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Selection and Ordering Populations: A New Statistical MethodologySelection and Ordering Populations: A New Statistical Methodology

Jean Dickinson Gibbons, Ingram Olkin, and Milton Sobel

Classics in Applied Mathematics 26

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.


Applied statisticians as well as researchers who use the basic methods of statistical analysis (psychologists, engineers, biologists, management scientists, etc.) will find this book a valuable reference. Readers should be familiar with standard first-year statistics; no knowledge of calculus is necessary.


Chapter 1: The Philosophy of Selecting and Ordering Populations; Chapter 2: Selecting the One Best Population for Normal Distributions with Common Known Variance; Chapter 3: Selecting the One Best Population for Other Normal Distribution Models; Chapter 4: Selecting the One Best Population Bionomial (or Bernoulli) Distributions; Chapter 5: Selecting the One Normal Population with the Smallest Variance; Chapter 6: Selecting the One Best Category for the Multinomial Distribution; Chapter 7: Nonparametric Selection Procedures; Chapter 8: Selection Procedures for a Design with Paired Comparisons; Chapter 9: Selecting the Normal Population with the Best Regression Value; Chapter 10: Selecting Normal Populations Better than a Control; Chapter 11: Selecting the t Best Out of k Populations; Chapter 12: Complete Ordering of k Populations; Chapter 13: Subset Selection (or Elimination) Procedures; Chapter 14: Selecting the Best Gamma Population; Chapter 15: Selection Procedures for Multivariate Normal Distributions; Appendix A: Tables for Normal Means Selection Problems; Appendix B: Figures for Normal Means Selection Problems; Appendix C: Table of the Cumulative Standard Normal Distribution F(z); Appendix D: Table of Critical Values for the Chi-Square Distribution; Appendix E: Tables for Binomial Selection Problems; Appendix F: Figures for Binomial Selection Problems; Appendix G: Tables for Normal Variances Selection Problems; Appendix H: Tables for Multinomial Selection Problems; Appendix I: Curtailment Tables for the Multinomial Selection Problem; Appendix J: Tables of the Incomplete Beta Function; Appendix K: Tables for Nonparametric Selection Problems; Appendix L: Tables for Paired-Comparison Selection Problems; Appendix M: Tables for Selecting from k Normal Populations Those Better Than a Control ; Appendix N: Tables for Selecting the t Best Normal Populations; Appendix O: Table of Critical Values of Fisher's F Distribution; Appendix P: Tables for Complete Ordering Problems; Appendix Q: Tables for Subset Selection Problems; Appendix R: Tables for Gamma Distribution Problems; Appendix S: Tables for Multivariate Selection Problems; Appendix T: Excerpt of Table of Random Numbers; Appendix U: Table of Squares and Square Roots; Bibliography; References for Applications; Index for Data and Examples; Name Index; Subject Index.

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1999 / xxvi + 569 pages / Softcover / ISBN-13: 978-0-898714-39-5 / ISBN-10: 0-89871-439-7 /
List Price $94.00 / SIAM Member Price $65.80 / Order Code CL26
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