An alternative to R2 for assessing linear models of effect size



Reviewers often use regression models in meta-analysis (‘meta-regressions’) to examine the relationships between effect sizes and study characteristics. In this paper, we propose and illustrate the use of an index (Rmath image) that expresses the amount of variance in the outcome that is explained by the meta-regression model. The values of R2 obtained from the standard computer output for linear models of effect size in the meta-analysis context are typically too small, because the typical R2 considers sampling variance to be unexplained whereas in meta-analysis it can be quantified. Although the idea of removing the unexplainable variance from the estimator of variance accounted for in meta-analysis is not new (Cook et al., 1992; Raudenbush, 1994) we explicitly define four estimators of variance explained, and illustrate via two examples that the typical R2 obtained in a linear model of effect size is always lower than our indices. Thus, the typical R2 underestimates the explanatory power of linear models of effect sizes. Our four estimators improve upon typical weighted R2 values. Copyright © 2011 John Wiley & Sons, Ltd.