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November 2011 Discussion of “Multiple Testing for Exploratory Research” by J. J. Goeman and A. Solari
Ruth Heller
Statist. Sci. 26(4): 598-600 (November 2011). DOI: 10.1214/11-STS356A


Goeman and Solari [Statist. Sci. 26 (2011) 584–597] have addressed the interesting topic of multiple testing for exploratory research, and provided us with nice suggestions for exploratory analysis. They defined properties that an inferential procedure should have for exploratory analysis: the procedure should be mild, flexible and post hoc. Their inferential procedure gives a lower bound on the number of false hypotheses among the selected hypotheses, and moreover whenever possible identifies elementary hypotheses that are false. The need to estimate a lower bound on the number of false hypotheses arises in various applications, and the partial conjunction approach was developed for this purpose in Biometrics 64 (2008) 1215–1222 (see also Philos. Trans. R. Soc. Lond. Ser. A 367 (2009) 4255–4271 for more details). For example, in a combined analysis of several studies that examine the same problem, it is of interest to give a lower bound on the number of studies in which the finding was reproduced. I will first address the relation between the method of Goeman and Solari and the partial conjunction approach. Then I will discuss possible extensions and address the issue of exploration in more general settings, where the local test may not be defined in advance or where the candidate hypotheses may not be known to begin with.


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Ruth Heller. "Discussion of “Multiple Testing for Exploratory Research” by J. J. Goeman and A. Solari." Statist. Sci. 26 (4) 598 - 600, November 2011.


Published: November 2011
First available in Project Euclid: 28 February 2012

zbMATH: 1331.62373
MathSciNet: MR2933770
Digital Object Identifier: 10.1214/11-STS356A

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.26 • No. 4 • November 2011
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