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Program : MBA

Semester : III

Subject Code : MB0050

Subject Name : Research Methodology

Unit Number : 11

Unit Title : Chi-Square Analysis

Lecture Number : 11

Lecture Title : Chi-Square Analysis

Book Id : B1700

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Objectives :

discuss various applications of chi-square tests like:

a chi-square test for the goodness of fit

a chi-square test for the independence of variables

a chi-square test for the equality of more than two population proportions

There are many applications of a chi-square test. Some of them

mentioned below will be discussed in this unit:

A chi-square test for the goodness of fit

A chi-square test for the independence of variables

A chi-square test for the equality of more than two population

proportions.

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Lecture Outline

Introduction

A Chi-square Test for the Goodness of Fit

A Chi-square Test for the Independence of Variables

A Chi-square Test for the Equality of More than: TwoPopulation Proportions

Summary

Check Your Learning

Activity

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Introduction

The chi-square test is widely used in research. For the use of chi-

square test, data is required in the form of frequencies.

The majority of the applications of chi-square are with discrete

data.

The test could also be applied to continuous data, provided it is

reduced to certain categories and tabulated in such a way that the

chi-square may be applied.

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A Chi-square Test for the Goodnessof Fit

The data in chi-square tests is often in terms of counts or

frequencies.

Common principles of all the chi-square tests:

State the null and the alternative hypothesis about a population.

Specify a level of significance.

Compute the expected frequencies of the occurrence of certain events

under the assumption that the null hypothesis is true.

Make a note of the observed counts of the data points falling in different

cells

Compute the chi-square value given by the formula.

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A Chi-square Test forIndependence of Variables

The chi-square test can be used to test the independence of two

variables each having at least two categories.

The test makes use of contingency tables, also referred to as

cross-tabs with the cells corresponding to a cross classification of

attributes or events.

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A Chi-square Test for the Equality ofMore than Two Population Proportions

The analysis is carried out exactly in the same way as was done

for the other two cases. The formula for a chi-square analysis

remains the same. However, two important assumptions here are

different.

We identify our population (e.g., age groups or various class employees)

and the sample directly from these populations.

As we identify the populations of interest and the sample from them

directly, the sizes of the sample from different populations of interest are

fixed. This is also called a chi-square analysis with fixed marginal totals.

The hypothesis to be tested is as under:

H0 : The proportion of people satisfying a particular characteristic is the

same in population.

H1 : The proportion of people satisfying a particular characteristic is not

the same in all populations.7

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Summary

Chi-square test has a variety of applications in research. Chi-

square is non-symmetrical distribution taking non-negative

values.

It can be used to test the goodness of fit of a distribution,

independence of variables and equality of more than two

population proportions.

A necessary condition for the application of chi-square test is that

the expected frequency in each cell should be at least 5.

The first and foremost thing for the application of chi-square is the

computation of expected frequencies.

The data in chi-square test is in terms of counts or frequencies. In

case the actual data is on a scale higher than that of nominal or

ordinal, it can always be converted into categories.8

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Check Your Learning

1. A cigarette company interested in the relation between gender of a person

and the type of cigarettes smoked has collected the following data from arandom sample of 150 persons:

Test whether the type of cigarette smoked and the gender are independent.Ans: This is the test for independence of variables.

2. The following figures show the distribution of the digits in numbers chosen at

random from a telephone directory:

Test whether the digits may be taken to occur equally in the directory.

Ans: This is the test on equality of more than two population proportion.

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Activity

Go to an MBA college where the students are admitted from

engineering, commerce, science and other backgrounds. Take a

sample of 200 students and examine whether they are uniformly

distributed over all the four abovementioned categories.

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Unit-11 Chi-Square Analysis