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On fuzzy familywise error rate and false discovery rate procedures for discrete distributions

<27> The validity of many multiple hypothesis-testing procedures relies on the assumption that p-values are uniformly distributed under the null hypotheses. However, this assumption fails if the test statistics have discrete distributions. Fuzzy multiple comparison procedures that extend the classical concept of randomised tests are introduced in this paper as a solution to this problem. This approach makes all theory of multiple comparisons developed for continuously distributed statistics automatically applicable to the discrete case. Citations include applications in metabolomics, genetics, and high dimensional data analysis.