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Comparing One-Step M-Estimators of Location Corresponding to Two Independent 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

Experience with real data indicates that psychometric measures often have heavy-tailed distributions. This is known to be a serious problem when comparing the means of two independent groups because heavy-tailed distributions can have a serious effect on power. Another problem that is common in some areas is outliers. This paper suggests an approach to these problems based on the one-step M-estimator of location. Simulations indicate that the new procedure provides very good control over the probability of a Type I error even when distributions are skewed, have different shapes, and the variances are unequal. Moreover, the new procedure has considerably more power than Welch's method when distributions have heavy tails, and it compares well to Yuen's method for comparing trimmed means. Wilcox's median procedure has about the same power as the proposed procedure, but Wilcox's method is based on a statistic that has a finite sample breakdown point of only 1/n, where n is the sample size. Comments on other methods for comparing groups are also included.

Keywords

Huber's Ψ functionL-statisticstrimmingmediansbootstrapMann-Whitney test
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 1 , March 1992 , pp. 141 - 154
Copyright
Copyright © 1992 The Psychometric Society

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