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Some properties of r equivalent: a simple effect size indicator.

Louis M Hsu1

  • 1School of Psychology, Fairleigh Dickinson University, Teaneck, NJ 07666, USA. lhsu@fdu.edu

Psychological Methods
|January 6, 2006
PubMed
Summary

This study compares statistical effect size estimators for small samples. The sample correlation coefficient (r sample) is often better than r equivalent* but can be outperformed by r hybrid in meta-analyses.

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Area of Science:

  • Psychometrics and Statistical Methods
  • Quantitative Psychology
  • Meta-Analysis

Background:

  • The r equivalent statistic, derived from Fisher's exact test p-values, is proposed as a more accurate population correlation estimate for small samples.
  • Existing research suggests r equivalent may offer advantages over the sample correlation coefficient (r sample) in specific contexts.

Discussion:

  • The sample correlation (r sample) demonstrates lower bias and mean squared error (MSE) compared to r equivalent* (unrestricted use of r equivalent).
  • The r hybrid estimator generally outperforms r equivalent* and is preferable to r sample in terms of MSE, except in cases of very large population correlations.
  • The study identifies specific conditions under which r sample is favored over r equivalent* and r hybrid in meta-analytic research.

Key Insights:

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  • For small samples, r sample is often a more accurate and less biased estimator than r equivalent*.
  • r hybrid offers advantages in MSE over r sample when population correlations are not extremely large.
  • The choice of estimator depends on sample size, population correlation, and the specific meta-analytic context.

Outlook:

  • Further research could explore the performance of these estimators with different types of data and under varying distributional assumptions.
  • Developing guidelines for selecting the most appropriate correlation estimator based on empirical data characteristics is recommended.
  • Investigating the impact of these estimator choices on the conclusions drawn from meta-analyses is a critical next step.