pendent within each study and the selection rule is valid. However, the assumption of independence may not be realistic. Extensive simulations demonstrated that the BH procedure controls the FDR for many types of dependence encountered in practice (Yekutieli, 2008). We conjecture that this robustness property carries over to Proce- dures 3.2 and 4.1, since Procedure 3.2 can be viewed as two-dimensional variant of the BH procedure. For simulated GWAS examples the average false discovery pro- portion was below the nominal FDR level, suggesting that the procedures are indeed valid for the type of dependency that occurs in GWAS. More conservative variants of Procedure 3.2 were given in Theorem 3.3 and in Section 3 of the Supplementary Material, that guarantee that the FDR is controlled for arbitrary dependence among the primary study p -values, and dependence of type PRDS or arbitrary dependence among the follow-up study p -values. We demonstrated the usefulness of the variants suggested in Theorem 3.3 in Example 2 of Section 5. Out of the 36 replicability dis- coveries with Procedure 3.2, 23 discoveries passed the more stringent requirement that came with the added guarantee that the FDR is controlled for arbitrary dependence among the 635,547 p -values in the primary study. Replicability analysis, as suggested in this paper, requires that the investigators make several key design choices in addition to the error level q : the selection rule, q$_{1}$ , and w$_{1}$ if two studies are available without division into primary and follow-up. The power of the procedure for replicability analysis varies with these choices. From our investigations, it appears reasonable in Procedure 3.2 to select hypotheses by BH at level q$_{1}$ , and to set w$_{1}$ = 0 . 5 in Procedure 4.1 if the p -value distributions for false null hypotheses may be assumed to be similar in both studies. We gave some guidelines for choosing q$_{1}$ in specific settings, and more general guidelines are a topic for future research. In replicability analysis, the primary study guides the design of the follow-up study 25