Two-Way MANOVA With Unequal Cell Sizes and Unequal Cell Covariance Matrices

In this article, we propose and study an approximate Hotelling T(2) (AHT) test for heteroscedastic two-way MANOVA. The AHT test is shown to be invariant under affine-transformations, different choices of the contrast matrix used to define the same hypothesis, and different labeling schemes of the cell mean vectors. We demonstrate via intensive simulations that the AHT test generally performs well and outperforms two existing approaches in terms of size and power. An extension of the AHT test for heteroscedastic multi-way MANOVA is briefly described. A dataset from a smoking cessation trial is analyzed to illustrate the methodologies. This article has supplementary material online in a single archive.