ROBUSTNESS OF PROCEDURES FOR THE BEHRENS-FISHER PROBLEMS: EXTENSION TO BIVARIATE NORMAL MIXTURES

Abstract

In the applied sciences, it is often important to be able to compare the mean values of two populations. However, testing a hypothesis can be complex, if the two populations are heteroscedastic and exhibit non-normality in the data. This paper reviews currently available strategies for the multivariate Behrens-Fisher problem. It then carries out Monte Carlo comparisons of selected procedures to assess their robustness when applied to data from normal mixture distributions. The overall conclusion is that Johansen's procedure appears to work best for small sample data both in terms of empirical power and significance level. Johansen's procedure works reasonably well even with mixture data. The simulation also provides researchers with specific guidelines to follow at the early designing and planning stages of the investigation.

Keywords:

• Approximate degrees of freedom solutions
• Non-normality
• Variance heterogeneity
• Mahalanobis distance

ACKNOWLEDGMENTS

This work was supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada and a Scholar Award (6609–2120–48) with the National Health Research Development Program of Canada. Additional funding was provided by a Senior Scholar Award and Establishment Grant from the Alberta Heritage Foundation for Medical Research.