We have presented TATES, a new, computationally feasible multivariate method to test genotype-phenotype relations. The false positive rate of TATES is correct for varying MAF, even if the multiple phenotypes are substantially correlated. Through simulations, we showed that TATES outperforms standard univariate analyses, unless the data-generating process is a unidimensional factor model and the GV affects the factor. TATES is only outperformed by MANOVA in the particular condition that the GV affects only one of multiple strongly correlated phenotypes.