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.

翻译：两组在感兴趣变量上差异的效应量可通过经典Cohen's $d$进行估计。近期提出的一种广义估计量允许在线性回归模型框架下对其他自变量进行条件化处理。本文展示了如何基于非中心$t$分布获得效应量参数的无偏估计及其对应的标准误。所描述的估计量可视为无偏Hedges' $g$的自然推广。此外，通过应用所谓的倒序置信区间原理，本文演示了未知参数的置信区间估计方法。当不存在任何额外自变量时，所讨论的性质将退化为已知情形。文中所述结论通过公开数据集进行了实证说明。