The results of all simulated scenarios are presented in detail in Tables S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S12. The false positive rates of TATES, the sum score and factor scores procedures, MANOVA, and MultiPhen were correct given our simulation settings with both MAF = 50% and MAF = 5%, while the original Simes procedure proved slightly conservative, if the phenotypes were highly correlated. (Note that the false positive rate of MANOVA is known to be inaccurate if the GV has low MAF (.5 or 5%) and the phenotypic data are dichotomous or non-normally distributed [11]). In contrast, the false positive rate of the Fisher combination test, Lancaster's weighted Fisher test, and the Z-transform test, which do not account for correlations between the 20 phenotypes, was often highly inflated (up to 20%, depending on the magnitude of the phenotypic correlations). Power results for these methods are therefore not discussed here (but see Tables S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S12). Since power results of the factor scores, MultiPhen, and the
