Meta-Analysis: A Comparision of Approaches

by Schulze, Ralf

• ISBN13: 9780889372801
• ISBN10: 0889372802
• Format: Hardcover
• Copyright: 2004-08-01
• Publisher: Hogrefe & Huber Pub

Summary

In many scientific fields, meta-analysis has become the standard method for summarizing research findings. The number of published applications of the method has been steadily growing in the last 25 years and the statistical procedures of meta-analysis continue to become more and more advanced. This book provides a comprehensive treatment of the statistical procedures for meta-analysis with correlations as an effect size. In the first part, the statistical fundamentals of existing meta-analytical approaches are explained in detail. Fixed as well as random effects models are described and several refinements to improve the performance of the procedures are presented. Additionally, the different procedures are compared from a theoretical viewpoint. In the second part, the results of a comprehensive Monte-Carlo study are presented to evaluate the performance of the major approaches in a large set of possible situations. It shows when the procedures of commonly applied app

Table of Contents

Preface	v
Part I Introduction	1	(16)
The Growth of Meta-Analysis and Implications for Methodological Controversies	3	(6)
Basic Steps of Meta-Analysis and the Emergence of Approaches	9	(8)
Basic Steps of Meta-Analysis	9	(5)
On the Emergence of Approaches	14	(3)
Part II Statistical Methods of Meta-Analysis	17	(74)
Effect Sizes	19	(14)
Correlation Coefficients as Effect Sizes	20	(8)
Standardized Mean Differences as Effect Sizes	28	(2)
Conversion of Effect Sizes	30	(3)
General Frameworks of Meta-Analysis	33	(22)
Fixed Effects Model	35	(4)
Random Effects Model	39	(3)
Mixture Models	42	(3)
Hierarchical Linear Models	45	(3)
Classes of Situations for the Application of Meta-Analysis	48	(7)
Statistical Approaches to Meta-Analysis	55	(32)
Hedges and Olkin	56	(5)
Procedures for r as Effect Size	57	(2)
Procedures for d as Effect Size	59	(2)
Rosenthal and Rubin	61	(1)
Hunter and Schmidt	62	(8)
Refined Approaches	70	(5)
DerSimonian-Laird	71	(1)
Olkin and Pratt	72	(3)
Consequences of Choosing an Approach: Different Estimated Parameters	75	(7)
Comparisons of Approaches: Statistical Procedures	82	(5)
Summary of Statistical Part	87	(4)
Part III Evaluation of Statistical Approaches: A Monte-Carlo Study	91	(90)
Aims, Design, and Implementation	93	(22)
General Aims and Procedure	94	(1)
General Expectations and Predictions for the Results	95	(5)
Distributions in the Universe of Studies	100	(2)
Parameters	102	(3)
Drawing Random Correlation Coefficients	105	(9)
Approximations to the Sampling Distribution of r	106	(3)
Evaluation of the Approximations	109	(5)
Details of Programming	114	(1)
Summary	114	(1)
Results	115	(66)
Preliminaries	115	(2)
Estimation of the Mean Effect Size in the Universe of Studies	117	(20)
Bias	118	(1)
Homogeneous Situation G1	118	(5)
Heterogeneous Situation G2	123	(7)
Heterogeneous Situation G3	130	(4)
Relative Efficiency	134	(3)
Significance Tests for the Mean Effect Size: Type I Errors and Power	137	(11)
Confidence Intervals	148	(10)
Homogeneity Tests	158	(12)
Homogeneity Tests Based on the Q-Statistic	159	(1)
Homogeneous Situation G1: Type I Errors	159	(2)
Heterogeneous Situations G2 and G3: Power	161	(3)
The Hunter-Schmidt Approach to the Test of Homogeneity: The 75%- and 90%-rule	164	(6)
Estimation of Heterogeneity Variance	170	(11)
Homogeneous Situation G1	171	(4)
Heterogeneous Situations G2 and G3	175	(6)
Part IV Putting It All Together	181	(16)
Synopsis of Statistical Methods and Monte Carlo Study Results	183	(8)
Discussion and Conclusions	191	(6)
Nomenclature	197	(4)
References	201	(14)
Appendices	215	(2)
Appendix A Beta Distributions in the Universe of Effect Sizes	217	(6)
Appendix B Annotated Mathematica Notebook	223	(6)
Appendix C Tables of Results	229	(6)
Author Index	235	(4)
Subject Index	239