factor analysis: factors influencing the academic performance of students

7/28/2019 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.




preferable. Bartletts measures test the null hypothesis that the original correlation matrix is an







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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




preferable. Bartletts measure tests the null hypothesis that the original correlation matrix is an






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


.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


.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



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


4.1. Average number of study hours after class per week during


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


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

factor analysis: factors influencing the academic performance of students

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