# Nonparametric Statistical Inference, Fifth Edition

#### By **Jean Dickinson Gibbons**, **Subhabrata Chakraborti**

Chapman and Hall/CRC – 2010 – 650 pages

Chapman and Hall/CRC – 2010 – 650 pages

__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.

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

**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.*

**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.

Name: Nonparametric Statistical Inference, Fifth Edition (Hardback) – Chapman and Hall/CRC

Description: By Jean Dickinson Gibbons, Subhabrata Chakraborti. 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...

Categories: Regression Analysis and Multivariate Statistics, Statistical Theory & Methods, Quantitative Methods