Some additional remarks on statistical properties of Cohen’s d in the presence of covariates

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.