Confidence Interval Coverage for Cohen's Effect Size Statistic

James J. Algina · Harvey J. Keselman · Randall D. Penfield

62 citations0/0 files storedEducational and Psychological Measurement

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Meta-analysis and systematic reviews Psychometric Methodologies and Testing Statistical Methods and Bayesian Inference

Abstract

Kelley compared three methods for setting a confidence interval (CI) around Cohen's standardized mean difference statistic: the noncentral- t-based, percentile (PERC) bootstrap, and biased-corrected and accelerated (BCA) bootstrap methods under three conditions of nonnormality, eight cases of sample size, and six cases of population effect size (ES) magnitude. Kelley recommended the BCA bootstrap method. The authors expand on his investigation by including additional cases of nonnormality. Like Kelley, they find that under many conditions, the BCA bootstrap method works best; however, they also find that in some cases of nonnormality, the method does not control probability coverage. The authors also define a robust parameter for ES and a robust sample statistic, based on trimmed means and Winsorized variances, and cite evidence that coverage probability for this parameter is good over the range of nonnormal distributions investigated when the PERC bootstrap method is used to set CIs for the robust ES.

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References

1981Distribution Theory for Glass's Estimator of Effect Size and Related Estimators 1999Statistical methods in psychology journals: Guidelines and explanations.2001A Primer on the Understanding, Use, and Calculation of Confidence Intervals That Are Based on Central and Noncentral Distributions 2005An Alternative to Cohen's Standardized Mean Difference Effect Size: A Robust Parameter and Confidence Interval in the Two Independent Groups Case.2004The Effects of Nonnormal Distributions on Confidence Intervals Around the Standardized Mean Difference: Bootstrap and Parametric Confidence Intervals

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