Economics at your fingertips  

Consonance and the Closure Method in Multiple Testing

Romano Joseph P., Azeem Shaikh () and Michael Wolf ()
Additional contact information
Romano Joseph P.: Stanford University

The International Journal of Biostatistics, 2011, vol. 7, issue 1, 1-25

Abstract: 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.

Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3) Track citations by RSS feed

Downloads: (external link) ... .1300.xml?format=INT (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
Working Paper: Consonance and the closure method in multiple testing (2009) Downloads
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from

Access Statistics for this article

The International Journal of Biostatistics is currently edited by Antoine Chambaz, Alan E. Hubbard and Mark J. van der Laan

More articles in The International Journal of Biostatistics from De Gruyter
Bibliographic data for series maintained by Peter Golla ().

Page updated 2019-08-12
Handle: RePEc:bpj:ijbist:v:7:y:2011:i:1:n:12