This article concerns the power of various data analytic strategies to detect the effect of a single genetic variant (GV) in multivariate data. We simulated exactly fitting monozygotic and dizygotic phenotypic data according to single and two common factor models, and simplex models. We calculated the power to detect the GV in twin 1 data in an ANOVA of phenotypic sum scores, in a MANOVA, and in exploratory factor analysis (EFA), in which the common factors are regressed on the genetic variant. We also report power in the full twin model, and power of the single phenotype ANOVA. The results indicate that (1) if the GV affects all phenotypes, the sum score ANOVA and the EFA are most powerful, while the MANOVA is less powerful. Increasing phenotypic correlations further decreases the power of the MANOVA; and (2) if the GV affects only a subset of the phenotypes, the EFA or the MANOVA are most powerful, while sum score ANOVA is less powerful. In this case, an increase in phenotypic correlations may enhance the power of MANOVA and EFA. If the effect of the GV is modeled directly on the phenotypes in the EFA, the power of the EFA is approximately equal to the power of the MANOVA.