Some Additional Remarks on Statistical Properties of Cohen's d from Linear Regression

TL;DR

This paper discusses an improved estimator for Cohen's d within linear regression, enabling unbiased effect size estimation and confidence intervals, generalizing existing methods and demonstrated with real data.

Contribution

It introduces a generalized, unbiased estimator for Cohen's d in regression models, extending Hedges' g and providing confidence interval methods.

Findings

Unbiased effect size estimation using non-central t distribution.

Extension of Hedges' g to regression with multiple variables.

Practical demonstration with real data set.

Abstract

The size of the effect of the difference in two groups with respect to a variable of interest may be estimated by the classical Cohen's $d$. A recently proposed generalized estimator allows conditioning on further independent variables within the framework of a linear regression model. In this note, it is demonstrated how unbiased estimation of the effect size parameter together with a corresponding standard error may be obtained based on the non-central $t$ distribution. The portrayed estimator may be considered as a natural generalization of the unbiased Hedges' $g$. In addition, confidence interval estimation for the unknown parameter is demonstrated by applying the so-called inversion confidence interval principle. The regarded properties collapse to already known ones in case of absence of any additional independent variables. The stated remarks are illustrated with a publicly available data set.