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# Chapter 3Computing effect sizes for meta-analysis

This chapter covers how to estimate common effect sizes and their sampling variances in a meta-analysis. We begin by introducing the formulas to compute effect sizes and their sampling variances for a univariate meta-analysis. Formulas to calculate effect sizes for a multivariate meta-analysis are then introduced. This chapter then introduces a general approach to calculate the sampling variances for the univariate effect sizes and the sampling covariance matrices for the multivariate effect sizes. The delta method is used to the approximate sampling variances of the effect sizes by considering the effect sizes as functions of the summary statistics. We show how structural equation modeling (SEM) can be used as a computational device to simplify the procedures on estimating the approximate sampling variances and covariances. Examples are used to illustrate the procedures in the R statistical environment.

## 3.1 Introduction

The main difference between a narrative review and a meta-analysis is that effect sizes are explicitly calculated and synthesized in a meta-analysis. An effect size summarizes the result of a study. A meta-analysis cannot be conducted without the effect sizes and their sample variances. This chapter introduces how to calculate some common effect sizes and their sample variances. These effect sizes serve as the ingredients for the statistical modeling that will be introduced in later chapters.

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