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- Title
CONTROL OF DIRECTIONAL ERRORS IN FIXED SEQUENCE MULTIPLE TESTING.
- Authors
Grandh, Anjana; Wenge Guo; Romano, Joseph P.
- Abstract
In this paper, we consider the problem of simultaneously testing many two-sided hypotheses when rejections of null hypotheses are accompanied by claims of the direction of the alternative. The fundamental goal is to construct methods that control the mixed directional familywise error rate (mdFWER), which is the probability of making any type 1 or type 3 (directional) error. In particular, atten- tion is focused on cases where the hypotheses are ordered as H1, . . . ,Hn, so that Hi+1 is tested only if H1,...,Hi have all been previously rejected. In this situation, one can control the usual familywise error rate under arbitrary dependence by the basic procedure which tests each hypothesis at level α, and no other multiplicity adjustment is needed. However, we show that this is far too liberal if one also ac- counts for directional errors. But, by imposing certain dependence assumptions on the test statistics, one can retain the basic procedure. Through a simulation study and a clinical trial example, we numerically illustrate good performance of the pro- posed procedures compared to the existing mdFWER controlling procedures. The proposed procedures are also implemented in the R-package FixSeqMTP.
- Subjects
FALSE positive error; ERROR rates; NULL hypothesis
- Publication
Statistica Sinica, 2019, Vol 29, Issue 2, p1047
- ISSN
1017-0405
- Publication type
Article
- DOI
10.5705/ss.202017.0072