Supplementary Material for Discovering associations that replicate from a primary study of high dimension to a follow-up study November 23, 2018 Marina Bogomolov Faculty of Industrial Engineering and Management, Technion – Israel Institute of Technology, Haifa, Israel. E-mail: marinabo@tx.technion.ac.il Ruth Heller Department of Statistics and Operations Research, Tel-Aviv university, Tel-Aviv, Israel. E-mail: ruheller@post.tau.ac.il When the FWER controlling procedure applied in each stage of Procedure 3.1 is Bonferroni, then H$_{NR,j}$ is rejected if p$_{1}$$_{j}$ ≤ α$_{1}$/m and p$_{2}$$_{j}$ ≤ ( α − α$_{1}$ ) / ∑ m i $_{=1}$I [ p$_{1}$$_{j}$ ≤ α$_{1}$/m ], where I [ · ] is the indicator function. An alternative to Procedure 3.1 is to apply a FWER controlling procedure, such as Bonferroni, on the maximum of p -values from the two studies. This alternative procedure also controls the FWER on the family E A computational example with FWER control 35