Nonparametric Hypothesis Testing

Stefano Bonnini, Assistant Professor of Statistics, Faculty of Economics, Department of Economics, University of Ferrara, Italy.Livio Corain, Assistant Professor of Statistics, Faculty of Engineering, Department of Management and Engineering, University of Padova, Italy.Marco Marozzi, Associate Professor of Statistics, Faculty of Economics, Department of Economics and Statistics, University of Calabria, Italy.Luigi Salmaso, Full Professor of Statistics, Faculty of Engineering, University of Padova, Italy.

• Presentation of the book xiPreface xiiiNotation and abbreviations xvii1 One- and two-sample location problems, tests for symmetry and tests on a single distribution 11.1 Introduction 11.2 Nonparametric tests 21.2.1 Rank tests 21.2.2 Permutation tests and combination based tests 31.3 Univariate one-sample tests 51.3.1 The Kolmogorov goodness-of-fit test 61.3.2 A univariate permutation test for symmetry 101.4 Multivariate one-sample tests 151.4.1 Multivariate rank test for central tendency 151.4.2 Multivariate permutation test for symmetry 181.5 Univariate two-sample tests 201.5.1 The Wilcoxon (Mann–Whitney) test 211.5.2 Permutation test on central tendency 271.6 Multivariate two-sample tests 291.6.1 Multivariate tests based on rank 291.6.2 Multivariate permutation test on central tendency 34References 372 Comparing variability and distributions 382.1 Introduction 382.2 Comparing variability 392.2.1 The Ansari–Bradley test 402.2.2 The permutation Pan test 432.2.3 The permutation O’Brien test 462.3 Jointly comparing central tendency and variability 492.3.1 The Lepage test 502.3.2 The Cucconi test 522.4 Comparing distributions 562.4.1 The Kolmogorov–Smirnov test 562.4.2 The Cram´er–von Mises test 59References 613 Comparing more than two samples 653.1 Introduction 653.2 One-way ANOVA layout 663.2.1 The Kruskal–Wallis test 673.2.2 Permutation ANOVA in the presence of one factor 733.2.3 The Mack–Wolfe test for umbrella alternatives 763.2.4 Permutation test for umbrella alternatives 833.3 Two-way ANOVA layout 873.3.1 The Friedman rank test for unreplicated block design 873.3.2 Permutation test for related samples 893.3.3 The Page test for ordered alternatives 913.3.4 Permutation analysis of variance in the presence of two factors 933.4 Pairwise multiple comparisons 953.4.1 Rank-based multiple comparisons for the Kruskal–Wallis test 963.4.2 Permutation tests for multiple comparisons 983.5 Multivariate multisample tests 993.5.1 A multivariate multisample rank-based test 993.5.2 A multivariate multisample permutation test 103References 1054 Paired samples and repeated measures 1074.1 Introduction 1074.2 Two-sample problems with paired data 1084.2.1 The Wilcoxon signed rank test 1084.2.2 A permutation test for paired samples 1144.3 Repeated measures tests 1164.3.1 Friedman rank test for repeated measures 1174.3.2 A permutation test for repeated measures 120References 1225 Tests for categorical data 1245.1 Introduction 1245.2 One-sample tests 1255.2.1 Binomial test on one proportion 1255.2.2 The McNemar test for paired data (or bivariate responses) with binary variables 1285.2.3 Multivariate extension of the McNemar test 1315.3 Two-sample tests on proportions or 2 × 2 contingency tables 1345.3.1 The Fisher exact test 1355.3.2 A permutation test for comparing two proportions 1385.4 Tests for R × C contingency tables 1395.4.1 The Anderson–Darling permutation test for R × C contingency tables 1405.4.2 Permutation test on moments 1455.4.3 The chi-square permutation test 148References 1516 Testing for correlation and concordance 1536.1 Introduction 1536.2 Measuring correlation 1546.3 Tests for independence 1566.3.1 The Spearman test 1576.3.2 The Kendall test 1606.4 Tests for concordance 1666.4.1 The Kendall–Babington Smith test 1676.4.2 A permutation test for concordance 172References 1747 Tests for heterogeneity 1767.1 Introduction 1767.2 Statistical heterogeneity 1777.3 Dominance in heterogeneity 1787.3.1 Geographical heterogeneity 1807.3.2 Market segmentation 1847.4 Two-sided and multisample test 1887.4.1 Customer satisfaction 1897.4.2 Heterogeneity as a measure of uncertainty 1917.4.3 Ethnic heterogeneity 1947.4.4 Reliability analysis 196References 197Appendix A Selected critical values for the null distribution of the peak-known Mack–Wolfe statistic 201Appendix B Selected critical values for the null distribution of the peak-unknown Mack–Wolfe statistic 203Appendix C Selected upper-tail probabilities for the null distribution of the Page L statistic 206Appendix D R functions and codes 213Index 219

“The book combines an up to date overview with useful practical guidance to applications in R, and will be a valuable resource for practitioners and researchers working in a wide range of scientific fields including engineering, biostatistics, psychology and medicine.”  (Zentralblatt MATH, 1 October 2014)