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Aesthetics and Power Considerations in Multiple Testing – A Contradiction?
Author(s) -
Hommel Gerhard,
Bretz Frank
Publication year - 2008
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200710463
Subject(s) - variance (accounting) , simple (philosophy) , monotonic function , computer science , contradiction , logical conjunction , power (physics) , test (biology) , mathematics , economics , epistemology , mathematical analysis , paleontology , philosophy , physics , accounting , quantum mechanics , biology , programming language
In this paper we discuss aesthetical concepts and requirements for reasonable multiple test procedures. Aesthetical considerations lead to logical decision patterns which are conceivable and, if possible, simple to use and to communicate. Such considerations are sometimes contradictory to the ubiquitous requirement of maximizing power for a multiple test procedure. We illustrate the necessary trade‐offs with several examples. We start by considering important logical properties and then discuss three different concepts of monotonicity. Afterwards we have a closer look at the recently proposed “fallback procedure” and show that it has some less appealing properties. Finally, we investigate the distribution of the numbers of significant results with respect to both expectation and variance. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)