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An alternative to R 2 for assessing linear models of effect size
Author(s) -
Aloe Ariel M.,
Becker Betsy Jane,
Pigott Therese D.
Publication year - 2010
Publication title -
research synthesis methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.376
H-Index - 35
eISSN - 1759-2887
pISSN - 1759-2879
DOI - 10.1002/jrsm.23
Subject(s) - estimator , statistics , linear regression , linear model , variance (accounting) , meta analysis , context (archaeology) , sample size determination , econometrics , regression analysis , mathematics , explanatory power , economics , medicine , paleontology , philosophy , accounting , epistemology , biology
Abstract 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 ( R 2 Meta ) that expresses the amount of variance in the outcome that is explained by the meta‐regression model. The values of R 2 obtained from the standard computer output for linear models of effect size in the meta‐analysis context are typically too small, because the typical R 2 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 R 2 obtained in a linear model of effect size is always lower than our indices. Thus, the typical R 2 underestimates the explanatory power of linear models of effect sizes. Our four estimators improve upon typical weighted R 2 values. Copyright © 2011 John Wiley & Sons, Ltd.