Not logged in.
Quick Search - Contribution
Contribution Details
| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Consonance and the closure method in multiple testing |
| Organization Unit | |
| Authors |
|
| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
|
| Journal Title | The International Journal of Biostatistics |
| Publisher | Berkeley Electronic Press |
| Geographical Reach | international |
| ISSN | 1557-4679 |
| Volume | 7 |
| Number | 1 |
| Page Range | online |
| Date | 2011 |
| Abstract Text | Consider the problem of testing s null hypotheses simultaneously. In order to deal with the multiplicity problem, the classical approach is to restrict attention to multiple testing procedures that control the familywise error rate (FWE). The closure method of Marcus et al. (1976) reduces the problem of constructing such procedures to one of constructing single tests that control the usual probability of a Type 1 error. It was shown by Sonnemann (1982, 2008) that any coherent multiple testing procedure can be constructed using the closure method. Moreover, it was shown by Sonnemann and Finner (1988) that any incoherent multiple testing procedure can be replaced by a coherent multiple testing procedure which is at least as good. In this paper, we first show an analogous result for dissonant and consonant multiple testing procedures. We show further that, in many cases, the improvement of the consonant multiple testing procedure over the dissonant multiple testing procedure may in fact be strict in the sense that it has strictly greater probability of detecting a false null hypothesis while still maintaining control of the FWE. Finally, we show how consonance can be used in the construction of some optimal maximin multiple testing procedures. This last result is especially of interest because there are very few results on optimality in the multiple testing literature. |
| Digital Object Identifier | 10.2202/1557-4679.1300 |
| PDF File |
Download from ZORA
|
| Export |
BibTeX
EP3 XML (ZORA)
|