The Annals of Statistics

Size, power and false discovery rates

Bradley Efron

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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.

Article information

Ann. Statist., Volume 35, Number 4 (2007), 1351-1377.

First available in Project Euclid: 29 August 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J07: Ridge regression; shrinkage estimators 62G07: Density estimation

Local false discovery rates empirical Bayes large-scale simultaneous inference empirical null


Efron, Bradley. Size, power and false discovery rates. Ann. Statist. 35 (2007), no. 4, 1351--1377. doi:10.1214/009053606000001460.

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