Isaac Scientific Publishing

Journal of Advanced Statistics

Modified Tests for Heteroscedastic Two-Way MANOVA

Download PDF (623.4 KB) PP. 1 - 16 Pub. Date: March 1, 2016

DOI: 10.22606/jas.2016.11001

Author(s)

  • Shengning Xiao*
    Department of Mathematics, School of Science, Tianjin University, China
  • Jin-Ting Zhang
    Department of Statistics and Applied Probability, National University of Singapore, Singapore

Abstract

In this article we consider testing for main and interaction effects in heteroscedastic two-way MANOVA model. We express the model in the form of the general linear hypothesis testing (GLHT) problem and construct the sum of squares and cross products (SSCP) matrices due to hypothesis and error respectively. We modify the classical Wilks’s Likelihood Ratio (WLR), Lawley-Hotelling Trace (LHT) and Bartlett-Nanda-Pillai trace (BNP) tests based on these two SSCP matrices with the approximate degrees of freedoms (ADF) obtained by matching the means and the total variations of the SSCP matrices and their respective approximating Wishart distributions. The resulting modified WLR, LHT, BNP tests are 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. Simulation studies presented in this paper also show that the proposed tests generally perform well and outperform one existing approach in terms of controlling the desired size and enhancing the powers. An example from a Smoking Cessation trial is given to illustrate the proposed methodologies.

Keywords

Two-way MANOVA, Heteroscedastic, General linear hypothesis test, Unbalanced, Wishart-approximation, Affine-invariant, Main-effect, Interaction-effect

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