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Preface xiii
1. Introduction 1
1.1. Advantages of Nonparametric Methods 1
1.2. The Distribution-Free Property 2
1.3. Some Real-World Applications 3
1.4. Format and Organization 6
1.5. Computing with R 8
1.6. Historical Background 9
2. The Dichotomous Data Problem 11 Introduction 11
2.1. A Binomial Test 11
2.2. An Estimator for the Probability of Success 22
2.3. A Confidence Interval for the Probability of Success (Wilson) 24
2.4. Bayes Estimators for the Probability of Success 33
3. The One-Sample Location Problem 39 Introduction 39 Paired Replicates Analyses by Way of Signed Ranks 39
3.1. A Distribution-Free Signed Rank Test (Wilcoxon) 40
3.2. An Estimator Associated with Wilcoxon''s Signed Rank Statistic (Hodges-Lehmann) 56
3.3. A Distribution-Free Confidence Interval Based on Wilcoxon''s Signed Rank Test (Tukey) 59 Paired Replicates Analyses by Way of Signs 63
3.4. A Distribution-Free Sign Test (Fisher) 63
3.5. An Estimator Associated with the Sign Statistic (Hodges-Lehmann) 76
3.6. A Distribution-Free Confidence Interval Based on the Sign Test (Thompson, Savur) 80 One-Sample Data 84
3.7. Procedures Based on the Signed Rank Statistic 84
3.8. Procedures Based on the Sign Statistic 90
3.9. An Asymptotically Distribution-Free Test of Symmetry (Randles-Fligner-Policello-Wolfe, Davis-Quade) 94 Bivariate Data 102
3.10. A Distribution-Free Test for Bivariate Symmetry (Hollander) 102
3.11. Efficiencies of Paired Replicates and One-Sample Location Procedures 112
4. The Two-Sample Location Problem 115 Introduction 115
4.1. A Distribution-Free Rank Sum Test (Wilcoxon, Mann and Whitney) 115
4.2. An Estimator Associated with Wilcoxon''s Rank Sum Statistic (Hodges-Lehmann) 136
4.3. A Distribution-Free Confidence Interval Based on Wilcoxon''s Rank Sum Test (Moses) 142
4.4. A Robust Rank Test for the Behrens-Fisher Problem (Fligner-Policello) 145
4.5. Efficiencies of Two-Sample Location Procedures 149
5. The Two-Sample Dispersion Problem and Other Two-Sample Problems 151 Introduction 151
5.1. A Distribution-Free Rank Test for Dispersion-Medians Equal (Ansari-Bradley) 152
5.2. An Asymptotically Distribution-Free Test for Dispersion Based on the Jackknife-Medians Not Necessarily Equal (Miller) 169
5.3. A Distribution-Free Rank Test for Either Location or Dispersion (Lepage) 181
5.4. A Distribution-Free Test for General Differences in Two Populations (Kolmogorov-Smirnov) 190
5.5. Efficiencies of Two-Sample Dispersion and Broad Alternatives Procedures 200
6. The One-Way Layout 202 Introduction 202
6.1. A Distribution-Free Test for General Alternatives (Kruskal-Wallis) 204
6.2. A Distribution-Free Test for Ordered Alternatives (Jonckheere-Terpstra) 215
6.3. Distribution-Free Tests for Umbrella Alternatives (Mack-Wolfe) 225
6.3A. A Distribution-Free Test for Umbrella Alternatives, Peak Known (Mack-Wolfe) 226
6.3B. A Distribution-Free Test for Umbrella Alternatives, Peak Unknown (Mack-Wolfe) 241
6.4. A Distribution-Free Test for Treatments Versus a Control (Fligner-Wolfe) 249 Rationale For Multiple Comparison Procedures 255
6.5. Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings-General Configuration (Dwass, Steel, and Critchlow-Fligner) 256
6.6. Distribution-Free One-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings-Ordered Treatment Effects (Hayter-Stone) 265
6.7. Distribution-Free One-Sided Treatments-Versus-Control Multiple Comparisons Based on Joint Rankings (Nemenyi, Damico-Wolfe) 271
6.8. Contrast Estimation Based on Hodges-Lehmann Two-Sample Estimators (Spjøtvoll) 278
6.9. Simultaneous Confidence Intervals for All Simple Contrasts (Critchlow-Fligner) 282
6.10. Efficiencies of One-Way Layout Procedures 287
7. The Two-Way Layout 289 Introduction 289
7.1. A Distribution-Free Test for General Alternatives in a Randomized Complete Block Design (Friedman, Kendall-Babington Smith) 292
7.2. A Distribution-Free Test for Ordered Alternatives in a Randomized Complete Block Design (Page) 304 Rationale for Multiple Comparison Procedures 315
7.3. Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Friedman Rank Sums-General Configuration (Wilcoxon, Nemenyi, McDonald-Thompson) 316
7.4. Distribution-Free One-Sided Treatments Versus Control Multiple Comparisons Based on Friedman Rank Sums (Nemenyi, Wilcoxon-Wilcox, Miller) 322
7.5. Contrast Estimation Based on One-Sample Median Estimators (Doksum) 328 Incomplete Block Data-Two-Way Layout with Zero or One Observation Per Treatment-Block Combination 331
7.6. A Distribution-Free Test for General Alternatives in a Randomized Balanced Incomplete Block Design (BIBD) (Durbin-Skillings-Mack) 332
7.7. Asymptotically Distribution-Free Two-Sided All-Treatments Multiple Comparisons for Balanced Incomplete Block Designs (Skillings-Mack) 341
7.8. A Distribution-Free Test for General Alternatives for Data From an Arbitrary Incomplete Block Design (Skillings-Mack) 343 Replications-Two-Way Layout with at Least One Observation for Every Treatment-Block Combination 354
7.9. A Distribution-Free Test for General Alternatives in a Randomized Block Design with an Equal Number c(>1) of Replications Per Treatment-Block Combination (Mack-Skillings) 354
7.10. Asymptotically Distribution-Free Two-Sided All-Treatments Multiple Comparisons for a Two-Way Layout with an Equal Number of Replications in Each Treatment-Block Combination (Mack-Skillings) 367 Analyses Associated with Signed Ranks 370
7.11. A Test Based on Wilcoxon Signed Ranks for General Alternatives in a Randomized Complete Block Design (Doksum) 370
7.12. A Test Based on Wilcoxon Signed Ranks for Ordered Alternatives in a Randomized Complete Block Design (Hollander) 376
7.13. Approximate Two-Sided All-Treatments Multiple Comparisons Based on Signed Ranks (Nemenyi) 379
7.14. Approximate One-Sided Treatments-Versus-Control Multiple Comparisons Based on Signed Ranks (Hollander) 382
7.15. Contrast Estimation Based on the One-Sample Hodges-Lehmann Estimators (Lehmann) 386
7.16. Efficiencies of Two-Way Layout Procedures 390
8. The Independence Problem 393 Introduction 393
8.1. A Distribution-Free Test for Independence Based on Signs (Kendall) 393
8.2. An Estimator Associated with the Kendall Statistic (Kendall) 413
8.3. An Asymptotically Distribution-Free Confidence Interval Based on the Kendall Statistic (Samara-Randles, Fligner-Rust, Noether) 415
8.4. An Asymptotically Distribution-Free Confidence Interval Based on Efron''s Bootstrap 420
8.5. A Distribution-Free Test for Independence Based on Ranks (Spearman) 427
8.6. A Distribution-Free Test for Independence Against Broad Alternatives (Hoeffding) 442
8.7. Efficiencies of Independence Procedures 450
9. Regression Problems 451 Introduction 451 One Regression Line 452
9.1. A Distribution-Free Test for the Slope of the Regression Line (Theil) 452
9.2. A Slope Estimator Associated with the Theil Statistic (Theil) 458
9.3. A Distribution-Free Confidence Interval Associated with the Theil Test (Theil) 460
9.4. An Intercept Estimator Associated with the Theil Statistic and Use of the Estimated Linear Relationship for Prediction (Hettmansperger-McKean-Sheather) 463 k(â?¥2) Regression Lines 466
9.5. An Asymptotically Distribution-Free Test for the Parallelism of Several Regression Lines (Sen, Adichie) 466 General Multiple Linear Regression 475
9.6. Asymptotically Distribution-Free Rank-Based Tests for General Multiple Linear Regression (Jaeckel, Hettmansperger-McKean) 475 Nonparametric Regression Analysis 490
9.7. An Introduction to Non-Rank-Based Approaches to Nonparametric Regression Analysis 490
9.8. Efficiencies of Regression Procedures 494
10. Comparing Two Success Probabilities 495 Introduction 495
10.1. Approximate Tests and Confidence Intervals for the Difference between Two Success Probabilities (Pearson) 496
10.2. An Exact Test for the Difference between Two Success Probabilities (Fisher) 511
10.3. Inference for the Odds Ratio (Fisher, Cornfield) 515
10.4. Inference for k Strata of 2 Ã? 2 Tables (Mantel and Haenszel) 522
10.5. Efficiencies 534
11. Life Distributions and Survival Analysis 535 Introduction 535
11.1. A Test of Exponentiality Versus IFR Alternatives (Epstein) 536
11.2. A Test of Exponentiality Versus NBU Alternatives (Hollander-Proschan) 545
11.3. A Test of Exponentiality Versus DMRL Alternatives (Hollander-Proschan) 555
11.4. A Test of Exponentiality Versus a Trend Change in Mean Residual Life (Guess-Hollander-Proschan) 563
11.5. A Confidence Band for the Distribution Function (Kolmogorov) 568
11.6. An Estimator of the Distribution Function When the Data are Censored (Kaplan-Meier) 578
11.7. A Two-Sample Test for Censored Data (Mantel) 594
11.8. Efficiencies 605
12. Density Estimation 609 Introduction 609
12.1. Density Functions and Histograms 609
12.2. Kernel Density Estimation 617
12.3. Bandwidth Selection 624
12.4. Other Methods 628
13. Wavelets 629 Introduction 629
13.1. Wavelet Representation of a Function 630
13.2. Wa