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Many multiple testing procedures make use of the p-values from the individualpairs of hypothesis tests, and are valid if the p-value statistics areindependent and uniformly distributed under the null hypotheses. However, ithas recently been shown that these types of multiple testing procedures areinefficient since such p-values do not depend upon all of the available data.This paper provides tools for constructing compound p-value statistics, whichare those that depend upon all of the available data, but still satisfy theconditions of independence and uniformity under the null hypotheses. As anexample, a class of compound p-value statistics for testing for location shiftsis developed. It is demonstrated, both analytically and through simulations,that multiple testing procedures tend to reject more false null hypotheses whenapplied to these compound p-values rather than the usual p-values, and at thesame time still guarantee the desired type I error rate control. The compoundp-values, in conjunction with two different multiple testing methods, are usedto analyze a real microarray data set. Applying either multiple testing methodto the compound p-values, instead of the usual p-values, enhances their powers.

Compound p-Value Statistics for Multiple Testing Procedures