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

Jürgen Groß () and Annette Möller ()
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Jürgen Groß: University of Hildesheim
Annette Möller: Bielefeld University

Statistical Papers, 2024, vol. 65, issue 6, No 24, 3979 pages

Abstract: 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.

Keywords: Effect size; Cohen’s d; Linear regression; Non-central t distribution; Confidence interval; 62J05; 62F03; 62F10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01527-9

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