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Control of the mean number of false discoveries, Bonferroni and stability of multiple testing
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 -values. Its
stability and the ability to provide strong control of the PFER make the
Bonferroni procedure an attractive choice in microarray studies.Comment: Published at http://dx.doi.org/10.1214/07-AOAS102 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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