A Guide to Conducting a Meta-Analysis with Non-Independent Effect Sizes

Conventional meta-analytic procedures assume that effect sizes are independent. When effect sizes are non-independent, conclusions based on these conventional models can be misleading or even wrong. Traditional approaches, such as averaging the effect sizes and selecting one effect size per study, are usually used to remove the dependence of the effect sizes. These ad-hoc approaches, however, may lead to missed opportunities to utilize all available data to address the relevant research questions. Both multivariate meta-analysis and three-level meta-analysis have been proposed to handle non-independent effect sizes. This paper gives a brief introduction to these new techniques for applied researchers. The first objective is to highlight the benefits of using these methods to address non-independent effect sizes. The second objective is to illustrate how to apply these techniques with real data in R and Mplus. Researchers may modify the sample R and Mplus code to fit their data.