Addressing dependency in meta-analysis: A companion to Assink and Wibbelink (2016)

This research note elaborates on addressing dependency in effect size data and serves as a companion to our tutorial on fitting three-level meta-analytic models in R (Assink and Wibbelink, 2016). We provide a description of effect size and standard error dependency, explain how both the multilevel and multivariate meta-analytic models handle these types of dependency, and discuss the role of alternative methods in addressing dependency in effect size data, including approximating a variance-covariance matrix and applying a cluster-robust inference method. These alternative methods are illustrated with example R code that builds upon the effect size dataset that we presented and analyzed in our tutorial. We conclude that more simulation studies are needed to provide clearer guidelines for modeling dependency in effect size data and urge statisticians to make the available technical literature further accessible to applied researchers.