Assessing replicability with the sceptical p$$ p $$ ‐value: Type‐I error control and sample size planning

We study a statistical framework for replicability based on a recently proposed quantitative measure of replication success, the sceptical p$$ p $$ ‐value. A recalibration is proposed to obtain exact overall Type‐I error control if the effect is null in both studies and additional bounds on the partial and conditional Type‐I error rate, which represent the case where only one study has a null effect. The approach avoids the double dichotomization for significance of the two‐trials rule and has larger project power to detect existing effects over both studies in combination. It can also be used for power calculations and requires a smaller replication sample size than the two‐trials rule for already convincing original studies. We illustrate the performance of the proposed methodology in an application to data from the Experimental Economics Replication Project.