Nonparametric Statistical Inference

Proven Material for a Course on the Introduction to the Theory and/or on the Applications of Classical Nonparametric Methods Since its first publication in 1971, Nonparametric Statistical Inference has been widely regarded as the source for learning about nonparametric statistics. The fifth edition carries on this tradition while thoroughly revising at least 50 percent of the material. New to the Fifth Edition Updated and revised contents based on recent journal articles in the literature A new section in the chapter on goodness-of-fit tests A new chapter that offers practical guidance on how to choose among the various nonparametric procedures covered Additional problems and examples Improved computer figures This classic, best-selling statistics book continues to cover the most commonly used nonparametric procedures. The authors carefully state the assumptions, develop the theory behind the procedures, and illustrate the techniques using realistic research examples from the social, behavioral, and life sciences. For most procedures, they present the tests of hypotheses, confidence interval estimation, sample size determination, power, and comparisons of other relevant procedures. The text also gives examples of computer applications based on Minitab, SAS, and StatXact and compares these examples with corresponding hand calculations. The appendix includes a collection of tables required for solving the data-oriented problems. Nonparametric Statistical Inference, Fifth Edition provides in-depth yet accessible coverage of the theory and methods of nonparametric statistical inference procedures. It takes a practical approach that draws on scores of examples and problems and minimizes the theorem-proof format. Jean Dickinson Gibbons was recently interviewed regarding her generous pledge to Virginia Tech.

Table of Contents:
Introduction and Fundamentals Introduction Fundamental Statistical Concepts Order Statistics, Quantiles, and Coverages Introduction Quantile Function Empirical Distribution Function Statistical Properties of Order Statistics Probability-Integral Transformation Joint Distribution of Order Statistics Distributions of the Median and Range Exact Moments of Order Statistics Large-Sample Approximations to the Moments of Order Statistics Asymptotic Distribution of Order Statistics Tolerance Limits for Distributions and Coverages Tests of Randomness Introduction Tests Based on the Total Number of Runs Tests Based on the Length of the Longest Run Runs Up and Down A Test Based on Ranks Tests of Goodness of Fit Introduction The Chi-Square Goodness-of-Fit Test The Kolmogorov–Smirnov One-Sample Statistic Applications of the Kolmogorov–Smirnov One-Sample Statistics Lilliefors’s Test for Normality Lilliefors’s Test for the Exponential Distribution Anderson–Darling Test Visual Analysis of Goodness of Fit One-Sample and Paired-Sample Procedures Introduction Confidence Interval for a Population Quantile Hypothesis Testing for a Population Quantile The Sign Test and Confidence Interval for the Median Rank-Order Statistics Treatment of Ties in Rank Tests The Wilcoxon Signed-Rank Test and Confidence Interval The General Two-Sample Problem Introduction The Wald–Wolfowitz Runs Test The Kolmogorov–Smirnov Two-Sample Test The Median Test The Control Median Test The Mann–Whitney U Test and Confidence Interval Linear Rank Statistics and the General Two-Sample Problem Introduction Definition of Linear Rank Statistics Distribution Properties of Linear Rank Statistics Usefulness in Inference Linear Rank Tests for the Location Problem Introduction The Wilcoxon Rank-Sum Test and Confidence Interval Other Location Tests Linear Rank Tests for the Scale Problem Introduction The Mood Test The Freund–Ansari–Bradley–David–Barton Tests The Siegel–Tukey Test The Klotz Normal-Scores Test The Percentile Modified Rank Tests for Scale The Sukhatme Test Confidence-Interval Procedures Other Tests for the Scale Problem Applications Tests of the Equality of k Independent Samples Introduction Extension of the Median Test Extension of the Control Median Test The Kruskal–Wallis One-Way ANOVA Test and Multiple Comparisons Other Rank-Test Statistics Tests against Ordered Alternatives Comparisons with a Control Measures of Association for Bivariate Samples Introduction: Definition of Measures of Association in a Bivariate Population Kendall’s Tau Coefficient Spearman’s Coefficient of Rank Correlation The Relations between R and T; E(R), τ, and ρ Another Measure of Association Applications Measures of Association in Multiple Classifications Introduction Friedman’s Two-Way Analysis of Variance by Ranks in a k × n Table and Multiple Comparisons Page’s Test for Ordered Alternatives The Coefficient of Concordance for k Sets of Rankings of n Objects The Coefficient of Concordance for k Sets of Incomplete Rankings Kendall’s Tau Coefficient for Partial Correlation Asymptotic Relative Efficiency Introduction Theoretical Bases for Calculating the ARE Examples of the Calculations of Efficacy and ARE Analysis of Count Data Introduction Contingency Tables Some Special Results for k × 2 Contingency Tables Fisher’s Exact Test McNemar’s Test Analysis of Multinomial Data Summary Appendix of Tables Answers to Problems References Index A Summary and Problems appear at the end of each chapter.

About the Author :
Jean Dickinson Gibbons is Russell Professor Emerita of Statistics at the University of Alabama. Subhabrata Chakraborti is a Robert C. and Rosa P. Morrow Faculty Excellence Fellow and professor of statistics at the University of Alabama.

Review :
! one of the best books available for a graduate (or advanced undergraduate) text for a theory course on nonparametric statistics. ! a very well-written and organized book on nonparametric statistics, especially useful and recommended for teachers and graduate students. --Biometrics, 67, September 2011 This excellently presented book achieves its aim of seeding the fundamentals of non-parametric inference. The theoretical concepts are illustrated with numerical examples and use of statistical software is illustrated, wherever possible. The book is undoubtedly well written and presents a good balance of theory and applications. It is suitable for teaching as well as self-learning. There are exercises in each chapter which will be helpful in teaching a course. ! I would strongly recommend this book to university libraries, teachers and undergraduate students who want to learn non-parametric inference in theory and practice. --Journal of the Royal Statistical Society, Series A, April 2011 Praise for the Fourth Edition: The facts that the first edition of this book was published in 1971 and that it is now in its fourth and revised edition are testimony to the book's success over a long period. ! The book is readable and clearly written and would be a valuable addition to every statistician's library. --ISI Short Book Reviews I learned nonparametric statistics ! from the first author's original version of the book. Having enjoyed that experience, I have unabashedly promoted this book ever since. The 4E is another very impressive updating of a classic text that should be part of every statistician's library. ! More than 100 pages have been added to the book. ! the authors have generally rewritten and enhanced a lot of the material. Now, in its fourth edition, this book offers a very comprehensive and integrated presentation on nonparametric inference. ! There is no competitor for this book and its comprehensive development and application of nonparametric methods. Users of one of the earlier editions should certainly consider upgrading to this new edition. --Technometrics, Vol. 46, No. 2, May 2004 The fourth edition includes new materials on quantiles, power and sample size, goodness-of-fit tests, multiple comparisons, and count data, as well as material on computing using SAS, Minitab, SPSS, and StatXact ! The authors have ! put a lot of effort to make the book more user-friendly by ! adding tabular guides for tests and confidence intervals, more figures ! and more exercises. --The American Statistician, May 2004 ! Useful to students and research workers !This edition will be a good textbook for a beginning graduate-level course in nonparametric statistics. --Journal of the American Statistical Association ! a good mix of nonparametric theory and methodology focused on traditional rank-based methods ! a good introduction to rank-based methods with a moderate amount of mathematical detail. --Journal of Quality Technology, Vol. 37, No. 2, April 2005