Nonparametric Statistical Inference

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.

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.