A Practical Guide to Calculating Cohen’s f2, a Measure of Local Effect Size, from PROC MIXED

TLDR

Reporting effect sizes is increasingly encouraged, yet selecting an appropriate measure for mixed‑effects or hierarchical models is challenging, and although Cohen’s f² provides a useful local effect size, it is not readily available in common software for repeated‑measures or multilevel data. This guide demonstrates how to extract Cohen’s f² for two variables in a mixed‑effects regression model using SAS PROC MIXED, aiming to simplify effect‑size calculation and reporting for single predictors in repeated‑measures or hierarchical analyses. The authors illustrate the method with two examples applied to a longitudinal cohort study of adolescent smoking development, showing how to compute f² for different research questions.

Abstract

Reporting effect sizes in scientific articles is increasingly widespread and encouraged by journals; however, choosing an effect size for analyses such as mixed-effects regression modeling and hierarchical linear modeling can be difficult. One relatively uncommon, but very informative, standardized measure of effect size is Cohen's f2, which allows an evaluation of local effect size, i.e. one variable's effect size within the context of a multivariate regression model. Unfortunately, this measure is often not readily accessible from commonly used software for repeated-measures or hierarchical data analysis. In this guide, we illustrate how to extract Cohen's f2 for two variables within a mixed-effects regression model using PROC MIXED in SAS ® software. Two examples of calculating Cohen's f2 for different research questions are shown, using data from a longitudinal cohort study of smoking development in adolescents. This tutorial is designed to facilitate the calculation and reporting of effect sizes for single variables within mixed-effects multiple regression models, and is relevant for analysis of repeated-measures or hierarchical/multilevel data that are common in experimental psychology, observational research, and clinical or intervention studies.