Improved power of familywise error rate procedures for discrete data under dependency

In many applications where it is necessary to test multiple hypotheses simultaneously, the data encountered are discrete. In such cases, it is important for multiplicity adjustment to take into account the discreteness of the distributions of the p-values, to assure that the procedure is not overly conservative. In this paper, we review some known multiple testing procedures for discrete data that control the familywise error rate, the probability of making any false rejection. Taking advantage of the fact that the exact permutation or exact pairwise permutation distributions of the p-values can often be determined when the sample size is small, we investigate procedures that incorporate the dependence structure through the exact permutation distribution and propose two new procedures that incorporate the exact pairwise permutation distributions. A step-up procedure is also proposed that accounts for the discreteness of the data. The performance of the proposed procedures is investigated through simulation studies and two applications. The results show that by incorporating both discreteness and dependency of p-value distributions, gains in power can be achieved.