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lecture_13 - Three-way Contingency Tables Lecture 13 ILRST...

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Three-way Contingency Tables Lecture 13 ILRST 212

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Cochran-Mantel Haenszel  This section shows whether sample data are consistent with  homogenous associations or conditional independence. Cochran Mantel Haenszel method present a test of  conditional independence and test of homogenous  association for the K conditional odds ratios in 2*2*K tables. Example: table 3.3, page 60
Cochran-Mantel Haenszel For a 2*2*K tables, the null hypothesis that X and Y are  conditionally independent, given Z, means that the  conditional odds ratio  θ xy(k)  between X and Y equals 1 in  each partial table. Ho:  θ xy(1) =  θ xy(2) =  θ xy(3) = ………………………………… θ xy(k)=   1        Ha: Atleast one of the odds ratio is not equal to 1

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Cochran-Mantel Haenszel The test statistic utilizes n 11k  in each partial table. When the true odds ratio  θ xy(k)  exceeds 1.0 in partial table k,  we expect to observe (n 11k  -    11k ) >0.  The test statistic combines these differences across all K  tables.            μ
Cochran-Mantel Haenszel Hence CMH statistic takes larger values when (n 11k  -     11k )   is consistently positive or consistently negative for all tables,  rather than positive for some or negative for others.

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