SIMULATION RESULTS ON SOLUTIONS TO THE MULTIVARIATE BEHRENS-FISHER PROBLEM VIA TRIMMED MEANS

A well-known result is that slight departures from normality towards a heavy-tailed distribution can substantially lower the power of methods for comparing means because heavy-tailed distributions inflate the standard error of the mean. One approach to this problem is to replace means with trimmed means. Trimmed means have standard errors that are less affected by heavy-tailed distributions, there are practical situations where they can have substantially higher power and the power remains relatively high when sampling from normal distributions, provided that the amount of trimming is not too high. This paper uses simulations to investigate the small sample characteristics of several solutions to the two-sample multivariate Behrens-Fisher problem based on trimmed means. Extant results when dealing with means are limited to normal distributions, so another goal is to report results on how three methods for means are affected by non-normality.