appropriate when the aim is to discover hypotheses with indices in I$_{11}$ , treating all discoveries from I$_{01}$ and I$_{10}$ , in addition to I$_{00}$ , as false discoveries. In Benjamini et al. (2009) the partial conjunction approach (Benjamini and Heller, 2008) has been suggested for replicability analysis when n ≥ 2 studies are available that examine the same problem. When exactly two studies are available, the pro- cedure in Benjamini et al. (2009) amounts to applying the Benjamini-Hochberg false discovery rate (FDR) controlling procedure (Benjamini and Hochberg, 1995), hence- forth referred to as the BH procedure, on the maximum of the two study p -values. However, this procedure may be too conservative, making it practically very difficult to discover false no replicability null hypotheses. As an example, suppose there is an original GWA study that examines the association of 10 6 SNPs with a phenotype. Now suppose 200 promising SNPs were selected to be examined in a follow-up study. If a SNP has a p -value of 0 . 025 / 10 6 in the first study, and of 0 . 025 / 200 in the second study, then the maximum p -value is 0 . 025 / 200. The BH procedure will, most probably, not reject the no replicability null hypothesis for a SNP with maximum p -value of 0 . 025 / 200, since this maximum p -value is not strong enough evidence when faced with 10 6 hypotheses, out of which most of the hypotheses are true no replicability null hypotheses. The alternative procedures we suggest in Sections 3 and 4 will view the evidence from this SNP as strong enough for it to be considered a replicated finding. 5 2.1 The partial conjunction approach