QQ-plot of Min-P, Cauchy and Simes p-values from type 1 error study.

P-values from 20 million simulation replicates under the null hypothesis are shown for each method. The p-values from Min-P, Cauchy and Simes are in blue, red and green, respectively. Because the values are so similar, the 3 curves lie almost perfectly on top of one another, except for the large p-values where the Bonferroni correction used for Min-P is conservative.

(TIF)