Hedges / Olkin Statistical Methods for Meta-Analysis

1. Auflage 2014
ISBN: 978-0-08-057065-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 369 Seiten, Web PDF

The main purpose of this book is to address the statistical issues for integrating independent studies. There exist a number of papers and books that discuss the mechanics of collecting, coding, and preparing data for a meta-analysis , and we do not deal with these. Because this book concerns methodology, the content necessarily is statistical, and at times mathematical. In order to make the material accessible to a wider audience, we have not provided proofs in the text. Where proofs are given, they are placed as commentary at the end of a chapter. These can be omitted at the discretion of the reader.Throughout the book we describe computational procedures whenever required. Many computations can be completed on a hand calculator, whereas some require the use of a standard statistical package such as SAS, SPSS, or BMD. Readers with experience using a statistical package or who conduct analyses such as multiple regression or analysis of variance should be able to carry out the analyses described with the aid of a statistical package.

Autoren/Hrsg.

Hedges, Larry V.

Olkin, Ingram

Inhaltsverzeichnis

1;Front Cover;1
2;Statistical Methods for Meta-Analysis;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;16
7;Acknowledgments;22
8;Chapter 1. Introduction;24
8.1;A. The Use of Statistical Procedures for Combining the Results of Research Studies in the Social Sciences;25
8.2;B. Failings in Conventional Statistical Methodology in Research Synthesis;30
8.3;C. Statistics for Research Synthesis;35
9;Chapter 2. Data Sets;38
9.1;A. Cognitive Gender Differences;39
9.2;B. Sex Differences in Conformity;44
9.3;C. The Effects of Open Education;46
9.4;D. The Relationship between Teacher Indirectness and Student Achievement;49
10;Chapter 3. Tests of Statistical Significance of Combined Results;50
10.1;A. Preliminaries and Notation;51
10.2;B. General Results on Tests of Significance of Combined Results;54
10.3;C. Combined Test Procedures;56
10.4;D. The Uses and Interpretation of Combined Test Procedures in Research Synthesis;68
10.5;E. Technical Commentary;69
11;Chapter 4. Vote-Counting Methods;70
11.1;A. The Inadequacy of Conventional Vote-Counting Methodology;71
11.2;B. Counting Estimators of Continuous Parameters;75
11.3;C. Confidence Intervals for Parameters Based on Vote Counts;76
11.4;D. Choosing a Critical Value;79
11.5;E. Estimating an Effect Size;79
11.6;F. Estimating a Correlation;86
11.7;G. Limitations of Vote-Counting Estimators;90
11.8;H. Vote-Counting Methods for Unequal Sample Sizes;92
12;Chapter 5. Estimation of a Single Effect Size: Parametric and Nonparametric Methods;98
12.1;A. Estimation of Effect Size from a Single Experiment;99
12.2;B. Distribution Theory and Confidence Intervals for Effect Sizes;108
12.3;C. Robust and Nonparametric Estimation of Effect Size;115
12.4;D. Other Measures of Effect Magnitude;123
12.5;E. Technical Commentary;127
13;Chapter 6. Parametric Estimation of Effect Size From a Series of Experiments;130
13.1;A. Model and Notation;131
13.2;B. Weighted Linear Combinations of Estimates;132
13.3;C. Other Methods of Estimation of Effect Size from a Series of Experiments;140
13.4;D. Testing for Homogeneity of Effect Sizes;145
13.5;E. Computation of Homogeneity Test Statistics;150
13.6;F. Estimation of Effect Size for Small Sample Sizes;151
13.7;G. The Effects of Measurement Error and Invalidity;154
14;Chapter 7. Fitting Parametric Fixed Effect Models to Effect Sizes: Categorical Models;170
14.1;A. An Analogue to the Analysis of Variance for Effect Sizes;172
14.2;B. Model and Notation;172
14.3;C. Some Tests of Homogeneity;176
14.4;D. Fitting Effect Size Models to a Series of Studies;180
14.5;E. Comparisons among Classes;182
14.6;F. Computational Formulas for Weighted Means and Homogeneity Statistics;186
15;Chapter 8. Fitting Parametric Fixed Effect Models to Effect Sizes: General Linear Models;190
15.1;A. Model and Notation;191
15.2;B. A Weighted Least Squares Estimator of Regression Coefficients;192
15.3;C. Testing Model Specification;195
15.4;D. Computation of Estimates and Test Statistics;196
15.5;E. The Accuracy of Large Sample Approximations;197
15.6;F. Other Methods of Estimating Regression Coefficients;206
15.7;G. Technical Commentary;210
16;Chapter 9. Random Effects Models for Effect Sizes;212
16.1;A. Model and Notation;214
16.2;B. The Variance of Estimates of Effect Size;216
16.3;C. Estimating the Effect Size Variance Component;216
16.4;D. The Variance of the Effect Size Variance Component;218
16.5;E. Testing That the Effect Size Variance Component Is Zero;220
16.6;F. Estimating the Mean Effect Size;221
16.7;G. Empirical Bayes Estimation for Random Effects Models;223
17;Chapter 10. Multivariate Models for Effect Sizes;228
17.1;A. Model and Notation;229
17.2;B. The Multivariate Distribution of Effect Sizes;232
17.3;C. Estimating a Common Effect Size from a Vector of Correlated Estimates;233
17.4;D. Estimating a Common Effect Size and Testing for Homogeneity of Effect Sizes;236
17.5;E. Estimating a Vector of Effect Sizes;239
17.6;F. Testing Homogeneity of Vectors of Effect Sizes;242
17.7;G. Is Pooling of Correlated Estimators Necessary?;243
18;Chapter 11. Combining Estimates of Correlation Coefficients;246
18.1;A. Estimating a Correlation from a Single Study;247
18.2;B. Effects of Measurement Error;251
18.3;C. Estimating a Common Correlation from Several Studies;252
18.4;D. Testing Homogeneity of Correlations across Studies;257
18.5;E. Fitting General Linear Models to Correlations;260
18.6;F. Random Effects Models for Correlations;265
19;Chapter 12. Diagnostic Procedures for Research Synthesis Models;270
19.1;A. How Many Observations Should Be Set Aside;272
19.2;B. Diagnostic Procedures for Homogeneous Effect Size Models;274
19.3;C. Diagnostic Procedures for Categorical Models;280
19.4;D. Diagnostic Procedures for General Linear Models;280
19.5;E. Diagnostic Procedures for Combining Estimates of Correlation Coefficients;285
19.6;F. Technical Commentary;285
20;Chapter 13. Clustering Estimates of Effect Magnitude;288
20.1;A. Theory for Clustering Unit Normal Random Variables;289
20.2;B. Clustering Correlation Coefficients;294
20.3;C. Clustering Effect Sizes;296
20.4;D. The Effect of Unequal Sample Sizes;299
20.5;E. Relative Merits of the Clustering Procedures;304
20.6;F. Computation of Tables;305
21;Chapter 14. Estimation of Effect Size When Not All Study Outcomes Are Observed;308
21.1;A. The Existence of Sampling Bias in Observed Effect Size Estimates;309
21.2;B. Consequences of Observing Only Significant Effect Sizes;310
21.3;C. Estimation of Effect Size from a Single Study When Only Significant Results Are Observed;313
21.4;D. Estimation of Effect Size from a Series of Independent Experiments When Only Significant Results are Observed;320
21.5;E. Other Methods for Estimating Effect Sizes When Not All Study Outcomes Are Observed;327
21.6;F. Technical Commentary;330
22;Chapter 15. Meta-Analysis in the Physical and Biological Sciences;334
22.1;A. A Multiplicative Model;338
22.2;B. Estimating Displacement and Potency Factor;341
22.3;C. A Multiplicative Model with Scaling;344
22.4;D. An Additive Model for Interlaboratory Differences;345
22.5;E. An Additive Model With a Control;346
23;Appendix;350
23.1;Appendix A: Table of the Standard Normal Cumulative Distribution Function;351
23.2;Appendix B: Percentiles of Chi-Square Distributions;353
23.3;Appendix C: Values of z = 1/2 log[(l1+r)/(l1- r ) ] and r = (e2z- l)/(e2z+ 1) and Graph of Fisher's z-Transformation;356
23.4;Appendix D: Values of v2 sinh-1 x and sinh(x/v2);358
23.5;Appendix E: Confidence Intervals of the Parameter p of the Binomial Distribution;360
23.6;Appendix F: Nomographs for Exact Confidence Intervals for Effect Size d When 2 =n=10;364
23.7;Appendix G: Confidence Intervals for the Correlation Coefficient for Different Sample Sizes;365
24;References;370
25;Author Index;384
26;Subject Index;388