Overlap between treatment and control distributions as an effect size measure in experiments

Larry Vernon Hedges, Ingram Olkin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The proportion π of treatment group observations that exceed the control group mean has been proposed as an effect size measure for experiments that randomly assign independent units into 2 groups. We give the exact distribution of a simple estimator of π based on the standardized mean difference and use it to study the small sample bias of this estimator. We also give the minimum variance unbiased estimator of π under 2 models, one in which the variance of the mean difference is known and one in which the variance is unknown. We show how to use the relation between the standardized mean difference and the overlap measure to compute confidence intervals for π and show that these results can be used to obtain unbiased estimators, large sample variances, and confidence intervals for 3 related effect size measures based on the overlap. Finally, we show how the effect size π can be used in a meta-analysis.

Original languageEnglish (US)
Pages (from-to)61-68
Number of pages8
JournalPsychological Methods
Volume21
Issue number1
DOIs
StatePublished - Mar 1 2016

Keywords

  • Meta-analysis
  • Research synthesis
  • Standardized mean difference
  • Tail probabilities
  • Unbiased estimation

ASJC Scopus subject areas

  • Psychology (miscellaneous)

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