Second, replacing I$_{0}$ by I$_{01}$ and | I$_{0}$ | by | I$_{01}$ | in the arguments that led to (A.3), we obtain: Finally, using (A.6) in the proof of Theorem 3.2 we obtain that the third term of the sum in (B.1) is bounded by q$_{2}$ = 2 q ′ − q ′ = q $^{′}$. Using this upper bound, together with the bounds for the first two terms derived in (B.2) and (B.3), we obtain: It follows that if | I$_{00}$ | and | I$_{01}$ | were known, one could guarantee FDR control at level q on the family of no replicability null hypotheses by applying Procedure 3.2 at levels ( q $^{′}$, 2 q $^{′}$), where q ′ is the solution to | I$_{00}$ | ( q $^{′}$) $^{2}$/m + ( | I$_{01}$ | /m + 1) q ′ = q. Let V$_{12}$ = ∑ j ∈ I$_{00}$ ∪ I$_{01}$ ∪ $_{I$_{10}$}$I [ j ∈ R 12 ,w$_{1}$$_{q}$] and R$_{12}$ = |R 12 ,w$_{1}$q | denote the number of erroneously rejected and the total number of rejected no replicability null hypothe- ses by Procedure 3.2 at level w$_{1}$q with study one as the primary study and study two as the follow-up study. Similarly, let V$_{21}$ = ∑ j ∈ I$_{00}$ ∪ I$_{01}$ ∪ $_{I$_{10}$}$I [ j ∈ R 21 , (1 − w$_{1}$ ) q ] and R$_{21}$ = |R 21 , (1 − w$_{1}$ ) q | denote the number of erroneously rejected and the total num- ber of rejected no replicability null hypotheses by Procedure 3.2 at level (1 − w$_{1}$ ) q with study two as the primary study and study one as the follow-up study. Define R s = R 12 ,w$_{1}$q ∪ R 21 , (1 − w$_{1}$ ) $_{q}$, the indices of the no replicability null hypotheses rejected by Procedure 4.1. Let V$_{s}$ = ∑ j ∈ I$_{00}$ ∪ I$_{01}$ ∪ $_{I$_{10}$}$I [ j ∈ R $_{s}$] and R$_{s}$ = |R s | , the number of erroneously rejected and the total number of rejected no replicability null hypotheses C Proof of Theorem 4.1 FDR ≤ | I$_{00}$ | m ( q $^{′}$) 2 + | I$_{01}$ | m q ′ + q ′ = | I$_{00}$ | m ( q $^{′}$) 2 + ( | I$_{01}$ | m + 1 ) q $^{′}$. E ( ∑ j ∈ $_{I$_{01}$}$R$_{j}$ max( R, 1) ) ≤ | I$_{01}$ | m q $^{′}$. (B.3) 32