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Testing each hypothesis marginally at alpha while still controlling FWER: how and when
Author(s) -
Li Jianjun David
Publication year - 2012
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5488
Subject(s) - multiple comparisons problem , statistical hypothesis testing , consistency (knowledge bases) , inflation (cosmology) , false discovery rate , statistics , econometrics , computer science , p value , mathematics , artificial intelligence , biochemistry , physics , chemistry , theoretical physics , gene
This paper proposes a multiple testing procedure that allows one to reject each individual hypothesis at a prespecified level α , while still controlling the familywise error rate at α in the strong sense. Typically, rejecting a hypothesis when its marginal p ‐value is ⩽ α in a multiple hypothesis testing setting will lead to an inflation of familywise error rate. However, this inflation can be avoided if a particular consistency criterion is prespecified and incorporated in the testing algorithm. The criterion is equivalent to requiring that all p ‐values be smaller than or equal to a particular threshold in the one‐sided hypothesis testing setting. Extensions to the two‐sided hypothesis testing setting and extensions to situations where the criterion can be chosen per user's preference are also presented. Copyright © 2012 John Wiley & Sons, Ltd.