IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Consonance and the closure method in multiple testing

  • Joseph P. Romano
  • Azeem M. Shaikh
  • Michael Wolf

Consider the problem of testing s hypotheses simultaneously. In order to deal with the multiplicity problem, the classical approach is to restrict attention to procedures that control the familywise error rate (FWE). Typically, it is known how to construct tests of the individual hypotheses, and the problem is how to combine them into a multiple testing procedure that controls the FWE. The closure method of Marcus et al. (1976), in fact, reduces the problem of constructing multiple test procedures which control the FWE to the construction of single tests which control the usual probability of a Type 1 error. The purpose of this paper is to examine the closure method with emphasis on the concepts of coherence and consonance. It was shown by Sonnemann and Finner (1988) that any incoherent procedure can be replaced by a coherent one which is at least as good. The main point of this paper is to show a similar result for dissonant and consonant procedures. We illustrate the idea of how a dissonant procedure can be strictly improved by a consonant procedure in the sense of increasing the probability of detecting a false null hypothesis while maintaining control of the FWE. We then show how consonance can be used in the construction of some optimal maximin procedures.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.iew.uzh.ch/wp/iewwp446.pdf
Download Restriction: no

Paper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 446.

as
in new window

Length:
Date of creation: Sep 2009
Date of revision:
Handle: RePEc:zur:iewwpx:446
Contact details of provider: Postal: Rämistrasse 71, CH-8006 Zürich
Phone: +41-1-634 21 37
Fax: +41-1-634 49 82
Web page: http://www.econ.uzh.ch/
Email:


More information through EDIRC

No references listed on IDEAS
You can help add them by filling out this form.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:zur:iewwpx:446. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marita Kieser)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.