Fig. 4
Benchmarking of correction procedures and significance-testing methods. A Histograms of the empirical FDR for 6000 simulated p value datasets with no outliers. Results are plotted for the extreme-value method used by Shi et al., the original BBUM procedure without outlier trimming at pBBUM < 0.05, and the modified BBUM procedure with automatic outlier trimming at pBBUM < 0.05. The frequency of the density near 0, which exceeded the y-axis scale, is indicated alongside its fraction among all trials for each histogram. The FDR cutoff of the BBUM methods at 0.05 is indicated on the x-axis in orange. The mean FDR of all simulation trials is indicated on the right with corresponding 95% CIs by bootstrapping. The CV of FDR is similarly indicated. B As in A, but for 6000 simulations with at least one programmed outlier. The mean FDR and mean sensitivities are indicated with corresponding 95% CIs by bootstrapping. C The mean empirical FDR of significance-testing methods at different pBBUM significance thresholds. Results are plotted for all six threshold values tested. If the empirical FDR matched the predetermined FDR cutoff, the point would lie on the gray diagonal line. Error bars indicate 95% CIs by bootstrapping. Because the Shi et al. method does not allow quantitative adjustments of significance thresholds, results are shown as green horizontal lines with the mean empirical FDR values as the y-intercepts