A Kurtosis-Adjusted Bias Correction for the Standardized Mean Difference: Extending Hedges' g to Nonnormal...

The standardized mean difference (SMD) is the most widely used effect size measure in the behavioral, educational, and social sciences. Hedges' g, which applies a bias correction factor to Cohen's d, assumes normally distributed populations. This article proposes a kurtosis-adjusted estimator, $g_{\kappa }^{*}$ , that extends Hedges' correction by incorporating an additional multiplicative factor based on the sample excess kurtosis. The estimator is intended for continuous, common-shape distributions that depart from normality primarily through excess kurtosis with at most moderate skewness; it is not intended for multimodal, infinite-variance, or severely skewed-and-heavy-tailed distributions. The proposed estimator uses the exact Hedges correction factor $J\left(\nu \right)$ as its anchor, so that it reduces algebraically to Hedges' g when the estimated excess kurtosis equals zero. We provide a formal derivation of the kurtosis-induced bias under explicit regularity conditions, including the treatment of the numerator-denominator dependence under nonnormality and the quantification of plug-in estimation error. A comprehensive Monte Carlo simulation study (400+ conditions × 10,000 replications) demonstrates that (a) under heavy-tailed distributions ( ${\gamma }_2\ge 4$ ), $g_{\kappa }^{*}$ reduces the residual bias of Hedges' g by 36% to 92% at sample sizes of 20-100 per group; (b) the associated 95% confidence interval achieves coverage of .952-.961 under the main nonnormal distributions examined (excluding severe g-and-h boundary cases), compared with .938-.947 for the classical Hedges interval and .954-.961 for the Bonett kurtosis-adjusted interval, with modestly narrower widths than Bonett; (c) under normality, the estimator's finite-sample behavior is very close to Hedges' g, with small differences induced by sampling variability and finite-sample bias in the moment-based kurtosis estimate; and (d) the estimator performed well across a broad range of symmetric and moderately skewed distributions, while its effectiveness was attenuated when severe skewness and extreme kurtosis co-occurred.