by supplying the subset of hypotheses to be followed-up. Since the primary study also yields information on effect sizes, if it is assumed that the effect sizes are the same across studies, then this information may be used in order to determine the sample size needed to obtain good power in the follow-up study. However, this assumption may be unrealistic in applications such as GWAS, where the LD pattern varies across populations. Finally, we saw that although Procedure 4.1 with parameters ( w$_{1}$, q$_{1}$, q ) is far less conservative than the BH procedure at level q on maximum p -values, it is still con- servative. We proved that Procedure 4.1 with less conservative parameters q ′ 1 > q$_{1}$ and q ′ > q , still controls the FDR at level q on the family of no replicability null hy- potheses, if | I$_{00}$ | and | I$_{01}$ | were known. In future research we will consider estimates of these unknown parameters. References Barrett et al. (2008). Genome-wide association defines more than 30 distinct suscep- tibility loci for Crohn’s disease. Nature Genetics , 40: 955–962. Benjamini, Y. and Heller, R. (2008). Screening for partial conjunction hypotheses. Biometrics , 64:1215–1222. Benjamini, Y., Heller, R., and Yekutieli, D. (2009). Selective inference in complex research. Philosophical Transactions of the Royal Society A (accepted) , 267:1–17. Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate - a practical and powerful approach to multiple testing. J. Roy. Stat. Soc. B Met. , 57 (1):289–300. Benjamini, Y. and Hochberg, Y. (2000). On the adaptive control of the false discovery 26