Nonparametric Statistical Methods

by ;
Edition: 2nd
Format: Hardcover
Pub. Date: 1999-01-25
Publisher(s): Wiley-Interscience
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Summary

The importance of nonparametric methods in modern statistics has grown dramatically since their inception in the mid-1930s. Requiring few or no assumptions about the populations from which data are obtained, they have emerged as the preferred methodology among statisticians and researchers performing data analysis. Today, these highly efficient techniques are being applied to an ever-widening variety of experimental designs in the social, behavioral, biological, and physical sciences. This long-awaited Second Edition of Myles Hollander and Douglas A. Wolfe's successful Nonparametric Statistical Methods meets the needs of a new generation of users, with completely up-to-date coverage of this important statistical area. Like its highly acclaimed predecessor, the revised edition, along with its companion ftp site, aims to equip students with the conceptual and technical skills necessary to select and apply the appropriate procedures for a given situation. An extensive array of examples drawn from actual experiments illustrates clearly how to use nonparametric approaches to handle one- or two-sample location and dispersion problems, dichotomous data, and one-way and two-way layout problems. Rewritten and updated, this Second Edition now includes new or expanded coverage of: * Nonparametric regression methods. * The bootstrap. * Contingency tables and the odds ratio. * Life distributions and survival analysis. * Nonparametric methods for experimental designs. * More procedures, real-world data sets, and problems. * Illustrated examples using Minitab and StatXact. An ideal text for an upper-level undergraduate or first-year graduate course, this text is also an invaluable source for professionals who want to keep abreast of the latest developments within this dynamic branch of modern statistics. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

Author Biography

MYLES HOLLANDER is Robert O. Lawton Distinguished Professor of Statistics at Florida State University in Tallahassee. He served as editor of the Theory and Methods Section of the Journal of the American Statistical Association from 1993-96.<br> <br> S A. WOLFE is a Professor of Statistics at Ohio State University in Columbus. He is a two-time recipient of the Ohio State University Alumni Distinguished Teaching Award, in 1973-74 and 1988-89.

Table of Contents

Preface xiii
1 Introduction
1(19)
1.1 Advantages of Nonparametric Methods
1(1)
1.2 The Distribution-Free Property
2(1)
1.3 Some Real-World Applications
2(2)
1.4 Scope
4(4)
1.5 Format and Organization
8(2)
1.6 Computing Packages
10(1)
1.7 Historical Background
11(2)
1.8 Guide
13(7)
2 The Dichotomous Data Problem
20(15)
2.1 A Binomial Test
20(9)
2.2 An Estimator for the Probability of Success
29(2)
2.3 A Confidence Interval for the Probability of Success
31(4)
Clopper-Pearson
3 The One-Sample Location Problem
35(71)
Paired Replicates Analyses By Way of Signed Ranks 35(25)
3.1 A Distribution-Free Signed Rank Test
36(15)
Wilcoxon
3.2 An Estimator Associated with Wilcoxon's Signed Rank Statistic
51(5)
Hodges-Lehmann
3.3 A Distribution-Free Confidence Interval Based on Wilcoxon's Signed Rank Test
56(4)
Tukey
Paired Replicate Analyses By Way of Signs 60(19)
3.4 A Distribution-Free Sign Test
60(12)
Fisher
3.5 An Estimator Associated with the Sign Statistic
72(3)
Hodges-Lehmann
3.6 A Distribution-Free Confidence Interval Based on the Sign Test
75(4)
Thompson
Savur
One-Sample Data 79(15)
3.7 Procedures Based on the Signed Rank Statistic
79(4)
3.8 Procedures Based on the Sign Statistic
83(4)
3.9 An Asymptotically Distribution-Free Test of Symmetry
87(7)
Randles-Fligner-Policello-Wolfe
Davis-Quade
Bivariate Data 94(12)
3.10 A Distribution-Free Test for Bivariate Symmetry
94(10)
Hollander
3.11 Efficiencies of Paired Replicates and One-Sample Location Procedures
104(2)
4 The Two-Sample Location Problem
106(35)
4.1 A Distribution-Free Rank Sum Test
106(19)
Wilcoxon
Mann
Whitney
4.2 An Estimator Associated with Wilcoxon's Rank Sum Statistic
125(7)
Hodges-Lehmann
4.3 A Distribution-Free Confidence Interval Based on Wilcoxon's Rank Sum Test
132(3)
Moses
4.4 A Robust Rank Test for the Behrens-Fisher Problem
135(4)
Fligner-Policello
4.5 Efficiencies of Two-Sample Location Procedures
139(2)
5 The Two-Sample Dispersion Problem and Other Two-Sample Problems
141(48)
5.1 A Distribution-Free Rank Test for Dispersion--Medians Equal
142(16)
Ansari-Bradley
5.2 An Asymptotically Distribution-Free Test for Dispersion Based on the Jackknife--Medians Not Necessarily Equal
158(11)
Miller
5.3 A Distribution-Free Rank Test for Either Location or Dispersion
169(9)
Lepage
5.4 A Distribution-Free Test for General Differences in Two Populations
178(9)
Kolmogorov-Smirnov
5.5 Efficiencies of Two-Sample Dispersion and Broad Alternatives Procedures
187(2)
6 The One-Way Layout
189(81)
6.1 A Distribution-Free Test for General Alternatives
190(12)
Kruskal-Wallis
6.2 A Distribution-Free Test for Ordered Alternatives
202(10)
Jonckheere
Terpstra
6.3 Distribution-Free Tests for Umbrella Alternatives
212(22)
Mack-Wolfe
6.3.A A Distribution-Free Test for Umbrella Alternatives, Peak Known
213(13)
Mack-Wolfe
6.3.B A Distribution-Free Test for Umbrella Alternatives, Peak Unknown
226(8)
Mack-Wolfe
6.4 A Distribution-Free Test for Treatments versus a Control
234(6)
Fligner-Wolfe
6.5 Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings--General Configuration
240(9)
Dwass
Steel
Critchlow-Fligner
6.6 Distribution-Free One-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings-Ordered Treatment Effects
249(5)
Hayter-Stone
6.7 Distribution-Free One-Sided Treatments versus Control Multiple Comparisons Based on Joint Rankings
254(6)
Nemenyi
Damico-Wolfe
6.8 Contrast Estimation Based on Hodges-Lehmann Two-Sample Estimators
260(4)
Spjotvoll
6.9 Simultaneous Confidence Intervals for All Simple Contrasts
264(4)
Critchlow-Fligner
6.10 Efficiencies of One-Way Layout Procedures
268(2)
7 The Two-Way Layout
270(93)
7.1 A Distribution-Free Test for General Alternatives in a Randomized Complete Block Design
272(12)
Friedman
Kendall-Babington Smith
7.2 A Distribution-Free Test for Ordered Alternatives in a Randomized Complete Block Design
284(11)
Page
7.3 Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Friedman Rank Sums--General Configuration
295(5)
Wilcoxon
Nemenyi
McDonald-Thompson
7.4 Distribution-Free One-Sided Treatments versus Control Multiple Comparisons Based on Friedman Rank Sums
300(5)
Nemenyi
Wilcoxon-Wilcox
Miller
7.5 Contrast Estimation Based on One-Sample Median Estimators
305(4)
Doksum
Incomplete Block Data--Two-way Layout with Zero or One Observation per Treatment-Block Combination 309(20)
7.6 A Distribution-Free Test for General Alternatives in a Randomized Balanced Incomplete Block Design (BIBD)
309(8)
Durbin
Skillings-Mack
7.7 Asymptotically Distribution-Free Two-Sided All-Treatments Multiple Comparisons for Balanced Incomplete Block Designs
317(2)
Skillings-Mack
7.8 A Distribution-Free Test for General Alternatives for Data from an Arbitrary Incomplete Block Design
319(10)
Skillings-Mack
Replications--Two-way Layout with at Least One Observation for Every Treatment-Block Combination 329(14)
7.9 A Distribution-Free Test for General Alternatives in a Randomized Block Design with an Equal Number c (greater than 1) of Replications per Treatment-Block Combination
329(11)
Mack-Skillings
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
340(3)
Mack-Skillings
Analyses Associated with Signed Ranks 343(20)
7.11 A Test Based on Wilcoxon Signed Ranks for General Alternatives in a Randomized Complete Block Design
343(5)
Doksum
7.12 A Test Based on Wilcoxon Signed Ranks for Ordered Alternatives in a Randomized Complete Block Design
348(3)
Hollander
7.13 Approximate Two-Sided All-Treatments Multiple Comparisons Based on Signed Ranks
351(2)
Nemenyi
7.14 Approximate One-Sided Treatments versus Control Multiple Comparisons Based on Signed Ranks
353(4)
Hollander
7.15 Contrast Estimation Based on One-Sample Hodges-Lehmann Estimators
357(4)
Lehmann
7.16 Efficiencies of Two-Way Layout Procedures
361(2)
8 The Independence Problem
363(52)
8.1 A Distribution-Free Test for Independence Based on Signs
363(19)
Kendall
8.2 An Estimator Associated with the Kendall Statistic
382(1)
Kendall
8.3 An Asymptotically Distribution-Free Confidence Interval Based on the Kendall Statistic
383(5)
Samara-Randles
Fligner-Rust
Noether
8.4 An Asymptotically Distribution-Free Confidence Interval Based on Efron's Bootstrap
388(6)
8.5 A Distribution-Free Test for Independence Based on Ranks
394(14)
Spearman
8.6 A Distribution-Free Test for Independence Against Broad Alternatives
408(5)
Hoeffding
8.7 Efficiencies of Independence Procedures
413(2)
9 Regression Problems
415(43)
One Regression Line 415(14)
9.1 A Distribution-Free Test for the Slope of the Regression Line
416(5)
Theil
9.2 A Slope Estimator Associated with the Theil Statistic
421(3)
Theil
9.3 A Distribution-Free Confidence Interval Associated with the Theil Test
424(2)
Theil
9.4 An Intercept Estimator Associated with the Theil Statistic and Use of the Estimated Linear Relationship for Prediction
426(3)
Hettmansperger-McKean-Sheather
k(is greater than or equal to 2) Regression Lines 429(9)
9.5 An Asymptotically Distribution-Free Test for the Parallelism of Several Regression Lines
429(9)
Sen
Adichie
General Multiple Linear Regression 438(15)
9.6 Asymptotically Distribution-Free Rank-Based Tests for General Multiple Linear Regression
438(15)
Jaeckel
Hettmansperger-McKean
Nonparametric Regression Analysis 453(5)
9.7 An Introduction to Non-Rank-Based Approaches to Nonparametric Regression Analysis
453(3)
9.8 Efficiencies of Regression Procedures
456(2)
10 Comparing Two Success Probabilities
458(37)
10.1 Approximate Tests and Confidence Intervals for the Difference between Two Success Probabilities
459(14)
Pearson
10.2 An Exact Test for the Difference between Two Success Probabilities
473(4)
Fisher
10.3 Inference for the Odds Ratio
477(7)
Fisher
Cornfield
10.4 Inference for k Strata of 2 X 2 Tables
484(9)
Mantel
Haenszel
10.5 Efficiencies
493(2)
11 Life Distributions and Survival Analysis
495(68)
11.1 A Test of Exponentiality versus IFR Alternatives
495(9)
Epstein
11.2 A Test of Exponentiality versus NBU Alternatives
504(9)
Hollander-Proschan
11.3 A Test of Exponentiality versus DMRL Alternatives
513(7)
Hollander-Proschan
11.4 A Test of Exponentiality versus a Trend Change in Mean Residual Life
520(6)
Guess-Hollander-Proschan
11.5 A Confidence Band for the Distribution Function
526(9)
Kolmogorov
11.6 An Estimator of the Distribution Function When the Data Are Censored
535(15)
Kaplan-Meier
11.7 A Two-Sample Test for Censored Data
550(7)
Mantel
11.8 Efficiencies
557(6)
Appendix A Tables and Charts 563(182)
Bibliography 745(22)
Answers to Selected Problems 767(4)
Author Index 771(8)
Subject Index 779

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