Nonparametric Statistical Inference

TLDR: Theoretical Bases for Calculating the ARE Examples of the Calculations of Efficacy and ARE Analysis of Count Data.

Abstract: 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), tau, and rho Another Measure of Association Applications Measures of Association in Multiple Classifications Introduction 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 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 x 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.