The Annals of Applied Statistics

Control of the mean number of false discoveries, Bonferroni and stability of multiple testing

Alexander Gordon, Galina Glazko, Xing Qiu, and Andrei Yakovlev

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Abstract

The Bonferroni multiple testing procedure is commonly perceived as being overly conservative in large-scale simultaneous testing situations such as those that arise in microarray data analysis. The objective of the present study is to show that this popular belief is due to overly stringent requirements that are typically imposed on the procedure rather than to its conservative nature. To get over its notorious conservatism, we advocate using the Bonferroni selection rule as a procedure that controls the per family error rate (PFER). The present paper reports the first study of stability properties of the Bonferroni and Benjamini–Hochberg procedures. The Bonferroni procedure shows a superior stability in terms of the variance of both the number of true discoveries and the total number of discoveries, a property that is especially important in the presence of correlations between individual p-values. Its stability and the ability to provide strong control of the PFER make the Bonferroni procedure an attractive choice in microarray studies.

Article information

Source
Ann. Appl. Stat. Volume 1, Number 1 (2007), 179-190.

Dates
First available in Project Euclid: 29 June 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1183143734

Digital Object Identifier
doi:10.1214/07-AOAS102

Mathematical Reviews number (MathSciNet)
MR2393846

Zentralblatt MATH identifier
1129.62065

Citation

Gordon, Alexander; Glazko, Galina; Qiu, Xing; Yakovlev, Andrei. Control of the mean number of false discoveries, Bonferroni and stability of multiple testing. Ann. Appl. Stat. 1 (2007), no. 1, 179--190. doi:10.1214/07-AOAS102. http://projecteuclid.org/euclid.aoas/1183143734.


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