RESEARCH METHODOLOGY

CONTENTS; BI VARIATE ANAYSIS

CONCEPT OF RELATIONSHIP

CROSS TABULATION &

PERCENTAGE DIFFERENCE

PROPORTIONAL ERROR

REDUCTION

MULTIVARIATE ANALYSIS

BIVARIATE ANALYSIS

Bivariate analysis means analysis of

two variables simultaneously.

Brand preference of LEVIS age

youth adults

YES 140(70%) 20(10%)

NO 60(30%) 180(90%)

TOTAL 200 200

CONCEPT OF RELATIONSHIP

Association means the relationship

between two variables under study.

It states how many categories of

variable x go with certain categories of

variable y.

This is called principle of co variance

and this is the basic notion of

association.

Eg; demand and price, crop yield and

fertilizer input..etc

Questions to be considered..

Is there any relationship between the

variables under study.??

If so,. then what is the direction and

degree of relationship??

Is the relationship is a casual one??

Is the relationship is statistically

significant??

Measures of association

Most important measures of association are;

1.Association coefficients

2.Cross tabulation and percentage difference.

3.Correlation coefficient

4.Regression analysis

Association coefficients

1. Lambda

2. Goodman and kruskal’s tau

3. Gamma

4. Kendall's tau

5. Somers’ d

Cross tabulation and percentage difference

It is used for measuring association

between nominal level variables.

Nominal level variable are purely

qualitative and can be categorized

only.

A.PEFERENCE OF BRAND X AND AGE

BRAND PREFERENCE AGE

YOUTH ADULT TOTAL

1. YES 120(60%) 120(60%) 240

1. NO 80(40%) 80(40%) 160

A two way table is prepared (table A).

The values for one variable is put

along one side of the table and the

values of the another variable is put

along the other side of the table . each

variable is categorized into two or

more categories and values are cross

tabulated for those sub categories

In table A variables of brand

preference and age are independent

i.e., not associated because

proportionately as many youths as

adults prefer brand X

B.PREFERENCE OF BRAND Y & AGE

BRAND

PREFERENCE

AGE

YOUTH ADULT TOTAL

YES 140(70%) 20(10%) 160

NO 60(30%) 180(90%) 240

TOTAL 2OO 200 400

In table B , we can find that the

variables are greatly associated

because higher proportion of youths

prefer brand Y than adults.

There we can say that the variables

age and brand preference are

associated.

Direction of relationship

Direction of association may be of two

types

1.positive relationship

2.negative relationship

When one variable increases other variable also increases , then a direct or positive relationship exists between the variables.

E.g. children’s age and weight, fertilizer input and crop yield.

When one variable increases other variable decreases then an indirect or negative relationship.

E.g.., price and demand , socio economic status and family size.

Strength of relationship

Strength of relationship is determined

by the pattern of differences between

the values of variables.

If there are marked percentage

difference between different

categories of variables, the

relationship between them is strong.

If the difference is slight then the

relationship is weak.

Table A – strong relationship.

Statistical significance

Statistical significance is determined

by using an appropriate tests of

significance.

Stronger the relationship is more likely

to be significant

PREDICTION OR PROPORTIONAL REDUCTION OF ERROR (PRE)

Loan status number

delinquent 30

Non delinquent 20

total 50

Best prediction to be made is based on mode.

Here the mode is delinquent.

By assuming all are delinquent ,,

Our prediction will result in 20 errors

Error rate =20/50 x100 = 40%

Loan repayment(x) Membership(y)

member Non member total

Delinquent 22 8 30

Non delinquent 4 16 20

total 26 24 50

Here we use within the category

mode.

With in the delinquent category the

mode is delinquent, if we guess all are

delinquent then;

Error rate = 4/26 x 100 = 15%

Within non delinquent category mode

is non delinquent, assuming all are

non delinquent,,

Error rate=8/24 x 100 = 33%

Proportional error reduction;

Total error = 4+8 = 12

Error rate =(4+8)/(26+24) = 24%

From 40 % we have reduced it to 24% this is known as PRE.

PRE = (E1 – E2) / E1

E1- original no. of errors after employing independent variable

E2- new error after employing independent variable as predictor

Rules of PRE..

PR1-to predict the dependent variable

use its own mode

PR2- to predict the dependent

variable, use within category modes of

the independent variable.

MULTIVARIATE ANALYSIS

Analysis of multiple variables of a

phenomenon is called multivariate

analysis.

It involves simultaneous analysis of

more than two variables.

It provides complete explanations of

for complex phenomena and permit

assessing casual relationship through

statistical control.

WHY MULTIVARIATE..???

The bi-variate measures of

relationship has only limited function

of establishing co variation and its

directions.

Many a time the relationship between

variables may affected by a third

variable or un revealed variable.

Some times the phenomenon under

study cannot be explained through bi

variate analysis.

THE CONCEPT OF CONTROL

A correlation between an independent and dependent variable is not a sufficient basis for inferring casual relationship between them.

The relationship may be caused by a third variable and that is the cause of both independent and dependent variable.

By eliminating such effects only ,the original bivariate association can be validated. it can be achieved through CONTROL

CONTROL; In social sciences research this can be

achieved through..; 1.CROSS TABULATION

2.PARTIAL CORRELATION

3.MULTPLE CORRELATION

4.MULTIPLE REGREESION

5.FACTOR ANALYSIS

CROSS TABULATION

First we establish the relationship between independent and dependent variable, through bivariate analysis.

We select a independent third variable which is associated with independent variable and use it as a control variable

Then the sample is subdivided into sub groups.

We may find an entirely different result;

1.dissappearence / weakening of original relationship.

2.new relationship

3.A strong relationship under one condition and not in another.

Example;

A . POLITICAL AWARNESS AND PLACE OF LIVING

POLITICAL AWARNESS LOCATION

URBAN RURAL

HIGH 200(50%) 140(28%)

LOW 200(50%) 360(72%)

TOTAL 400(100%) 500(100%)

B. PLACE OF LIVING BY EDUCATIONAL LEVEL

PLACE OF LIVING EDUCATIONAL LEVEL

HIGH LOW

URBAN 300(75%) 100(20%)

RURAL 100(25%) 400(80%)

TOTAL 400(100%) 500(100%)

C. POLITICAL AWARNESS BY

EDUCATIONAL LEVEL

POLITICAL AWARNESS EDUCATIONAL LEVEL

HIGH LOW

HIGH 240(60%) 100(20%)

LOW 160(40%) 400(80%)

TOTAL 400(100%) 500(100%)

D. POLITICAL AWARNESS BY PLACE OF

LIVING CONTROLLING FOR EDUCATION

LEVEL

POLITICAL

AWARNESS

HIGH EDUCATION LOW EDUCATION TOTAL

URBAN RURAL URBAN RURAL

HIGH 180(60%

)

60(60%) 20(20%) 80(20%) 340

LOW 120(40%

)

40(40%) 80(80%) 320(80%) 560

TOTAL 300(100) 100(100%

)

100(100%

)

400(100%

)

900

Findings..

Educational level determines for both

political awareness and place of living.

that is people who are educated tend

to live in urban area and they are

more politically aware .

There is no inherent link between

political awareness and place of living

and the relationship between them is

spurious.

EVALUATION..

It used in all levels of measurement.

It is a tedious process.

It necessitates sub division of sample

to sub categories.

Validity and reliability is questionable

PARTIAL CORRELATION

It is a statistical method designed to

measure the relationship between an

independent variable and dependent

variable by holding all other variables

constant.

It cancels out the effect of control

variable on dependent and

independent variable and thus shows

the unmarred direct association

between them.

A partial correlation with one

control variable is known as

first order correlation, and with

two it is known as second

order correlation, and so on.

interpretation

It ranges from -1.00 to +1.00 .

If the value of partial correlation is not

very much difference from correlation

of independent and dependent

variables, original association between

them may be real. If on the other hand

if the partial correlation is far below the

orginal zero order correlation, the

original association found to be

spurious

MULTIPLE CORRELATION

Multiple correlation shows (R)

shows the combined effects of

two or more independent

variables on dependent

variable.

The value of r2 is termed as

coefficient of multiple

determination.

Interpretation.

The r2 ranges from 0 to +1.00

The value 1.00 shows that

independent variables perfectly predict

the dependent variable.

And the value zero indicating that

there is no linear relationship.

REFERENCES

METHODOLOGY OF SOCIAL

SCIENCES RESEARCH by

M. RANGANATHAM

O.R. KRISHNASWAMI

RESEARCH METHODOLOGY

METHODS AND TECHIQUES by

C.R.KOTHARI