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On familywise type I error control for multiplicity in equivalence trials with three or more treatments
Author(s) -
Röhmel Joachim
Publication year - 2011
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.201100073
Subject(s) - bonferroni correction , pairwise comparison , mathematics , equivalence (formal languages) , multiple comparisons problem , directed acyclic graph , type i and type ii errors , statistics , discrete mathematics , combinatorics
For the all pairwise comparisons for equivalence of k ( k ≥2) treatments Lauzon and Caffo proposed simply to divide the type I error level α by k −1 to achieve a Bonferroni‐based familywise error control when declaring pairs of two treatments equivalent. This rule is shown to be too liberal for k ≥4. It works for k =3 yet for reasons not considered by Lauzon and Caffo. Based on the two one‐sided testing procedures and using the closure test principle we develop valid alternatives based on Bonferroni's inequality. The set H of intersection hypotheses reveals a rich structure, leading to the possibility to present H as a directed acyclic graph (DAG). This in turn allows using some graph theoretical theorems and eases proving properties of the resulting multiple testing problems.