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On Robust Estimation of Effect Size Under Semiparametric Models

Published online by Cambridge University Press:  01 January 2025

Zhiyi Zhang  and
Nancy Schoeps
Zhiyi Zhang*
Affiliation:
University of North Carolina at Charlotte
Nancy Schoeps
Affiliation:
University of North Carolina at Charlotte
*
Requests for reprints should be sent to Zhiyi Zhang, Mathematics Department, University of North Carolina, Charlotte NC 28223.
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Abstract

Estimation of effect size is of interest in many applied fields such as Psychology, Sociology and Education. However there are few nonparametric estimators of effect size proposed in the existing literature, and little is known about the distributional characteristics of these estimators. In this article, two estimators based on the sample quantiles are proposed and studied. The first one is the estimator suggested by Hedges and Olkin (see page 93 of Hedges & Olkin, 1985) for the situation where a treatment effect is evaluated against a control group (Case A). A modified version of the robust estimator by Hedges and Olkin is also proposed for the situation where two parallel treatments are compared (Case B). Large sample distributions of both estimators are derived. Their asymptotic relative efficiencies with respect to the normal maximum likelihood estimators under several common distributions are evaluated. The robust properties of the proposed estimators are discussed with respect to the sample-wise breakdown points proposed by Akritas (1991). Simulation studies are provided in which the performing characteristics of the proposed estimator are compared to that of the nonparametric estimators by Kraemer and Andrews (1982). Interval estimation of the effect sizes is also discussed. In an example, interval estimates for the data set in Kraemer and Andrews (1982) are calculated for both cases A and B.

Keywords

effect sizerobust estimationrelative efficiencymeta-analysis
Type
Original Paper
Information
Psychometrika , Volume 62 , Issue 2 , June 1997 , pp. 201 - 214
Copyright
Copyright © 1997 The Psychometric Society

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References

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