when σ$_{1}$ = 0 . 3 and σ$_{2}$ = 1. Since the oracle Procedure 3.2 and the BH procedure on maximum p -values do not depend on q$_{1}$ , their power curves are the same in figures (a), (b), and (c). We see that Procedure 4.1 with w$_{1}$ = 1 is a close second to the oracle when q$_{1}$ is 0.01 but is farther from the oracle as q$_{1}$ increases. Similarly, the power of Procedure 4.1 with w$_{1}$ = 0 . 5 decreases as q$_{1}$ increases. However, Procedure 4.1 with w$_{1}$ = 0 has largest power for q$_{1}$ = 0 . 04, and the least power for q$_{1}$ = 0 . 01. These results are reasonable since the p -values of study one tend to be much smaller than the p -values of study two when the no replicability null hypotheses are false. In Table 4 we see that if the p -value distribution of false no replicability null hypotheses is the same across studies, then the optimal choice of q$_{1}$ is q$_{1}$ > q/ 2. For example, when µ = µ$_{1}$ = µ$_{2}$ = 2 (row 2), the power is 0.65 with q$_{1}$ = 0 . 005, 0.77 with q$_{1}$ = 0 . 045, and the maximum power is 0.81 with q$_{1}$ = 0 . 035. Table 4: The power of Procedure 3.2 with parameters (0 . 05 c, 0 . 05) and the BH se- lection rule at level 0 . 05 c , for different values of µ = µ$_{1}$ = µ$_{2}$ , with σ$_{1}$ = σ$_{2}$ = 0 . 5, f$_{00}$ = 0 . 9 , f$_{01}$ = f$_{10}$ = 0 . 025 , f$_{11}$ = 0 . 05. The optimal value of c is in bold. c = q$_{1}$/ 0 . 05 µ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.5 0.143 0.195 0.224 0.245 0.257 0.258 0.248 0.226 0.181 2.0 0.646 0.718 0.755 0.778 0.794 0.803 0.805 0.800 0.769 2.5 0.934 0.955 0.965 0.971 0.975 0.977 0.978 0.978 0.974 Figure 2 compares the procedures (1) and (2) above for the same configuration of f$_{ij}$ , but for fixed µ = µ$_{1}$ = µ$_{2}$ and varying sample size of the two studies. The varying power is described by the fraction ζ of sample allocated to the first study. For the symmetric procedures, we see that for ζ = 0 . 1 the power is the lowest, and it increases to reach its maximum for equal allocation ζ = 0 . 5. Procedure 4.1 with w$_{1}$ = 0 . 5 dominates the BH procedure on the maximum two study p -values. For Procedure 4.1 with w$_{1}$ = 1, the maximum is reached for ζ > 0 . 5. It is the most powerful of the three procedures examined for ζ > 0 . 6. 21