A random effects model for effect sizes

Recent interest in quantitative research synthesis has led to the development of rigorous statistical theory for some of the methods used in meta-analysis. Statistical theory proposed previously has stressed the estimation of fixed but unknown population effect sizes (standardized mean differences). Theoretical considerations often suggest that treatment effects are not fixed but vary across different implementations of a treatment. The present author presents a random effects model (analogous to random effects ANOVA) in which the population effect sizes are not fixed but are sample realizations from a distribution of possible population effect sizes. An analogy to variance component estimation is used to derive an unbiased estimator of the variance of the effect-size distribution. An example shows that these methods may suggest insights that are not available from inspection of means and standard deviation of effect-size estimates. (13 ref) (PsycINFO Database Record (c) 2006 APA, all rights reserved).