An Approximate Hotelling T²-Test for Heteroscedastic One-Way MANOVA

Jin-Ting Zhang

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DOI: 10.4236/ojs.2012.21001                

Abstract

In this paper, we consider the general linear hypothesis testing (GLHT) problem in heteroscedastic one-way MANOVA. The well-known Wald-type test statistic is used. Its null distribution is approximated by a Hotelling T² distribution with one parameter estimated from the data, resulting in the so-called approximate Hotelling T² (AHT) test. The AHT test is shown to be invariant under affine transformation, different choices of the contrast matrix specifying the same hypothesis, and different labeling schemes of the mean vectors. The AHT test can be simply conducted using the usual F-distribution. Simulation studies and real data applications show that the AHT test substantially outperforms the test of [1] and is comparable to the parametric bootstrap (PB) test of [2] for the multivariate k-sample Behrens-Fisher problem which is a special case of the GLHT problem in heteroscedastic one-way MANOVA.

Keywords

Approximate Hotelling T²Test; Multivariate k-Sample Behrens-Fisher Problem; Wishart-Approximation; Wishart Mixture

Conflicts of Interest

The authors declare no conflicts of interest.

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