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Abstract:
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Nonparametric tests, such as the Wilcoxon-Mann-Whitney test, usually lead to discrete p-values, hence will not possess exact uniform distribution under the null hypothesis. On the other hand, multiple testing procedures, such as the FDR-controlling Benjamini-Hochberg procedure, rely on the assumption that the p-values for each of the tests is uniformly distributed under the null hypotheses. The issue arises therefore on whether in such multiple testing problems, nonparametric procedures should be avoided, or if utilized, what are the consequences, and whether there are possible corrective measures that could be performed? One such correction is the use of randomized p-values, but this is viewed as controversial approach in some quarters of the statistics community. A discussion on the compatibility of nonparametric procedures and multiple testing is therefore of interest.
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