We consider random n× n matrices of the form (XX∗ + Y Y ∗)− 1 2 Y Y ∗ (XX∗ + Y Y ∗)− 1 2 , where X and Y have independent entries with zero mean and variance one. These matrices are the natural generalization of the Gaussian case, which are known as MANOVA matrices and which have joint eigenvalue density given by the third classical ensemble, the Jacobi ensemble. We show that, away from the spe...

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 i...

Multivariate analysis of variance (MANOVA) is a widely used technique for simultaneously comparing means for multiple dependent variables across two or more groups. MANOVA rests on several assumptions, including that of multivariate normality. Much prior research has investigated the performance of standard MANOVA with continuous, nonnormally distributed variables. However, very little work has...

The argument for preceding multiple analysis of variance (ANOVAS) with a multivariate analysis of variance (MANOVA) to control for Type I error is challenged. Several situations are discussed in which multiple ANOVAS might be conducted without the necessity of a preliminary MANOVA. Three reasons for considering a multivariate analysis are discussed: to identify outcome variable system construct...

This article teaches the multivariate analysis of variance (MANOVA) method for repeated measures analysis to researchers who are already familiar with regular analysis of variance (ANOVA) methods. Repeated measures designs are traditionally analyzed with mixed-model ANOVAS. However, sphericity violations markedly affect the true Type I error rates and power for the mixed-model tests. However, t...

We find the joint generalized singular value distribution and largest generalized singular value distributions of the β-MANOVA ensemble with positive diagonal covariance, which is general. This has been done for the continuous β > 0 case for identity covariance (in eigenvalue form), and by setting the covariance to I in our model we get another version. For the diagonal covariance case, it has ...