Gibbons J., Chakraborti S. Nonparametric Statistical Inference

Fourth Edition, Revised and Expanded. — Marcel Dekker, 2003. — 646 p. — ISBN: 0-8247-4052-1.Thoroughly revised and reorganized, the fourth edition presents in-depth coverage of the theory and methods of the most widely used nonparametric procedures in statistical analysis and offers example applications appropriate for all areas of the social, behavioral, and life sciences. The book presents new material on the quantiles, the calculation of exact and simulated power, multiple comparisons, additional goodness-of-fit tests, methods of analysis of count data, and modern computer applications using MINITAB, SAS, and STATXACT. It includes tabular guides for simplified applications of tests and finding P-values and confidence interval estimates.Introduction and Fundamentals.Fundamental Statistical Concepts.
Order Statistics, Quantiles, and Coverages.
The Quantile Function.
The Empirical Distribution Function.
Statistical Properties of Order Statistics.
Probability-Integral Transformation (PIT).
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.
Rank-Order Statistics.
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.
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.
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.
Confidence-Interval Procedures.
Other Tests for the Scale Problem.
Applications.
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.
The Chi-Square Test for k Proportions.
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.
Friedman’s Two-Way Analysis of Variance by Ranks in a k x 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 Calculation of Efficacy and ARE.
Analysis of Count Data.
Contingency Tables.
Some Special Results for k x 2 Contingency Tables.
Fisher’s Exact Test.
McNemar’s Test.
Analysis of Multinomial Data.
Appendix of Tables:
Normal Distribution, Chi-Square Distribution, Cumulative Binomial Distribution,
Total Number of Runs Distribution, Runs Up and Down Distribution, Kolmogorov-Smirnov One-Sample Statistic,
Binomial Distribution for θ = 0.5, Probabilities for the Wilcoxon, Signed-Rank Statistic,
Kolmogorov-Smirnov Two-Sample Statistic, Probabilities for the Wilcoxon Rank-Sum Statistic,
Kruskal-Wallis Test Statistic, Kendall’s Tau Statistic, Spearman’s Coefficient of Rank Correlation,
Friedman’s Analysis-of-Variance Statistic and Kendall’s Coefficient of Concordance,
Lilliefors’s Test for Normal Distribution Critical Values,
Significance Points of T_XY.Z (for Kendall’s Rank-Correlation Coefficient),
Page’s L Statistic, Critical Values and Associated Probabilities for the Jonckheere-Terpstra Test,
Rank von Neumann Statistic, Lilliefors’s Test for Exponential Distribution Critical Values.
Answers to Selected Problems.