language: en

[Computer Methods and Programs in Biomedicine (2005) 77, 129—139]

Robust tests for the multivariate Behrens—Fisher problem

Lisa M. Lix a, * , H.J. Keselman b , Aynslie M. Hinds a
a Department of Community Health Sciences, Faculty of Medicine, University of Manitoba,
408-727 McDermot Avenue, Winnipeg, Man., Canada R3E 3P5
b Department of Psychology, University of Manitoba,
Winnipeg, Man., Canada R3T 2N2

[Received]

2 December 2003 ;

[received in revised form 9 July 2004; accepted 9 September 2004]

KEYWORDS Multivariate; Mean equality; Two-group design; Robust estimation; Covariance heterogeneity

Summary Hotelling's T 2 procedure is used to test the equality of means in twogroup multivariate designs when covariances are homogeneous. A number of alternatives to T 2 , which are robust to covariance heterogeneity, have been proposed in the literature. However, all are sensitive to departures from multivariate normality. We demonstrate how to obtain multivariate tests that are robust to covariance heterogeneity and non-normality with estimators of location and scale based on trimming and Winsorizing. The performance of six alternatives to T 2 was examined via Monte Carlo methods when characteristics of the research design, degree of covariance heterogeneity, and degree of non-normality were manipulated. We have recently developed a program written in the SAS/IML language that can be used to implement these robust multivariate tests. Recommendations are provided on the specific data-analytic conditions under which these tests should be adopted.

[© 2004 Elsevier Ireland Ltd. All rights reserved.]

1. Introduction