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.

Reviews

! 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