  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.
