Selecting and Ordering Populations: A New Statistical Methodology

Jean Dickinson Gibbons, Ingram Olkin, Milton Sobel9780898714395, 0898714397

This SIAM Classics edition is an unabridged, corrected republication of the work first published in 1977. It provides a compendium of applied aspects of ordering and selection procedures and includes tables that permit the practitioner to carry out the experiment and draw statistically justified conclusions. These tables are not readily available in other texts. Although more than 1000 papers and several books on the general theory of ranking and selection have been published since this book first appeared, the methodology is presented in a more elementary fashion, with numerous examples to help the reader apply it to a specific problem.
There is a dichotomy in modern statistics that distinguishes between analyses done before an experiment is completed and those done afterward. Ranking and selection methods are useful in both of these categories. The authors provide an alternative to the overused “testing the null hypothesis” when what the practitioner really needs is a method of ranking k given populations, selecting the t best populations, or some similar goal. That need and purpose is as important today as when the subject was first developed nearly 50 years ago.

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Table of contents :
Selecting and Ordering Populations A New Statistical Methodol……Page 1
Contents……Page 10
Preface to the Classics Edition……Page 22
Preface……Page 24
CHAPTER 1 The Philosophy of Selecting and Ordering Populations……Page 28
CHAPTER 2 Selecting the One Best Population for Normal Distributions with Common Known Variance……Page 54
CHAPTER 3 Selecting the One Best Population for Other Normal Distribution Models……Page 88
CHAPTER 4 Selecting the One Best Population for Binomial (or Bernoulli)Distributions……Page 130
CHAPTER 5 Selecting the One Normal Population with the Smallest Variance……Page 154
CHAPTER 6 Selecting the One Best Category for the Multinomial Distribution……Page 185
CHAPTER 7 Nonparametric Selection Procedures……Page 214
CHAPTER 8 Selection Procedures for a Design with Paired Comparisons……Page 237
CHAPTER 9 Selecting the Normal Population with the Best Regression Value……Page 261
CHAPTER 10 Selecting Normal Populations Better than a Control……Page 271
CHAPTER 11 Selecting the t Best Out of k Populations……Page 300
CHAPTER 12 Complete Ordering of k Populations……Page 310
CHAPTER 13 Subset Selection (or Elimination) Procedures……Page 323
CHAPTER *14 Selecting the Best Gamma Populations……Page 355
CHAPTER *15 Selection Procedures for Multivariate Normal Distributions……Page 368
APPENDIX A Tables for Normal Means Selection Problems……Page 422
APPENDIX B Figures for Normal Means Selection Problems……Page 441
APPENDIX C Table of the Cumulative Standard Normal Distribution ?(z)……Page 443
APPENDIX D Table of Critical Values for the Chi-Square Distribution……Page 444
APPENDIX E Tables for Binomial Selection Problems……Page 446
APPENDIX F Figures for Binomial Selection Problems……Page 454
APPENDIX G Tables for Normal Variances Selection Problems……Page 461
APPENDIX H Tables for Multinomial Selection Problems……Page 470
APPENDIX I Curtailment Tables for the Multinomial Selection Problem……Page 478
APPENDIX J Tables of the Incomplete Beta Function……Page 484
APPENDIX K Tables for Nonparametric Selection Problems……Page 488
APPENDIX L Tables for Paired-Comparison Selection Problems……Page 492
APPENDIX M Tables for Selecting from k Normal Populations Those Better than a Control……Page 497
APPENDIX N Tables for Selecting the t Best Normal Populations……Page 509
APPENDIX O Table of Critical Values of Fisher’s F Distribution……Page 511
APPENDIX P Tables for Complete Ordering Problems……Page 515
APPENDIX Q Tables for Subset Selection Problems……Page 526
APPENDIX R Tables for Gamma Selection Problems……Page 535
APPENDIX S Tables for Multivariate Selection Problems……Page 543
APPENDIX T Excerpt of Table of Random Numbers……Page 558
APPENDIX U Tables of Squares and Square Roots……Page 560
Bibliography……Page 570
References for Applications……Page 580
Index for Data and Examples……Page 584
Name Index……Page 588
Subject Index……Page 592