A practical guide to calculating Cohen's f 2, a measure of local effect size, from PROC MIXED

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 f 2, which allows an eval-uation 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 com-monly used software for repeated-measures or hierarchical data analysis. In this guide, we illustrate how to extract Cohen's f 2 for two variables within a mixed-effects regression model using PROC MIXED in SAS ® software. Two examples of calculating Cohen's f 2 for different research questions are shown, using data from a longitudinal cohort study of smok-ing development in adolescents. This tutorial is designed to facilitate the calculation and reporting of effect sizes for single variables within mixed-effects multiple regression mod-els, and is relevant for analyses of repeated-measures or hierarchical/multilevel data that are common in experimental psychology, observational research, and clinical or intervention studies. © 2012 Selya, Rose, Dierker, Hedeker and Mermelstein.