replicability null hypotheses with parameters ( w$_{1}$, q$_{1}$, q ) , where 0 ≤ w$_{1}$ ≤ 1 and 0 < q$_{1}$ < q < 1 : 

1. Apply Procedure 3.2 with parameters ( w$_{1}$q$_{1}$, w$_{1}$q ) with study one as the primary study and study two as the follow-up study. Denote the set of indices of rejected no replicability null hypotheses by R 12 ,w$_{1}$$_{q}$. 

2. Reverse the roles of study one and study two. Apply Procedure 3.2 with parame- ters ((1 − w$_{1}$ ) q$_{1}$, (1 − w$_{1}$ ) q ) . Denote the set of indices of rejected no replicability null hypotheses by R 21 , (1 − w$_{1}$ ) $_{q}$. 

3. The set of indices of rejected no replicability null hypotheses is R 12 ,w$_{1}$q ∪R 21 , (1 − w$_{1}$ ) $_{q}$. 

Theorem 4.1. Procedure 4.1 controls the FDR at level q for the family of no repli- cability null hypotheses H$_{NR,}$$_{1}$, . . . , H$_{NR,m}$ if all p -values are jointly independent and the selection rule in step 1 of Procedure 3.2 is a valid selection rule. 

See Appendix C for the proof. 

Choosing w$_{1}$ = 1 results in Procedure 3.2, where study one has the role of the primary study and study two has the role of the follow-up study. Similarly, choosing w$_{1}$ = 0 results in Procedure 3.2 with the roles of study one and study two reversed. The choice 0 < w$_{1}$ < 1 reflects the similarity of Procedure 4.1 to Procedure 3.2 in the following way: when w$_{1}$ is close to one (zero), Procedure 4.1 gives similar results to Procedure 3.2 with study one (two) as the primary study. The choice w$_{1}$ = 0 . 5 results in a variant of Procedure 3.2 that is symmetric with respect to both studies. 

