where the last inequality follows from the fact that V$_{f}$ is independent of the data from the primary study, and that in both studies a FWER controlling procedure is applied. Using Bonferroni in Procedure 3.1 amounts to rejecting H$_{NR,j}$ if ( p$_{1}$$_{j}$, p$_{2}$$_{j}$ ) ≤ ( α$_{1}$/m, ( α − α$_{1}$ ) / |R 1 | ), for j ∈ R $_{1}$. Alternatively, the results can be reported in terms of Bonferroni- replicability adjusted p -values p Bonf − REPadj j = max ( mp$_{1}$$_{j}$/c, |R 1 | p$_{2}$$_{j}$/ (1 − c )), where c = α$_{1}$/α . Procedure 3.1 using Bonferroni is equivalent to rejecting all hypotheses with Bonferroni-replicability adjusted p -values at most α . The selection rule affects the power of Procedure 3.1. A natural choice for a selection rule is the set of rejected hypotheses by the FWER controlling procedure at level α$_{1}$ on the primary study p -values, since the set of indices of rejected no replicability null hypotheses is a subset of this set. A rule that selects by the FWER controlling procedure at level α is not as good, since any additional hypotheses selected will not be rejected but will result in a more severe multiple testing problem for the follow-up study. The choice of α$_{1}$ also affects the power of Procedure 3.1. We observed in simulations (Supplementary Material) that although the optimal α$_{1}$ varies with effect size, the power function is quite flat as long as α$_{1}$/α is not too close to zero or one. In many modern applications, controlling the FWER is unnecessary and results in overly conservative inferences. In genomics research, it is often enough to guaran- tee FDR control, see Storey and Tibshirani (2003) and Reiner et al. (2003), among others. Procedure 3.2. The two stage FDR controlling procedure for testing a family of no replicability null hypotheses with parameters ( q$_{1}$, q ) , where 0 < q$_{1}$ < q < 1 : 1. Let R 1 be the set of indices of elementary hypotheses that are selected for testing in a follow-up study based on the data from the primary study. Let R$_{1}$ = |R 1 | 7