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Multiple Comparison Procedures

Multiple Comparison Procedures

Yosef Hochberg, Ajit C. Tamhane

ISBN: 978-0-470-31667-2

May 2008

480 pages

Description

Offering a balanced, up-to-date view of multiple comparison procedures, this book refutes the belief held by some statisticians that such procedures have no place in data analysis. With equal emphasis on theory and applications, it establishes the advantages of multiple comparison techniques in reducing error rates and in ensuring the validity of statistical inferences. Provides detailed descriptions of the derivation and implementation of a variety of procedures, paying particular attention to classical approaches and confidence estimation procedures. Also discusses the benefits and drawbacks of other methods. Numerous examples and tables for implementing procedures are included, making this work both practical and informative.
1. Introduction 1

1. Two Early Multiple Comparison Procedures 2

2. Basic Notions and Philosophy of Multiple Comparisons 5

3. Examples 12

Part I. Procedures Based in Classical Approaches for Fixed-Effects Linear Models with Normal Homoscedastic Independent Errors 17

2. Some Theory of Multiple Comparison Procedures for Fixed-Effects Linear Models 17

2. Single-Step Procedures for Nonhierarchical Families 28

3. Single-Step Procedures for Hierarchical Families 43

4. Step-Down Procedures 53

3. Single-Step Procedures for Pairwise and More General Comparisons among All Treatments 72

1. Scheffé’s S-Procedure 73

2. Tukey’s T-Procedure for Balanced Designs 80

3. Modifications of the T-Procedure for Unbalanced Designs 85

4. Comparisons among Single-Step Procedures 102

5. Additional Topics 107

4. Stepwise Procedures for Pairwise and More General Comparisons among All Treatments 110

1. Step-Down Procedures Based on F-Statistics 111

2. Step-Down Procedures Based in Studentized Range Statistics 114

3. Peritz’s Closed Step-Down Procedure 121

4. Step-Up Procedures 124

5. A Comparison of Single-Step and Stepwise Procedures 128

5. Procedures for Some Nonhierarchical Finite Families of Comparisons 134

1. Orthogonal Comparisons 135

2. Comparisons with a Control 139

3. Comparisons with the “Best” Treatment 150

4. Two Miscellaneous Families 157

6. Designing Experiments for Multiple Comparisons 161

1. Single-Stage Procedures 163

2. Two-Stage Procedures 171

3. Incomplete Block Designs for Comparing Treatments with a Control 174

Part II. Procedures for Other Models and Problems, and Procedures Based on Alternative Approaches 179

7. Procedures for One-Way Layouts with Unequal Variances 181

1. Single-Stage Procedures 182

2. Two-Stage Procedures 194

3. Step-Down Procedures 204

8. Procedures for Mixed Two-Way Layouts and Designs with Random Covariates 207

1. Procedures for One-Way Repeated Measures and Mixed Two-Way Designs 208

2. Procedures for Analysis of Covariance Designs with Random Covariates 219

9. Distribution-Free and Robust Procedures 234

1. Procedures for One-Way Layouts 235

2. Procedures for Randomized Complete Block Designs 250

3. Procedures Based on Other Approaches 267

4. Robust Procedures 271

10. Some Miscellaneous Multiple Comparison Problems 274

1. Multiple Comparison Procedures for Categorical Data 274

2. Multiple Comparisons of Variances 282

3. Graphical Procedures 286

4. Multiple Comparisons of Means under Order Restrictions 290

5. Interactions in Two-Way Layouts 294

6. Partitioning Treatment Means into Groups 303

11. Optimal Procedures Based on Decision-Theoretic, Bayesian, and Other Approaches 310

1. A Decision-Theoretic Approach 311

2. A Neyman-Pearson Type Approach 314

3. A Bayesian Approach 318

4. A Combined Bayesian and Neyman-Pearson Type Approach 334

5. A Г-Minimax Approach 336

Appendixes 341

1. Some General Theory of Multiple Comparison Procedures 343

2. Some Probability Inequalities Useful in Multiple Comparisons 362

3. Some Probability Distributions and Tables Useful in Multiple Comparisons 373

References 417

Author Index 439

Subject Index 445