A comparison of fixed-effects and mixed (random-effects) models for meta-analysis tests of moderator variable effects

The growing popularity of meta-analysis has focused increased attention on the statistical models analysts are using and the assumptions underlying these models. Although comparisons often have been limited to fixed-effects (FE) models, recently there has been a call to investigate the differences between FE and random-effects (RE) models, differences that may have substantial theoretical and applied implications (National Research Council, 1992). Three FE models (including L.V. Hedges & I. Olkin's, 1985, and R. Rosenthal's, 1991, tests) and 2 RE models were applied to simulated correlation data in tests for moderator effects. The FE models seriously underestimated and the RE models greatly overestimated sampling error variance when their basic assumptions were violated, which caused biased confidence intervals and hypothesis tests. The implications of these and other findings are discussed as are methodological issues concerning meta-analyses.