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Confidence Interval Coverage for Cohen's Effect Size Statistic

University of Florida

H. J. Keselman

University of Manitoba

Randall D. Penfield

University of Miami

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.

Key Words: effect size • confidence interval • nonnormality • robust parameter • statistic • interval

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