Isaac Scientific Publishing

Journal of Advanced Statistics

A Modified Bartlett Test for Heteroscedastic Two-way MANOVA

Download PDF (552.6 KB) PP. 94 - 108 Pub. Date: June 13, 2016

DOI: 10.22606/jas.2016.12006

Author(s)

  • Jin-Ting Zhang*
    Department of Statistics and Applied Probability, National University of Singapore, Singapore
  • Bu Zhou
    Department of Statistics and Applied Probability, National University of Singapore, Singapore
  • Jia Guo
    Department of Statistics and Applied Probability, National University of Singapore, Singapore
  • Xuefeng Liu
    IBM, Xi-An, China

Abstract

A two-way multivariate analysis of variance (MANOVA) aims to compare the effects of several levels of two factors in a factorial experiment with two-way layout. It is widely used in experimental sciences, e.g., biology, psychology, physics, among others. When the cell covariance matrices are the same, it can be solved using the well-known Wilks likelihood ratio, Lawley-Hotelling trace, Bartlett-Nanda-Pillai trace and Roy’s largest root tests ([1]). However, when the homogeneous assumption is violated, these tests may become seriously biased. To overcome this problem, several authors have proposed and studied different approximation solutions. In this paper, we propose and study a Modified Bartlett (MB) test using a Wald-type statistic and the modified Bartlett correction ([2]) for heteroscedastic two-way MANOVA problems. The MB test can be easily implemented using the usual χ2-distribution with known degrees of freedom. We show that it admits several invariant properties. Simulation studies show that the MB test generally outperforms the classical Lawley- Hotelling trace (LHT) test and a modified LHT test of [3] under various parameter configurations in terms of size controlling and power. A real data example illustrates our method and the effect of heteroscedasticity.

Keywords

Heteroscedastic two-way MANOVA, Tests of linear hypotheses, Modified Bartlett correction, Wald-type statistic.

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