Power of Bonferroni on maxPV mu11 mu12 0 2 4 6 8 10 0 2 4 6 8 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.0 0.2 0.4 0.6 0.8 1.0 Power of Procedure 3.1 mu11 mu12 0 2 4 6 8 10 0 2 4 6 8 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.0 0.2 0.4 0.6 0.8 1.0 Figure 5: The power as function of the expectation in the first study (x-axis) and the expectation in the second study (y-axis), for the false no replicability null hypothesis, in a setting where one no replicability null hypothesis is false out of 100 no replicability null hypotheses. Left panel: Procedure that applies a Bonferroni correction on the maximum two study p -values for FWER control at level 0.05. Right panel: Procedure 3.1 with ( α$_{1}$, α ) = (0 . 025 , 0 . 05) and Bonferroni as the FWER controlling procedure. dure. Moreover, for fixed µ$_{1}$ > µ$_{2}$ , the power of the two stage procedure is larger if ( µ$_{11}$, µ$_{21}$ ) = ( µ$_{1}$, µ$_{2}$ ) than if ( µ$_{11}$, µ$_{21}$ ) = ( µ$_{2}$, µ$_{1}$ ) . Figure 6 shows the difference in power of Procedure 3.1 using Bonferroni with c = α$_{1}$/α ∈ { 0 . 2 , 0 . 5 , 0 . 8 } , as well as the Bonferroni procedure on maximum p -values, from the power of Procedure 3.1 with optimal choice of c . Clearly, Procedure 3.1 with optimal choice of c can be much more powerful than the Bonferroni procedure on maximum p -values. Moreover, for the three choices c = 0 . 2 , c = 0 . 5 and c = 0 . 8 , the difference in power from the optimal power is fairly small, especially when the optimal power is above 0.9 (right panel). Figure 7 shows the power as a function of c for three configurations of ( µ$_{11}$, µ$_{21}$ ) , for which the power using the optimal c is 0.9. The power function is quite flat. The optimal c is below 0.5 in the top left panel, and above 0.5 in the top right and bottom panel. However, the difference in power between Procedure 3.1 with c = 0 . 5 and Procedure 3.1 with optimal c is small. 37