0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 mu Power (a) q $_{1}$=0.01 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 mu Power (b) q $_{1}$=0.025 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 mu Power (c) q $_{1}$=0.04 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Power Zeta (a) µ = 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Zeta Power (b) µ = 3 Figure 1: Power as a function of µ = µ$_{1}$ = µ$_{2}$ , for q$_{1}$ of (a) 0.01, (b) 0.025, and (c) 0.04, using the following procedures: the oracle Procedure 3.2 (solid with circles); the BH procedure at level 0.05 applied on maximum p -values (dash-dotted); Procedure 4.1 at level 0.05 with w$_{1}$ = 0 (dashed), w$_{1}$ = 0 . 5 (dotted), and w$_{1}$ = 1 (solid), where the selection rule in steps 1 and 2 is the BH procedure at levels w$_{1}$q$_{1}$ and (1 − w$_{1}$ ) q$_{1}$ , respectively. The remaining parameters were f$_{00}$ = 0 . 9 , f$_{01}$ = 0 . 025 , f$_{10}$ = 0 . 025 , f$_{11}$ = 0 . 05, µ$_{1}$ = µ$_{2}$ = µ , σ$_{1}$ = 0 . 3 and σ$_{2}$ = 1. Figure 2: Power as a function of fraction ζ of sample size allocated to the primary study, for (a) µ$_{1}$ = µ$_{2}$ = 2, and (b) µ$_{1}$ = µ$_{2}$ = 3, for Procedure 4.1 with w$_{1}$ = 1 (solid), with w$_{1}$ = 0 . 5 (dotted), and for the BH procedure on the maximum of two studies p -values (dash-dotted) at level q = 0 . 05. The remaining parameters were f$_{00}$ = 0 . 9 , f$_{01}$ = 0 . 025 , f$_{10}$ = 0 . 025 , f$_{11}$ = 0 . 05, sample size N = 1000, standard deviation σ = 10. 23