Effect sizes in cluster-randomized designs

Multisite research designs involving cluster randomization are becoming increasingly important in educational and behavioral research. Researchers would like to compute effect size indexes based on the standardized mean difference to compare the results of cluster-randomized studies (and corresponding quasi-experiments) with other studies and to combine information across studies in meta-analyses. This article addresses the problem of defining effect sizes in multilevel designs and computing estimates of those effect sizes and their standard errors from information that is likely to be reported in journal articles. Three effect sizes are defined corresponding to different standardizations. Estimators of each effect size index are also presented along with their sampling distributions (including standard errors).