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Abstract:
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In many applications where it is necessary to test multiple hypotheses simultaneously, the data encountered are categorical. In such cases, it is important for multiplicity adjustments to take into account the discreteness of the sampling distribution, to assure that the procedure is not overly conservative. Various multiple testing procedures have been developed for discrete data with this point in mind. When the number of hypotheses is very small, it is possible to obtain the complete joint distribution of the test statistics, which can be used to derive exact multiple testing procedures that simultaneously adjust for both the discreteness and the dependency among the test statistics. In this paper, these ideas are explored and we derive exact versions of some commonly used multiple testing procedures designed to control the familywise error rate (FWER) using the complete joint distribution of the discrete test statistic. These modifications are compared with their corresponding continuous analogs through simulation studies. We also illustrate our methods by applying them to a real data set involving multiple trend tests.
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