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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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