Open Access
August 2007 Size, power and false discovery rates
Bradley Efron
Ann. Statist. 35(4): 1351-1377 (August 2007). DOI: 10.1214/009053606000001460


Modern scientific technology has provided a new class of large-scale simultaneous inference problems, with thousands of hypothesis tests to consider at the same time. Microarrays epitomize this type of technology, but similar situations arise in proteomics, spectroscopy, imaging, and social science surveys. This paper uses false discovery rate methods to carry out both size and power calculations on large-scale problems. A simple empirical Bayes approach allows the false discovery rate (fdr) analysis to proceed with a minimum of frequentist or Bayesian modeling assumptions. Closed-form accuracy formulas are derived for estimated false discovery rates, and used to compare different methodologies: local or tail-area fdr’s, theoretical, permutation, or empirical null hypothesis estimates. Two microarray data sets as well as simulations are used to evaluate the methodology, the power diagnostics showing why nonnull cases might easily fail to appear on a list of “significant” discoveries.


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Bradley Efron. "Size, power and false discovery rates." Ann. Statist. 35 (4) 1351 - 1377, August 2007.


Published: August 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1123.62008
MathSciNet: MR2351089
Digital Object Identifier: 10.1214/009053606000001460

Primary: 62G07 , 62J07

Keywords: Empirical Bayes , empirical null , large-scale simultaneous inference , local false discovery rates

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 4 • August 2007
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