content_image/298147.jpg content_image/298148.jpg content_image/298149.jpg content_image/298150.jpg
be the cardinality of this set. 

2. Let 

Then the set of indices of rejected no replicability null hypotheses is 

<img src='content_image/298147.jpg'>

<img src='content_image/298148.jpg'>

The results of Procedure 3.2 can be reported in terms of FDR-replicability adjusted p -values. Let c = q$_{1}$/q , 

<img src='content_image/298149.jpg'>

and let Z$_{(1)}$ ≤ . . . ≤ Z$_{(}$$_{R}$$_{1}$$_{)}$ be the sorted Z -values. Then the i th largest FDR- replicability adjusted p -value is 

<img src='content_image/298150.jpg'>

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 . 

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 $_{1}$. 

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. 

