A multivariate mixed-effects approach for meta-analysis is presented. The approach (a) incorporates as outcomes multiple effect sizes per study; (b) allows different studies to have different subsets of effect sizes; and (c) treats each study's effect sizes as random realizations from a population of possible effect sizes. Application is illustrated via reanalysis of data from studies assessing the effects of coaching on verbal and mathematical subtests of the Scholastic Aptitude Test. Co variance components are estimated via restricted maximum likelihood (REML); inferences about regression coefficients and specific study effect sizes are based on their joint conditional distribution given the REML covariance component estimates. The approach can be implemented via now-standard software for unbalanced hierarchical data. Meta-analysis (Glass, 1976) or quantitative research synthesis (Hedges & Olkin, 1985) is the statistical analysis of data from a collection of independent studies that test the same hypotheses. A statistical indicator often used for integrating primary study results is an effect size estimate, for example, a standardized mean difference between the experimental and control groups from each individual study. Most meta-analyses to date have treated such effect size estimates as independent, and this is appropriate when each study produces a single effect size estimate. However, studies commonly produce multiple effect size estimates, and methodologists have recently proposed statistical methods for such multivariate effect size data (

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The students' initial dependence on the tutor progressed to an emphasis on learning resources. This shift is congruent with the theoretical model of the dynamics of PBL. The results suggest that the survey instrument provides a reliable measure of the multidimensional constructs underlying students' experience with PBL.