MANOVA for Nested Designs with Unequal Cell Sizes and Unequal Cell Covariance Matrices

Abstract

We propose and study parametric bootstrap (PB) tests for heteroscedastic two-factor MANOVA with nested designs. For the problem of testing “main effects” of both factors, we develop a flexible test based on a parametric bootstrap approach. The PB test is shown to be invariant under affine-transformations. Moreover, the PB test does not depend on the chosen weights used to define the parameters uniquely. The proposed test is compared with the approximate Hotelling $T^2$ (AHT) test by the simulations. Simulation results indicate that the PB test performs satisfactorily for various cell sizes and parameter configurations and generally outperforms the AHT test in terms of controlling the nominal size. For the heteroscedastic cases, the PB test outperforms the AHT test in terms of power. In addition, the PB test does not lose too much power when the homogeneity assumption is actually valid.