Generalized cochran-mantel-haenszel test statistics for correlated categorical data

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Abstract
Three new test statistics are introduced for correlated categorical data in stratified R×C tables. They are similar in form to the standard generalized Cochran-Mantel-Haenszel statistics but modified to handle correlated outcomes. Two of these statistics are asymptotically valid in both many-strata (sparse data) and large-strata limiting models. The third one is designed specifically for the many-strata case but is valid even with a small number of strata. This latter statistic is also appropriate when strata are assumed to be random.