A Note on Cohen's d From a Partitioned Linear Regression Model

TL;DR

This paper introduces a generalized formula for Cohen's d in the context of partitioned linear regression models, enabling effect size measurement considering additional variables, and relates it to t and F statistics.

Contribution

It provides a novel generalization of Cohen's d using the Frisch-Waugh-Lovell theorem in partitioned regression models, linking effect size to statistical tests.

Findings

Derived a generalized Cohen's d formula for models with covariates

Connected effect size to t and F statistics in regression context

Illustrated the approach with real data analysis

Abstract

In this note we introduce a generalized formula for Cohen's $d$ under the presence of additional independent variables, providing a measure for the size of a possible effect concerning the location difference of a variable in two groups. This is done by employing the so-called Frisch-Waugh-Lovell theorem in a partitioned linear regression model. The generalization is motivated by demonstrating the relationship to appropriate $t$ and $F$ statistics. Our discussion is further illustrated by inference from a publicly available data set.