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Biometrika Advance Access originally published online on January 24, 2009
Biometrika 2009 96(1):201-211; doi:10.1093/biomet/asn061
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© 2009 Biometrika Trust

Articles

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

Elena Kulinskaya

Statistical Advisory Service, Imperial College, 8 Princes Gardens, London SW7 1NA, U.K. e.kulinskaya{at}imperial.ac.uk

Alex Lewin

Department of Epidemiology and Public Health, Imperial College, St Mary's Campus, Norfolk Place, London W2 1PG, U.K. a.m.lewin{at}imperial.ac.uk

Received for publication 1 February 2007. Revision received 1 May 2008.
  Abstract

Fuzzy multiple comparisons procedures are introduced as a solution to the problem of multiple comparisons for discrete test statistics. The critical function of the randomized p-values is proposed as a measure of evidence against the null hypotheses. The classical concept of randomized tests is extended to multiple comparisons. This approach makes all theory of multiple comparisons developed for continuously distributed statistics automatically applicable to the discrete case. Examples of familywise error rate and false discovery rate procedures are discussed and an application to linkage disequilibrium testing is given. Software for implementing the procedures is available.

Key Words: Benjamini–Hochberg procedure • Bonferroni procedure • False discovery rate • Fuzzy decision-making • Multiple comparisons • Randomized test


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