue or latent root. Eigenvalue indicates the relative importance of
each factor in accounting for the particular set of variables being analyzed.
2.14.4 Correlation Matrix
The most often employed techniques of factor analysis are applied to a matrix of
correlation coefficients among all the variables. The full correlation matrix involved in
the factor analysis is usually shown if the number of variables analyzed is not overly
large. Often, however, the matrix is presented without comment. Specifically, the
correlation matrix has the following features.
The coefficients of correlation express the degree of linear relationship between the
row and column variables of the matrix. The closer to zero the coefficient, the less the
relationship; the closer to one, the greater the relationship. A negative sign indicates
that the variables are inversely related.
To interpret the coefficient, square it and multiply by 100. This will give the percent
variation in common, for the data on the two variables.
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The correlation coefficient between two variables is the cosine of the angle between
the variables as vectors plotted on the cases (coordinate axes)..
2.14.5 KMO and Bartletts test
KMO and Bartletts test of sphericity produces the Kaiser-Meyer-Olkin measure of sampling
adequacy and Bartletts test. KMO value should be greater than 0.5 if the sample is adequate.
The KMO statistic varies between 0 and 1.A value close to 1, indicating the factor analysis is
preferable. Bartletts measure test the null hypothesis that the original correlation matrix is an
identity matrix. For factor analysis to work we need some relationships between variables and if
the R-matrix were an identity matrix then all correlation coefficients would be zero. Therefore,
we want this test to be significant (i.e. have a significant value less than .05). A significant test
tells us that the R-matrix is not an identity matrix; therefore there are some relationships between
variables we hope to include in the analysis.
2.14.5 Rotation
There are various methods that can be used in factor rotation...
1. Varimax Rotation: - Varimax Rotation attempts to achieve loadings of ones and
zeros in the columns of the component matrix (1.0 & 0.0).
2. Quartimax Rotation: - Quartimax Rotation attempts to achieve loadings of ones and
zeros in the rows of the component matrix (1.0 & 0.0).
3. Equimax Rotation: - Equimax Rotation combines the objectives of both varimax and
quartimax rotations
4. Orthogonal Rotation: - Orthogonal Rotation preserves the independence of the
factors, geometrically they remain 90 apart.
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5. Oblique Rotation: - Oblique Rotation produce factors that are not independent,
geometrically not 90 apart.
Rotation, in the context of factor analysis, is some thing like staining a microscope
slide. Just as different structures in the data. Though different rotations give results that
appear to be entirely different, but from a statistical point of view, all results are taken
as equal, none superior or inferior to others. However, from the stand point of making
sense of the results of factor analysis, one must select of the right rotation. If the factors
are independent orthogonal rotation is done and if the factors are correlation, an
oblique rotation is made. Communality for each variable will remain undisturbed
regardless of rotation but the eigenvalue will change as a result of rotation.
2.14.6 Factor Rotation
All factor loadings obtained from the initial loadings by an orthogonal transformation
have the same ability to reproduce the covariance matrix. From matrix algebra we
know that an orthogonal transformation corresponds to a rigid rotation of the
coordinate axes. For this reason an orthogonal transformation of the factor loadings and
the implied orthogonal transformation of the factors are called factor rotation.
2.14.7 Unrotated Factor Matrix
Two different factor matrices are often displayed in a report on a factor analysis. The
first is the unrelated factor matrix; it is usually given without comment. The features of
the matrix which are useful for interpretation are as follows
The number of factors (columns) is the number of substantively meaningful
independent (uncorrelated) patterns of relationship among the variables.
The loadings, ,, measure which variables are involved in which factor pattern and to
what degree The square of the loading multiplied by 100 equals the percent variation
that a variable has in common with an unrotated pattern.
The first unrotated factor pattern delineates the largest pattern of relationships in the
data; the second delineates the next largest pattern that is independent of (uncorrelated
with) the first; the third pattern delineates the third largest pattern that is independent of
the first and second; and so on. Thus the amount of variation in the data described by
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each pattern decreases successively with each factor; the first pattern defines the
greatest amount of variation, the last pattern the least.
The column headed "h2" displays the communality of each variable. This is the
proportion of a variable's total variation that is involved in the patterns. The coefficient(communality) shown in this column, multiplied by 100, gives the percent of variation
of a variable in common with each pattern.
The percent of common variance figures indicate how whatever regularity exists in the
data is divided among the factor patterns. The percent of total variance figures measure
bow much of the data variation is involved in a pattern; the percent of common
variance figures measure how much of the variation accounted for by all the patterns is
involved in each pattern.
The eigenvalues equal the sum of the column of squared loadings for each factor.
They measure the amount of variation accounted for by a pattern. Dividing the
eigenvalues either by the number of variables or by the sum of h2
values and
multiplying by 100 determines the percent of either total or common variance,
respectively.
2.14.8 Rotated Factor Matrix
The rotated factor matrix should not differ in format from the unrelated factor matrix,
except that the h2 may not be given and eigenvalues are inappropriate. The following
features characterize the rotated matrix:
If the rotated matrix is orthogonal then several features of the unrotated matrix are
preserved by the orthogonally rotated matrix. In the unrotated matrix, factor patterns
are ordered by the amount of data variation they account for, with the first defining the
greatest degree of relationship in the data. In the orthogonally rotated matrix, no
significance is attached to factor order. If the rotated matrix is oblique rather than
orthogonal then Oblique rotation takes place in one of two coordinate systems: either a
system of primary axes or a system of reference axes. The primary factor pattern matrix
and the reference factor structure matrix delineate the oblique patterns or clusters of
interrelationship among the variables. Their loadings define the separate patterns and
degree of involvement in the patterns for each variable.
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2.14.9 Factor Scores
A useful by product of factor analysis is factor scores. Factor scores are composite
measures that can be computed for each subject on each factor. They are standardized
measures with a mean = 0.0 and a standard deviation of 1.0, computed from the factorscore coefficient matrix. Factor score represents the degree to which each respondent
gets high scores on the group of items that load high on each factor. Factor scores can
explain what the factors mean with such scores, several other multivariate analyses can
be performed.
2.15 Advantages of Factor Analysis
The advantages of Factor Analysis are discussed below
1. Factor analysis can simultaneously manage over a hundred variables, compensate for
random error and invalidity, and disentangle complex interrelationships into their major
and distinct regularities.
2. The technique of factor analysis is quite useful when we want to condense and
simplify the multivariate data.
3. The technique is useful to verify conceptualization of a construct of interest.
4. The technique is helpful in pointing out important and interesting relationships
among observed data that were there all the time, but not easy to see from the data
alone.
5. The technique can reveal the latent factors (i.e., underlying factors not directly
observed that determine relationships among several variables concerning a research
study.
6. The technique may be used in the context of empirical clustering of products, media
or people i.e., for providing a classification scheme when data scored on various rating
scales have to be grouped together.
7. The technique may be used in the context of empirical clustering of products, media
or people i.e., for providing a classification scheme when data scored on various rating
scales have to be grouped together.
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2.16 Disadvantages of Factor Analysis
The disadvantages of Factor Analysis are discussed below
1. It is mathematically complicated and entails diverse and numerous considerations inapplication.
2. Its technical vocabulary includes strange terms such as eigenvalues, rotate, simple
structure, orthogonal, loadings, and communality etc.
3. The problem of communicating factor analysis is especially crucial for peace
research. Scholars in this field are drawn from many disciplines and professions, and
few of them are acquainted with the method.
4. It involves laborious computations involving heavy cost burden. With computer
facility available these days, there is no doubt that factor analyses have become
relatively faster and easier, but the cost factor continues to be the same i.e., large factor
analyses are still bound to be quite expensive.
5. The results of a single factor analysis are considered generally less reliable and
dependable for very often a factor analysis starts with a set of imperfect data
6. Factor analysis is a complicated decision tool that can be used only when one has
through knowledge and enough experience of handling this tool. Even then, at times it
may not work well and may even disappoint the user.
2.17 Uses of Factor Analysis
The uses of factor analysis are discussed below
1. Interdependency and pattern delineation: - If a scientist has a table of data-say, UN
votes, personality characteristics, or answers to a questionnaire-and if he suspects that
these data are interrelated in a complex fashion and then factor analysis may be used to
untangle the linear relationships into their separate patterns.
2. Parsimony or data reduction: - Factor analysis can be useful for reducing a mass of
information to an economical description. For example, data on fifty characteristics for
300 nations are unwieldy to handle, descriptively or analytically. The management,
analysis, and understanding of such data are facilitated by reducing them to their
common factor patterns.
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3. Structure: - Factor analysis may be employed to discover the basic structure of a
domain. As a case in point, a scientist may want to uncover the primary independent
lines or dimensions-such as size, leadership, and age-of variation in group
characteristics and behavior. Data collected on a large sample of groups and factoranalyzed can help disclose this structure
4. Classification or description: - Factor analysis is a tool for developing an empirical
typology. It can be used to group interdependent variables into descriptive categories,
such as ideology, revolution, liberal voting, and authoritarianism. It can be used to
classify nation profiles into types with similar characteristics or behavior.
5. Scaling:-A scientist often wishes to develop a scale on which individuals, groups, or
nations can be rated and compared. The scale may refer to such phenomena as political
participation, voting behavior, or conflict. A problem in developing a scale is to weight
the characteristics being combined. Factor analysis offers a solution by dividing the
characteristics into independent sources of variation (factors).
6. Hypothesis testing:- Hypotheses abound regarding dimensions of attitude,
personality, group, social behavior, voting, and conflict. Since the meaning usually
associated withx
"dimension" is that of a cluster or group of highly intercorrelated
characteristics or j behavior, factor analysis may be used to test for their empirical
existence.
7. Data transformation: - Factor analysis can be used to transform data to meet the
assumptions of other techniques. If the predictor variables are correlated in violation of
the assumption, factor analysis can be employed to reduce them to a smaller set of
uncorrelated factor scores.
8. Exploration: - In a new domain of scientific interest like peace research, the complex
interrelations of phenomena have undergone little systematic investigation. The
unknown domain may be explored through factor analysis. It can reduce complex
interrelationships to a relatively simple linear expression and it can uncover
unsuspected, perhaps startling, relationships.
9. Mapping: - Besides facilitating exploration, factor analysis also enables a scientist to
map the social terrain. This means the systematic attempt to chart major empirical
concepts and sources of variation. These concepts may then be used to describe a
domain or to serve as inputs to further research.
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Data and Variables
3.1 Target population
The intended target population for this study isthe 3rd, 4th and the M.SC students of the
Shahidullah Hall of University of Dhaka. Each student is considered as sampling unit.
Shahidullah Hall is one of the biggest halls of university of Dhaka. In that hall every
kind of students lives. So for data collection this hall is considered. The 3rd
, 4th
and the
M.SC students were considered in this study because they have at least spent three
years in this university and for that reason their academic performances can beconsidered as adequate for this kind of analysis.
For sampling cluster sampling technique is used, this is because enough information
was not available to construct the sampling frame for other probability sampling
techniques. For data collection only the main building of the Shahidullah Hall is
considered because most of the 3rd
, 4th and
the M.SC students live in that building. In
that building hall rooms were considered as clusters. There are 178 clusters in the
sampling frame. Among them 32 were selected randomly. From this selected clusters
56 sampling units are taken.
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3.2 Data
The questionnaire was distributed to the selected hall students. The questionnaire is given
in appendix. A total of56 questionnaires were completed. Of the 56 sample units, 16.07% are 3rd year students, 64.28 % are 4th year students and rest of them are M.SC
students.
Figure 4.1: Data
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Figure 4.2: Data
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3.3 Variables
We consider here 11 Variables which influence students academic performances.Qualitative variables are ignored for this study to avoid complications.
The 11 Variables are given below:
1.Attendance in class.
2. Study hours per week after class.
3.Family income.
4. Involvement in political activities.
5. Involvement in extracurricular activities.
6. Past academic performances (SSC and HSC results).
7. Entertainment.
8. Involvement in financial (income earning) activities.
9. How long it took to get a seat in the hall.
10. Number of roommate.
11. Sleeping hours.
1. Attendance in class:
Attendance in class refers to the attendance of the 3rd, 4 th and the M.SC students in
their class of the Shahidullah hall of University of Dhaka
2. Study hours per week after class:
This variable refers to the time spent for study in a week after class of the 3rd, 4th
and the
M.SC students of the Shahidullah hall of University of Dhaka
3. Family income:
This variable refers to the monthly income of the earning members of the family of the of the
3rd, 4th and the M.SC students of the Shahidullah hall of University of Dhaka
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4. Involvement in political activities:
This variable refers to the time spent for political works, discussions, meetings and
other political activities of the 3rd, 4th and the M.SC students of the Shahidullah hall of
University of Dhaka.
5. Involvement in extracurricular activities:
This variable refers to the time spent for the extracurricular activities such as playing
different types indoor and outdoor games, participate in debate competitions etc of the
3rd, 4th
and the M.SC students of the Shahidullah hall of University of Dhaka.
6. Past academic performances (SSC and HSC results).
This variable refers to the SSC and HSC result of the 3rd, 4th
and the M.SC students of
the Shahidullah hall of University of Dhaka.
7. Entertainment:
It refers to the time spent for watching TV, listening to music, reading novels etc of the
3rd, 4th
and the M.SC students of the Shahidullah hall of University of Dhaka.
8. Involvement in financial (income earning) activities:
It refers to the time spent for the income earning activities such as tutoring students,
part time jobs, business etc.
9. How long it took to get a seat in the hall:
This variable refers to the time taken to get seat in the hall.
10. Number of roommate:
It refers to the number of roommate of the 3rd, 4th and the M.SC students of the
Shahidullah hall of University of Dhaka.
11. Sleeping hours:
It refers to the time a student used to sleep over 24 hours.
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Analysis of Data
Factor Analysis is a statistical approach that can be used to analyze interrelationships
among a large number of variables and to explain these variables in terms of their
common underlying dimensions (factors). Thousands of variables have been proposed
to explain or describe the complex variety and interconnections of social and
international relations. Perhaps an equal number of hypotheses and theories linking
these variables have been suggested. So this method is chosen for analysis.
The first thing to do when conducting a factor analysis is to look at the inter-correlation between
variables. We expect that our variables correlate with each other. If we find any variables that do
not correlate with any other variables then we should consider excluding these variables before
the factor analysis is run. The correlations between variables can be checked using the correlate
procedure to create a correlation matrix of all variables. This matrix can also be created as part of
the main factor analysis.
KMO and Bartletts test of sphericity produces the Kaiser-Meyer-Olkin measure of sampling
adequacy and Bartletts test. KMO value should be greater than 0.5 if the sample is adequate.
The KMO statistic varies between 0 and 1.A value close to 1, indicating the factor analysis is
preferable. Bartletts measures test the null hypothesis that the original correlation matrix is an
identity matrix. For factor analysis to work we need some relationships between variables and if
the R-matrix were an identity matrix then all correlation coefficients would be zero. Therefore,
we want this test to be significant (i.e. have a significant value less than .05). A significant test
tells us that the R-matrix is not an identity matrix; therefore there are some relationships between
variables we hope to include in the analysis.
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4.1 Correlation matrix, KMO-Barletts test, Eigenvalues, Factor analysis and
interpretation
SPSS software is used to analyze the data.
Table 4.1: The correlation matrix involved in the factor analysis for academic
performance
Previous result 1.000
Number of roommate -.197 1.000
Time taken to get a hall seat .106 .084 1.000
average attendance .655 -.218 .025 1.000
average study hour per week .505 -.352 .022 .734 1.000
Family income .182 -.162 .203 -.025 .094 1.000
average financial activity -.368 .066 -.084 -.319 -.391 -.608 1.000
average extracurricular activity .175 -.010 -.149 .130 .127 .210 -.366 1.000
average entertainment per day -.174 .144 .098 -.074 -.255 .073 -.043 .118 1.000
average political activity -.390 .072 -.124 -.661 -.370 -.017 .234 -.319 -.170 1.000
average sleep per day .029 .112 -.122 .181 -.007 -.049 -.074 .091 .299 -.183 1.000
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From table 4.1 we can see that students average attendance and average study per week after
class have high positive correlation with previous result, and strong negative correlation with
average political activity. It means students have good previous result who attends the class
regularly and who studies a good amount of time after class than the other students. Average
attendance has positive correlation with average study per week after class and negative
correlation with political activity. That means if a student is regular in class then he spends good
amount of time for his study and can not spend a lot of time for his political activities. We found
that the family income has negative correlations with the financial activity and positive
correlation with extracurricular activity. That means students whose parents have high income do
not have to involve in much financial activities and their involvements in extracurricular
activities are better for this reason.
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Table 4.2: KMO- Barletts test for academic performance
Kaiser-Meyer-Olkin Measure of Sampling Adequacy. .616
Approx. Chi-Square 194.031
df 55
Bartlett's Test of Sphericity
Sig. .000
KMO and Bartletts test of sphericity produces the Kaiser-Meyer-Olkin measure of sampling
adequacy and Bartletts test. KMO value should be greater than 0.5 if the sample is adequate.
The KMO statistic varies between 0 and 1.A value close to 1, indicating the factor analysis is
preferable. Bartletts measure tests the null hypothesis that the original correlation matrix is an
identity matrix. For factor analysis to work we need some relationships between variables and if
the R-matrix were an identity matrix then all correlation coefficients would be zero. Therefore,
we want this test to be significant (i.e. have a significant value less than .05). A significant test
tells us that the R-matrix is not an identity matrix; therefore there are some relationships between
variables we hope to include in the analysis.
As the value of KMO is .616 (Values between 0.5 and 0.7 are considered as mediocre) it
indicates that the patterns of correlations are relatively compact and so factor analysis yield
distinct and reliable factors. For these data, Bartletts test is significant as p < .05.So, factor
analysis is appropriate here.
Also in Bartlett's Test of Sphericity, our null Hypothesis is Correlation Matrix Is a Singular
Matrix. Which is Rejected for tabulated Chi-Square Value 194.031 (for df 55 and level of
significance .01) .So we can say that Correlation matrix of 11 variable is not a singular but
positive definite matrix and we can move forward to Extract the Factors.
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4.1.1 Total Variance Explained By Eigenvalue
The Eigenvalue of the Correlation matrix is the variance of the variables explained by the
factors. We calculate twelve Eigenvalues as same number of the variables. Here in Table 4.3 1st
column shows the Calculated Eigenvalues of factor components. 2nd column shows the variance
explained by each factor and 3rd
column shows the cumulative variance.
Table 4.3: Initial Eigenvalues for students academic performance
Initial Eigenvalues
Component Total
% of
Variance Cumulative %
1 3.199 29.078 29.078
2 1.648 14.981 44.059
3 1.510 13.729 57.788
4 1.169 10.623 68.411
5 .882 8.018 76.429
6 .800 7.271 83.700
7 .520 4.729 88.429
8 .490 4.458 92.887
9 .404 3.677 96.564
10 .253 2.296 98.860
11 .125 1.140 100.000
1 3.199 29.078 29.078
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The largest eigenvalue is 3.199, which is greater than unity. Then the percentage of total
sample variance explained by the first factor is 29.078%.
The second factor has an eigenvalue= 1.648. Since, this is greater than 1.0, it explains
more variance than a single variable, in fact 1.648 times as much. The percent a
variance explained = 14.981%.The third factor has an eigenvalue= 1.510.. The percent a
variance explained = 13.729%.The fourth factor has an eigenvalue= 1.169. The percent a
variance explained 10.623%.
Factors 5 through 11 have eigenvalues less than 1 & therefore explain less variancethan a single variable. We have found four eigenvalues greater than unity here & in this
study this four factors can explain the 68.411% the total variation.
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4.1.2 Scree Plot
Scree plot is special kind of graph showing Eigenvalues for the component factor. here
component under the line is not considered because eigenvalues less than 1 is can not explain
variance of more than one variable.
Figure 4.3: Scree plot
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4.1.3 Extracted factors
Here factor having Eigenvalues greater than 1 is extracted
Table 4.4: Extracted Factor with Variance
Extraction Sums of Squared Loadings
Component Total
% of
Variance
Cumulative
%
1 3.199 29.078 29.078
2 1.648 14.981 44.059
3 1.510 13.729 57.788
4 1.169 10.623 68.411
Extracted four factors by Scree Plot describe almost 70 % of the total variance (Table 4.4). That
is, Factor Analysis by PCA is effective.
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4.1.4 Extracted factor after Rotation
Extracted factors after rotation also explain more than 70 % of variation. After rotation 1st factor
components described variation reduces where other factor components variation increase. (See
Table 4.5). This improves the result.
Table 4.5: Rotation of Extracted Factor with Variance
Rotation Sums of Squared Loadings
Component Total
% of
Variance
Cumulative
%
1 2.869 26.078 26.078
2 1.856 16.871 42.949
3 1.595 14.501 57.450
4 1.206 10.962 68.411
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4.1.5 Factor Loading to Each Variable:
Table 4.6: Component matrix
Component
variable 1 2 3 4
Previous result .763 -.164 -.008 .119
Number of roommate -.342 .385 .229 .254
Time taken to get a hall
seat .097 .147 -.277 .865
average attendance .852 -.199 .348 .123
average study hour per
week.788 -.351 .010 -.017
Family income .334 .435 -.719 -.031
average financial activity -.637 -.400 .430 .126
average extracurricular
activity.388 .451 -.015 -.484
average entertainment per
day-.085 .718 .279 .161
average political activity -.672 -.174 -.414 -.189
average sleep per day
.130 .437 .555 -.121
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4.1.6 Communality
The proportion of the variance Explained by the factor loading is the communality of a variable.
It is the sum of squared factor loading to each variable. In PCA we assumed all the variables
have same variance in common.
Table 4.7: Communalities for students academic performance
Variable
Communalities
Previous result.623
Number of roommate.382
Time taken to get a hallseat .856
average attendance.902
average study hour per
week .744
Family income.818
average financial activity.766
average extracurricularactivity .588
average entertainment perday .626
average political activity .689
average sleep per day
.531
From the Table 4.7 we have seen that almost every variable has high communality (common or
shared variance explained by the factors) except number of roommate.
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4.1.7 Suppressed factor loadings
We omit the factor loading less than 40 % for better understanding of factor description.
Table 4.8: Suppressed Component Matrix
Component
variable 1 2 3 4
Previous result .763
Number of roommate
Time taken to get a hall seat .865
average attendance .852
average study hour per week .788
Family income .435 -.719
average financial activity -.637 -.400 .430
average extracurricular
activity.451 -.484
average entertainment per
day.718
average political activity -.672 -.414
average sleep per day.437 .555
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Here we see, Factor-1 holds all variables except Number of roommate, Time taken to get a hallseat, Family income, average extracurricular activity, average entertainment per day and average
sleep per day. Factor-2 holds Family income, average financial activity, average extracurricular
activity and average entertainment per day. Factor-3 holds Family income, average
entertainment per day, average political activity and average sleep per day. Factor-4 holds Time
taken to get a hall seat and average extracurricular activity. This factor does not give us precise
idea. So we will check the factor loading for Varimax rotated factor Rotation.
4.1.8 Suppressed Rotated Factor Loadings
Table 4.9: Suppressed Rotated Component Matrix
variable 1 2 3 4
Previous result.737
Number of roommate.502
Time taken to get a hall seat .905
average attendance.949
average study hour per week.784
Family income.880
average financial activity-.816
average extracurricular activity .532 -.464
average entertainment per day.766
average political activity-.740
average sleep per day
.641
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Here we see
Factor-1 holds
Previous result, Average attendance,
Average study hour per week,
Average political activity.
Factor-2 holds
Family income ,
Average financial activity ,
Average extracurricular activity.
Factor-3 holds
Average entertainment per day,
Average sleep per day.
Number of roommate
Factor-4 holds
Time taken to get a hall seat
Average extracurricular activity.
4.1.9 Factor naming
Factor1: Academic effort factor
Factor 2: Financial factor
Factor 3: Leisure and entertainment factor
Factor 4: Hall seat factor
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Table 4.10: Factor score
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4.2: Regression Model
Here, we consider
CGPA= dependent variable
Factor 1= independent variable
Factor 2 = independent variable
Factor 3= independent variable
Factor 4= independent variable
The linear regression model
CGPA=b0 + b1.factor 1+b2.factor 2 + b3.factor 3+ b4.factor 4
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Table 4.11: Correlations between Each Pair of Variables
CGPA factor1 factor2 factor3 factor4
CGPA 1.000 .925 .042 -.124 -.011
factor1 .925 1.000 .000 .000 .000
factor2 .042 .000 1.000 .000 .000
factor3 -.124 .000 .000 1.000 .000
Pearson Correlation
factor4 -.011 .000 .000 .000 1.000
CGPA . .000 .380 .181 .469
factor1 .000 . .500 .500 .500
factor2 .380 .500 . .500 .500
factor3 .181 .500 .500 . .500
Sig. (1-tailed)
factor4 .469 .500 .500 .500 .
CGPA 56 56 56 56 56
factor1 56 56 56 56 56
factor2 56 56 56 56 56
factor3 56 56 56 56 56
N
factor4 56 56 56 56 56
This table gives details of the correlation between each pair of variables. We do not want strong
correlations between the criterion and the predictor variables. From the above table we can see
that factor 1 has strong correlation with CGPA and factor 3 and factor has negative correlation
with CGPA. Factor 2 has very small correlation with the CGPA.
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Table 4.12: Model Summary
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .934a
.872 .862 .12733
This table is important. The Adjusted R Square value tells us that our model accounts for 86.2%
of variance in the CGPA scores a very good model.
Table 4.13: ANOVA
ANOVA
Model
Sum of
Squares df Mean Square F Sig.
Regression 5.647 4 1.412 87.066 .000a
Residual .827 51 .016
1
Total 6.474 55
This table reports an ANOVA, which assesses the overall significance of our model. As p < 0.05
our model is significant.
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Table 4.14: Collinearity diagnostics
Coefficients
Unstandardized Coefficients
Standardized
Coefficients Collinearity Statistics
Model B Std. Error Beta t Sig. Tolerance
(Constant) 3.232 .017 189.952 .000
factor1 .317 .017 .925 18.477 .000 1.000
factor2 .014 .017 .042 .833 .409 1.000
factor3 -.043 .017 -.124 -2.479 .017 1.000
1
factor4 -.004 .017 -.011 -.212 .833 1.000
The Standardized Beta Coefficients give a measure of the contribution of each variable to the
model. A large value indicates that a unit change in this predictor variable has a large effect on
the criterion variable. The t and Sig (p) values give a rough indication of the impact of each
predictor variable a big absolute t value and small p value suggests that a predictor variables
having a large impact on the criterion variable.
From the table we can see that the factor 1 is highly significant as expected. Academic
perseverance has positive effect on outcome meaning, larger values of this factor result in better
academic performance. Also factor 3 is significant and has negative effect on outcome, meaning
that higher values for this factor score result in poorer academic performance. Average time
spent on entertainment, number of hours of sleep per day and to some extent, numbers of
roommate has high loadings on this factor. Thus, these variables are correlated and they have a
negative impact on academic performance.
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Conclusion
This study is conducted to identify the factors influencing the performance of students living at
Shahidullah Hall in University of Dhaka. The factor analysis is done with eleven variables which
are attendance in class, study hours per week after class, family income, political influences,
extracurricular activities, past academic performances (SSC and HSC results), entertainment,
involvement in financial activities, how long it took to get a seat in the hall, number of
roommate, sleeping hours. From the analysis our finding is that we reduce the variables to four
factors that are academic effort factor, financial factor, leisure and entertainment factor and hall
seat factor. Then a regression model is fitted with this factors which are considered as
impendent variables and Current CGPA is considered as dependent variable. We test
significance of the model. The result of the significance test is that our model is significant with
these factors. That means this four factors mainly influence the academic performance of the
students living at Shahidullah Hall in University of Dhaka. The findings of the study were
summarized and discussed in the following paragraphs.
The result of the analysis indicates that the academic effort factor has very high positive effect onthe CGPA that means students who have good previous result, who attends the class regularly,
who studies a good amount of time after class have, better CGPA than the other students.
We found that the financial factor has very small influence to the academic performance. That
means if a student is busy with income earning activities then it will have little effect on his
CGPA.
From the result we also found that entertainment factor has negative influence to the academic
performance of the students. That means if a student is too busy with entertainment that it will
have bad effect on his academic performance.
We also found that hall seat factor, factor 3 is significant and has negative effect on outcome,
meaning that higher values for this factor score result in poorer academic performance. Average
time spent on entertainment, number of hours of sleep per day and to some extent, numbers of
roommate has high loadings on this factor. Thus, these variables are correlated and they have a
negative impact on academic performance.
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The result of the analysis indicates the previous result, attendance, study hour after class have
the positive correlation and political activity has negative correlation with the CGPA that means
students who have good previous result, who attends the class regularly, who studies a good
amount time after class have better CGPA than the other students. Again if a student is spendinglots of time for his political activities then he has less CGPA then others who have not involved
in political activities. We found that students who were actively engage in extracurricular
activities obtained greater CGPA. This is proved by the result that involvement in extracurricular
activities has positive relationship with CGPA.
We found that the family income has negative correlations with the financial activity and
positive correlation with extracurricular activity. That means students whose parents have high
income do not have to involve in much financial activities and their involvements in
extracurricular activities are better for this reason.
We also found that Time taken to get a hall seat has negative correlation with Average
extracurricular activity. That means if time taken to get a hall seat is too long for a student then a
he can not involve in extracurricular activities as much as other can. This is because if a student
can not get a seat in the hall in proper time then he has to face many problems So he does not get
proper time for involvement in extracurricular activities.
From the result we also found that entertainment has positive correlation with the sleep per day
and has negative correlation with political activity. We can interpret this as if a student is busy
with entertainment then he gets tired and sleep more than usual and can not involve in much
political activities.
After discussing all these, we can comment that, the students performance (academic
achievement) plays an important role in producing the best quality graduates who will become
great leader and manpower for the country thus responsible for the countries economic and social
development. The performance of students in universities should be a concern not only to the
administrators and educators, but also to corporations in the labour market. Academic
achievement is one of the main factors considered by the employer in recruiting workers
especially the fresh graduates. Thus, students have to place the greatest effort in their study not
only to obtain a good grade but also in order to developing a set of moral and ethical values,
developing social competency and consistent attendance.
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Appendix
Questionnaire
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A survey to determine the factors influencing
academic performance of students living in
Shahidullah Hall of University of Dhaka
Questionnaire
Department:
Current year:
Division:
1.1. Current CGPA:
1.2. Your GPA at
1st year 2nd year 3rd year 4th year
1.3. S.S.C. result: 1.4. H.S.C. result:
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2.1. Have you been allocated a seat in the Hall?
a. yes b. no
2.2.If yes, how long did it take for you to get a seat?
2.3. How many roommates do you have?
3. Attendance in class (in percentage) during
1st year 2nd year 3rd year 4th year
4.1. Average number of study hours after class per week during
1st year 2nd year 3rd year 4th year
4.2. At which times of the day do you usually study after class? (e.g., 6p.m.-
10 p.m.)
5.1 What is your fathers occupation?
5.2. What is your familys monthly income?
5.3. What is your fathers educational status?
a) No formal education b) Primary (class 1 to 5) c) Secondary (class 6 to 10)
d) Higher secondary (class 11 to 12) e) Undergraduate f) Postgraduate
5.4. What is your mothers educational status?
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a) No formal education b) Primary (class 1 to 5) c) Secondary (class 6 to 10)
d) Higher secondary (class 11 to 12) e) Undergraduate f) Postgraduate
6. What is your birth order (i.e. eldest, second child, youngest, etc)?
7. Have you been involved in money earning activities (for example, tutoring students,
part time jobs, business, etc) during
a) 1st year a. no b. yes If yes, average amount of time (in hrs) spent in a day:
b) 2nd year a. no b. yes If yes, average amount of time (in hrs) spent in a day:
c) 3rd year a. no b. yes If yes, average amount of time (in hrs) spent in a day:
d) 4th year a. no b. yes If yes, average amount of time (in hrs) spent in a day:
8. 1. Have you ever been involved in extracurricular activities (say, playing football or cricket,
participating in debate competitions, etc.)?
a) yes b) no
8.2. If yes, how many hours did you spend on average per day during the
1st year 2nd year 3rd year 4th year
9. What is the average amount of time (in hrs) you spend each day for entertainment (say,
watching TV, listening to music, reading novels, etc.)?
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10. Have you ever been involved in political activities?
a) 1st year a. no b. yes If yes, average amount of time spent per week: hrs
b) 2nd year a. no b. yes If yes, average amount of time spent per week: hrs
c) 3rd year a. no b. yes If yes, average amount of time spent per week: hrs
d) 4th year a. no b. yes If yes, average amount of time spent per week: hrs
11.1. On average, how many hours do you sleep in a day (i.e. over a 24hr period)?
11. 2. Have you ever been seriously ill during the academic year?
a) yes b) no
11. 3. At present, what is the condition of your physical heath?
a) good b) somewhat good c) bad
12. Do you wear eye glasses?
a) yes b) no
13. Do you smoke?
a) yes b) no
14 How many hours do you spend with friends outside class each day? hrs
15.1 Are classes conducted regularly and in a timely manner for most of the courses?
a) yes b) no.
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15.2. Are course teachers very helpful in general?
a) yes b) no
16.1. How many students are there in your class?
16.2. Do you find other students in your class helpful?
a) yes b) no
16.3. Do you engage in group study?
a) yes b) no
16.4. Where do you usually study?
a) library b) own room c) class room d) other places
e) reading room
17. Do you rely on financial support from your family?
a) yes b) no
18. What is your marital status?
a) single b) engaged c) married
19. Are you satisfied with your current academic performance?
a. yes, I am satisfied.
b. yes, but I want to improve it.
c. no, I really need to improve it.
20. Comment on the quality of food served in the dining halls.
a. good . b average c poor quality
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Bibliography
Richard A. Johnson and Dean W. Wichern (1982). Applied Multivariate Statistical
Analysis. Prentic- Hall, Inc. Englewood Cliffs, New Jersy 07632.
Mc Donald, R. (1985). Factor Analysis and Related Methods. Hillsdale, NJ: Erlbaum.
Economic Trends, July 2007, July 2008, July 2009, Statistics Department, Bangladesh
Bank.
Syeda Shamima Sultana (2003) Factor Analysis: An application to Gross Domestic
Product Data. Institute of Statistical Research and Training. University of Dhaka.
Md. Omar Faruque (2008) An application of factor analysis to the Agricultural
Production in Bangladesh. Institute of Statistical Research and Training. University of
Dhaka.
Websites:
http://www.hawaii.edu
http://www.wikiedia.com
http://www.cscanada.org
http://www.cscanada.net
http://www.moedu.gov.bd