Is the Meta-Analysis of Correlation Coefficients Accurate When Population Correlations Vary?

One conceptualization of meta-analysis is that studies within the meta-analysis are sampled from populations with mean effect sizes that vary (random-effects models). The consequences of not applying such models and the comparison of different methods have been hotly debated. A Monte Carlo study compared the efficacy of Hedges and Vevea's random-effects methods of meta-analysis with Hunter and Schmidt's, over a wide range of conditions, as the variability in population correlations increases. (a) The Hunter-Schmidt method produced estimates of the average correlation with the least error, although estimates from both methods were very accurate; (b) confidence intervals from Hunter and Schmidt's method were always slightly too narrow but became more accurate than those from Hedges and Vevea's method as the number of studies included in the meta-analysis, the size of the true correlation, and the variability of correlations increased; and (c) the study weights did not explain the differences between the methods.