However, the fitted Beta distributions do suggest that an effective number of tests exists and could be useful. Figure 3 compares the empirical distribution of the minimum P–value for the combined samples, to the fitted Beta (1,nE) and Beta (a,b) distributions. Both Beta distributions are clearly a good fit to the observed data. The maximum likelihood estimate = 0.97 is close to 1; the null hypothesis of equality was formally rejected (P = 0.01), but this is not surprising given our high power to reject strict equality, and the test was not significant in the separate NBS and 58BC samples. This is in line with our results on an early version of HapMap [Dudbridge and Koeleman, 2004], in which the test of equality was extremely significant, suggesting that the effective number of tests is a worse fit at higher marker densities. The effective numbers of tests were similar to those estimated from the permutation procedure for both cohorts (Table II).
