R$_{2}$ ≜ max { r : ∑ j ∈R$_{1}$ I [ ( p$_{1}$$_{j}$, p$_{2}$$_{j}$ ) ≤ ( rq$_{1}$ m , r ( q − q$_{1}$ ) R$_{1}$ )] = r } . R 2 = { j : ( p$_{1}$$_{j}$, p$_{2}$$_{j}$ ) ≤ ( R$_{2}$q$_{1}$ m , R$_{2}$ ( q − q$_{1}$ ) R$_{1}$ ) , j ∈ R 1 } . Z$_{j}$ = max ( mp$_{1}$$_{j}$ c , R$_{1}$p$_{2}$$_{j}$ 1 − c ) , j ∈ R $_{1}$, (3.1) p REP adj ( i ) = min j ≥ i Z$_{(}$$_{j}$$_{)}$ j . (3.2) 8 It is easy to see that this condition is satisfied if R 1 contains the smallest fixed number of p -values, all hypotheses with p -value below a given threshold, or if R 1 contains the rejected indices from a BH procedure on the p -values from the pri- mary study. Adaptive FDR procedures on the p -values from the primary study, e.g. Definition 3.1. A valid selection rule for step 1 of Procedure 3.2 satisfies the follow- ing condition: for any j ∈ R $_{1}$, fixing all the p -values except for p$_{1}$$_{j}$ and changing p$_{1}$$_{j}$ so that H$_{1}$$_{j}$ is still selected, will not change the set R $_{1}$. Procedure 3.2 with parameters ( q$_{1}$, q ) = ( cq, q ) is equivalent to rejecting all no repli- cability null hypotheses with FDR-replicability adjusted p -values at most q . and let Z$_{(1)}$ ≤ . . . ≤ Z$_{(}$$_{R}$$_{1}$$_{)}$ be the sorted Z -values. Then the i th largest FDR- replicability adjusted p -value is The results of Procedure 3.2 can be reported in terms of FDR-replicability adjusted p -values. Let c = q$_{1}$/q , Then the set of indices of rejected no replicability null hypotheses is 2. Let be the cardinality of this set.