# lec27 - Lecture 27 27.1 Test of homogeneity Suppose that...

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Lecture 27 27.1 Test of homogeneity. Suppose that the population is divided into R groups and each group (or the entire population) is divided into C categories. We would like to test whether the distribu- tion of categories in each group is the same. Table 27.1: Test of homogeneity Category 1 ··· Category C Group 1 N 11 ··· N 1 C N 1+ . . . . . . . . . . . . . . . Group R N R 1 ··· N RC N R + N +1 ··· N + C n If we denote (Category j | Group i ) = p ij so that for each group i R we have C X j =1 p ij = 1 then we want to test the following hypotheses: ± H 1 : p ij = p j for all groups i R H 2 : otherwise If the observations X 1 , . . . , X n are sampled independently from the entire popu- lation then the homogeneity over groups is the same as independence of groups and 107

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LECTURE 27. 108 categories. Indeed, if have homogeneity (Category j | Group i ) = (Category j ) then we have (Group i , Category j ) = (Category j | Group i ) (Group i ) = (Category j ) (Group
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lec27 - Lecture 27 27.1 Test of homogeneity Suppose that...

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