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 close to weak control of the FWER [Benjamini and Hochberg, 1995]. Moreover, in this situation strong control of FWER is close to the best methods for weak control [Dudbridge and Koeleman, 2003]. Also when the evidence is strong and the power is high, there is a strong correlation between the Bayes factor and the P–value [Thomas and Clayton, 2004]. In what follows we will therefore consider strong control of FWER by the Bonferroni method, or its permutational equivalent [Westfall and Young, 1993], as a conservative baseline to which other methods can be calibrated.
