lecture30!31!19075 chi square

7252019 Lecture303119075 Chi Square

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Hypothesis Testing for Categorical Data

(Chi-Square Test)



Learning Objectives

Upon completion of this chapter you will be ableto

Understand the concept of chi-square statistic andchi-square distribution

Understand the concept of chi-square goodness-of-ttest

Understand the concept of chi-square test ofindependence



Defining Chi-Square Test Statistic

Some researchers place the chi-square technique in the category of non-parametric tests fortesting of the hypothesis

Chi-square distribution is the family of curveswith each distribution dened by the degree offreedom associated to it In fact chi-square is acontinuous probability distribution with range0 to infin



Figure Chi-Square distribution with and

degrees of freedom



Figure $cceptance or reection region in a Chi-Square

test



Chi-Square ooness-of-it Test

Chi-square test provides a platform that can be used toascertain whether theoretical probability distributionsmatch with actual sample distributions

$ample $ company is concerned about theincreasing violent altercations between its employees

amphe number of violent incidents recorded by themanagement during si randomly selected months isgiven in ampable ()



Coputation of $pecte requencies an

Chi-square Statistic for $aple ampamp

Solved amples+cel+ (ls



Chi-square Test of nepenence

hen observations are classied on the basis of twovariables and arranged in a table the resultingtable is referred to as a contingency table Chi-

square test of independence uses this contingencytable for determining independence of twovariables this is why this test is sometimes referredto as contingency analysis

hen we add the row or column totals the grandtotal Namp is obtained amphis grand total is the sum ofall the frequencies and represents the sample sie



The epecte frequency of cell j+ is

here RT is the row total CT the column total and N thetotal number of frequencies

pected frequency forany cell



Chi-Square Test Statistic





Chi-square Test of oogeneity

Chi-square test of homogeneity is used todetermine whether two or more independentvariables are drawn from the same population orfrom dierent populations

In other words we can say that chi-square test ofhomogeneity is used to determine whether two ormore populations are homogenous with respect tosome characteristic of interest



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Learning Objectives

Upon completion of this chapter you will be ableto

Understand the concept of chi-square statistic andchi-square distribution

Understand the concept of chi-square goodness-of-ttest

Understand the concept of chi-square test ofindependence









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