The multiple testing problem arises because, if many hypotheses are tested simultaneously, some test statistics will be surprisingly extreme, even if no associations exist. Multiple test procedures are designed to exercise control over the entire set of hypotheses, to prevent study–wide conclusions being drawn that could be attributed to chance alone. The family–wise error rate (FWER) is the probability of committing at least one type–1 error, and may be controlled in the weak sense, when all null hypotheses are true, or in the strong sense, when any subset of hypotheses is true [Hochberg and Tamhane, 1987]. More recently, the false discovery rate (FDR) [Benjamini and Hochberg, 1995] and variations [Efron and Tibshirani, 2002] have gained support, as we may tolerate some type–1 errors so long as they are a small proportion of the rejected hypotheses. Bayes factors have also been advocated to quantify the strength of evidence in each test [WTCCC, 2007]. Here we are not concerned with discriminating between different error measures, but note that when the number of false hypotheses is small, control of the standard FDR is
