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Comparing One-Step M-Estimators of Location when there are More than Two Groups

Published online by Cambridge University Press:  01 January 2025

Rand R. Wilcox
Rand R. Wilcox*
Affiliation:
University of Southern California
*
Requests for reprints should be sent to Rand R. Wilcox, Department of Psychology, University of Southern California, Los Angeles, CA 90089-1061.
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Abstract

Methods for comparing means are known to be highly nonrobust in terms of Type II errors. The problem is that slight shifts from normal distributions toward heavy-tailed distributions inflate the standard error of the sample mean. In contrast, the standard error of various robust measures of location, such as the one-step M-estimator, are relatively unaffected by heavy tails. Wilcox recently examined a method of comparing the one-step M-estimators of location corresponding to two independent groups which provided good control over the probability of a Type I error even for unequal sample sizes, unequal variances, and different shaped distributions. There is a fairly obvious extension of this procedure to pairwise comparisons of more than two independent groups, but simulations reported here indicate that it is unsatisfactory. A slight modification of the procedure is found to give much better results, although some caution must be taken when there are unequal sample sizes and light-tailed distributions. An omnibus test is examined as well.

Keywords

testing hypothesesresistant measures of locationbootstrapcontamination
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 1 , March 1993 , pp. 71 - 78
Copyright
Copyright © 1993 The Psychometric Society

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