Meta-Analysis: A Comparison of Approaches

Abstract

Preface Introduction Theory: Statistical Methods of Meta-Analysis Effect Sizes Families of Effect Sizes The r Family: Correlation Coefficients as Effect Sizes The d Family: Standardized Mean Differences as Effect Sizes Conversion of Effect Sizes A General Framework of Meta-Analysis Fixed Effects Model Random Effects Model Mixture Models Classes of Situations for the Application of Meta-Analysis Approaches to Meta-Analysis Hedges and Olkin Procedures for r as Effect Size Procedures for d as Effect Size Rosenthal and Rubin Hunter and Schmidt Refined Approaches DerSimonian-Laird Olkin and Pratt Changes in Parameters to be Estimated by the Choice of an Approach Comparisons of the Approaches Summary Method: Monte Carlo Study Aims and General Procedure Distributions in the Universe of Studies Parameters Drawing Random Correlation Coefficients Approximations to the Sampling Distribution of r Evaluation of the Approximations Details of Programming Summary Results Preliminaries Estimation of Parameter [mu]r Bias and Accuracy Homogeneous Situation S1 Heterogeneous Situation S2 Heterogeneous Situation S3 Relative Efficiency of the Estimators Significance Tests: Testing [mu]r = 0 Confidence Intervals Homogeneity Tests The Q-Test Homogeneous Situation S1: Type I Error Rates Heterogeneous Situations S2 and S3: Power The Hunter-Schmidt Approach to the Test of Homogeneity: The 75 per cent and 90 per cent Rule Estimates of Heterogeneity Variance Homogeneous situation S1 Heterogeneous Situations S2 and S3 Summary Discussion List of Figures List of Tables Nomenclature References Appendix A: Technical Details of the Simulation Procedure Beta Distributions in the Universe of Effect Sizes An Annotated Mathematica[trademark] Notebook for a Comparison of Approximations to the Exact Density of R Appendix B: Tables and Figures of Results Estimation of the Parameter [mu]r Subject Index Author Index

Keywords

Affiliated Institutions

• University of Münster DE

Related Publications