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
Fundamental Statistical Concepts
Order Statistics, Quantiles, and Coverages
Empirical Distribution Function
Statistical Properties of Order Statistics
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
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
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
Visual Analysis of Goodness of Fit
One-Sample and Paired-Sample Procedures
Confidence Interval for a Population Quantile
Hypothesis Testing for a Population Quantile
The Sign Test and Confidence Interval for the Median
Treatment of Ties in Rank Tests
The Wilcoxon Signed-Rank Test and Confidence Interval
The General Two-Sample Problem
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
Definition of Linear Rank Statistics
Distribution Properties of Linear Rank Statistics
Usefulness in Inference
Linear Rank Tests for the Location Problem
The Wilcoxon Rank-Sum Test and Confidence Interval
Other Location Tests
Linear Rank Tests for the Scale Problem
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
Other Tests for the Scale Problem
Tests of the Equality of k Independent Samples
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
Measures of Association in Multiple Classifications
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
Theoretical Bases for Calculating the ARE
Examples of the Calculations of Efficacy and ARE
Analysis of Count Data
Some Special Results for k × 2 Contingency Tables
Fisher’s Exact Test
Analysis of Multinomial Data
Appendix of Tables
Answers to Problems
A Summary and Problems appear at the end of each chapter.
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.
"… a classic with a long history. Now in its fifth edition, many students have learned the basics of nonparametric statistics from one of the previous versions. The latest edition is updated with material from recent research and a new summarizing chapter with instructions for implementation of the imparted knowledge. Additional problems pose new challenges and better, readable figures improve the textbook’s ease of use. … a comprehensive compilation and should be useful as supplemental material for any course on nonparametrics …"
—Statistical Papers (2014) 55
"Overall, this remains a very fine book suitable for a graduate-level course in nonparametric statistics. I recommend it for all people interested in learning the basic ideas of nonparametric statistical inference."
—Eugenia Stoimenova, Journal of Applied Statistics, June 2012
"… 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