When the phenotype is univariate, we can use the one-way analysis of variance (ANOVA) with three levels of the genotype for GWAS. When we have correlated multivariate phenotypic traits, the natural extension of the one-way ANOVA is the one-way multivariate analysis of variance (MANOVA) [5]. Similar to ANOVA, MANOVA tests the equality of mean phenotypic vectors by comparing the within genotypes and between genotypes variance-covariance matrices. The strength of MANOVA is that the multivariate normal distribution provides many good statistical properties for testing and estimation [6]. However, in practice, multivariate phenotype data are very unlikely to meet the multivariate normal assumption. Furthermore, MANOVA is most powerful when the phenotypes are negatively correlated and yet this situation is also unlikely in practice, especially when the number of phenotypes is larger than 2. With respect to its relevant applications, this method has been used in GWAS on dose-response [7] and facial morphology [8].
