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arXiv · 2309.02069

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

Jürgen Groß·Annette Möller
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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.

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Jürgen Groß, Annette Möller. 2023-09-05. Some Additional Remarks on Statistical Properties of Cohen's d from Linear Regression. https://arxiv.org/abs/2309.02069

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