fore, an approach that provides control over false positives in each study separately, does not guarantee control over false positives for evaluating whether the results were replicated. Figure 3, left panel, shows that the FDR level can be as high as one when naively declaring results as replicated if they were discovered by applying an FDR controlling procedure at the nominal 0.05 level separately in each study. Moreover, reducing the nominal 0.05 level does not resolve the problem, see Remark 3.1. The paper is organized as follows. Section 2 gives the notation and review. Section 3 suggests novel multiple testing procedures for replicability analysis, when the primary study guides the selection of hypotheses to be examined in a follow-up study. Section 4 considers the setting where there is no division of roles into a primary and a follow- up study. In Section 5, we revisit the example of Bis et al. (2012). We also analyze an additional GWAS study, and show additional examples from the GWAS simulator HAPGEN2 (Su et al., 2011). Section 6 describes a simulation study, and Section 7 gives some final remarks. 2 Notation, Goal, and Review Consider a family of m elementary null hypotheses H$_{1}$, . . . , H$_{m}$ . These elementary null hypotheses, or a subset thereof, are tested in each of two independent studies. Let h$_{ij}$ be the indicator of whether H$_{j}$ is false in study i . The pair of indicators ( h$_{1}$$_{j}$, h$_{2}$$_{j}$ ) identifies four possible settings for each j , 3 ( h$_{1}$$_{j}$, h$_{2}$$_{j}$ ) =      (0 , 0) if H$_{j}$ is true in both studies , (1 , 0) if H$_{j}$ is false in the primary study but true in the follow-up study , (0 , 1) if H$_{j}$ is true in the primary study but false in the follow-up study , (1 , 1) if H$_{j}$ is false in both studies .