Meta-Analysis - A Comparison of Approaches

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