Multiple Comparison Procedures

Yosef Hochberg, PhD, is Professor in the Department of Statistics and Operations Research at Tel Aviv University, Israel. Dr. Hochberg's areas of research interest include multiple comparisons, categorical data analysis, and medical applications of biostatistical methods. Ajit C. Tamhane, PhD, is Senior Associate Dean of the McCormick School of Engineering and Applied Science at Northwestern University, where he is also Professor in the Department of Industrial Engineering and Management Sciences. A Fellow of the American Statistical Society, Dr. Tamhane has more than thirty years of academic and consulting experience in the areas of applied and mathematical statistics. He is the author of Statistical Analysis of Designed Experiments: Theory and Applications, also published by Wiley.

• 1. Introduction 1 1. Two Early Multiple Comparison Procedures 22. Basic Notions and Philosophy of Multiple Comparisons 53. Examples 12Part I. Procedures Based in Classical Approaches for Fixed-Effects Linear Models with Normal Homoscedastic Independent Errors 172. Some Theory of Multiple Comparison Procedures for Fixed-Effects Linear Models 172. Single-Step Procedures for Nonhierarchical Families 283. Single-Step Procedures for Hierarchical Families 434. Step-Down Procedures 533. Single-Step Procedures for Pairwise and More General Comparisons among All Treatments 721. Scheffé’s S-Procedure 732. Tukey’s T-Procedure for Balanced Designs 803. Modifications of the T-Procedure for Unbalanced Designs 854. Comparisons among Single-Step Procedures 1025. Additional Topics 1074. Stepwise Procedures for Pairwise and More General Comparisons among All Treatments 1101. Step-Down Procedures Based on F-Statistics 1112. Step-Down Procedures Based in Studentized Range Statistics 1143. Peritz’s Closed Step-Down Procedure 1214. Step-Up Procedures 1245. A Comparison of Single-Step and Stepwise Procedures 1285. Procedures for Some Nonhierarchical Finite Families of Comparisons 1341. Orthogonal Comparisons 1352. Comparisons with a Control 1393. Comparisons with the “Best” Treatment 1504. Two Miscellaneous Families 1576. Designing Experiments for Multiple Comparisons 1611. Single-Stage Procedures 1632. Two-Stage Procedures 1713. Incomplete Block Designs for Comparing Treatments with a Control 174Part II. Procedures for Other Models and Problems, and Procedures Based on Alternative Approaches 1797. Procedures for One-Way Layouts with Unequal Variances 1811. Single-Stage Procedures 1822. Two-Stage Procedures 1943. Step-Down Procedures 2048. Procedures for Mixed Two-Way Layouts and Designs with Random Covariates 2071. Procedures for One-Way Repeated Measures and Mixed Two-Way Designs 2082. Procedures for Analysis of Covariance Designs with Random Covariates 2199. Distribution-Free and Robust Procedures 2341. Procedures for One-Way Layouts 2352. Procedures for Randomized Complete Block Designs 2503. Procedures Based on Other Approaches 2674. Robust Procedures 27110. Some Miscellaneous Multiple Comparison Problems 2741. Multiple Comparison Procedures for Categorical Data 2742. Multiple Comparisons of Variances 2823. Graphical Procedures 2864. Multiple Comparisons of Means under Order Restrictions 2905. Interactions in Two-Way Layouts 2946. Partitioning Treatment Means into Groups 30311. Optimal Procedures Based on Decision-Theoretic, Bayesian, and Other Approaches 3101. A Decision-Theoretic Approach 3112. A Neyman-Pearson Type Approach 3143. A Bayesian Approach 3184. A Combined Bayesian and Neyman-Pearson Type Approach 3345. A Г-Minimax Approach 336Appendixes 3411. Some General Theory of Multiple Comparison Procedures 3432. Some Probability Inequalities Useful in Multiple Comparisons 3623. Some Probability Distributions and Tables Useful in Multiple Comparisons 373References 417Author Index 439Subject Index 445