A difficulty with FDR methods is that they control an expected proportion, whereas an investigator will be more concerned with the actual proportion of false positives within a study. Some insight is gained by considering the variation in within-study false discovery proportion or false discovery variance. Let i be an integer with p(i) the i-th smallest p-value from a set of m tests. If the i most significant tests are declared positive, then mp(i) estimates the maximum number of false positives. The associated variance is mp(i)(1 - p(i)) (because the truth of a positive test is a binomial outcome) and the coefficient of variation is 1-p(i)p(i) for the within-study false discovery proportion. This is greatest when p(i) is small, so, for a fixed set of p-values, this coefficient of variation is greatest when the fewest tests are declared significant. This will occur when a low error rate is set, or when there are few true associations, or when the power is low. In genome-wide association scans, the number of true associations is expected to be small by comparison with the
