Chapter 6Three-level meta-analysis

This chapter reviews issues of nonindependent effect sizes in a meta-analysis and some of the conventional approaches used to address these issues. A three-level meta-analysis is then put forward to address the problem of dependence in the effect sizes. A model and analyses of three-level meta-analysis are introduced. This chapter also seeks to extend the key concepts of Q statistics, c06-math-001, and c06-math-002 from a two-level meta-analysis to a three-level meta-analysis. A structural equation modeling (SEM) approach to conducting a three-level meta-analysis is introduced. The relationships between a three-level meta-analysis and a multivariate meta-analysis are described. An example is used to illustrate the procedures in the R statistical environment.

6.1 Introduction

Most statistical methods used in meta-analyses assume that the effect sizes are independent. The assumption of independence among the effect sizes does not seem plausible in many research settings. When the effect sizes are nonindependent, the results of conventional meta-analyses conducted on the assumption that effect sizes are independent are no longer correct. Broadly speaking, there are two types of dependence—either the conditional sampling covariance matrices of the studies are known or it ...

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