1st Edition

A Contingency Table Approach to Nonparametric Testing




ISBN 9781584881612
Published December 7, 2000 by Chapman and Hall/CRC
264 Pages - 20 B/W Illustrations

USD $220.00

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Book Description

Most texts on nonparametric techniques concentrate on location and linear-linear (correlation) tests, with less emphasis on dispersion effects and linear-quadratic tests. Tests for higher moment effects are virtually ignored. Using a fresh approach, A Contingency Table Approach to Nonparametric Testing unifies and extends the popular, standard tests by linking them to tests based on models for data that can be presented in contingency tables.

This approach unifies popular nonparametric statistical inference and makes the traditional, most commonly performed nonparametric analyses much more complete and informative. It also makes tied data easily handled, and almost exact Monte Carlo p-values can be obtained. With data in contingency tables, one can then calculate a Pearson-type, chi-squared statistic and its components. For univariate data, the initial tests based on these components detect mean differences between treatments. For bivariate data, they detect correlations. This approach leads to tests that detect variance, skewness, and higher moment differences between treatments with univariate data, and higher bivariate moment differences with bivariate data.

Although the methods advanced in this book have their genesis in traditional nonparametrics, incorporating the power of modern computers makes the approach more complete and more valid than previously possible. The authors' unified treatment and readable style make the subject easy to follow and the techniques easily implemented, whether you are a fledgling or a seasoned researcher.

Table of Contents

INTRODUCTION
Parametric or Nonparametric?
Instructors Example
Quadratic Differences and Ranking
Outline and Scope
Applications of Nonparametric Methods to Sensory Evaluation
MODELLING TIES
Introduction
The Sign Test and Ties
Modelling Partitioned Ties in the Sign Test
Modelling Unpartitioned Ties in the Sign Test
McNemar's Test
Partitioning into Components
Ties in a Multinomial Test
Ties When Testing for Independence
TESTS ON ONE-WAY LAYOUT DATA: EXTENSIONS TO THE MEDIAN AND KRUSKAL-WALLIS TESTS
Introduction
A Model and Pearson's c2 Test
Partitioning Pearson's Statistic
The Kruskal-Wallis Test with No Ties
The Kruskal-Wallis Test with Ties
Generalised Median Tests
TESTS BASED ON A PRODUCT MULTINOMIAL MODEL: YATES´ TEST AND ITS EXTENSIONS
Introduction
One-Way Tables
Partitioning c2p Using Score Statistics
Other Methods for Ordered Data
Small Sample Size and Power Comparisons
Examples
FURTHER TESTS BASED ON A PRODUCT MULTINOMIAL MODEL: ORDER IN THE SIGN TEST AND ORDINAL CATEGORICAL DATA WITH A FACTORIAL RESPONSE
Introduction
How Order Affects the Sign Test
The Sign Test and Gart's Tests
A New Model and Score Test
Comparison of the Sign and Score Tests
Sports Drink Example
Recommendations
Nonparametric Analysis of Ordinal Categorical Data with Factorial Response
Olives Data Example
Cross Cultural Study Example
TESTS ON COMPLETE RANDOMISED BLOCKS: EXTENSIONS TO THE FRIEDMAN AND COCHRAN TESTS
Peach Example
Friedman's Test and Its Extensions
Derivations
Page's Test and Its Relationship to Friedman's, Anderson's and Pearson's Tests
An Alternative Partition of the Anderson Statistic: An Umbrella Test
Ties
Cochran's Test
Stuart's Test and Its Extensions
FURTHER TESTS ON RANDOMISED BLOCKS: EXTENSIONS TO DURBIN'S TEST
Introduction
Durbin's Test and Its Extensions
Derivations
A Page-Type Test
Paired Comparisons with a 2n Factorial Structure
EXTENSIONS TO A NONPARMETRIC CORRELATION TEST: SPEARMAN'S TEST
Introduction
A Smooth Model and Tests for Independence
Smooth Extensions
Interpretation of the Components
Discussion
Multi-way Tables
ONE AND S-SAMPLE SMOOTH TESTS OF GOODNESS OF FIT
Introduction
One-Sample Testing for Uncategorised Distributions
One-Sample Testing for Categorised Distributions
S-Sample Testing
Derivations and Simulation Study
CONCLUSION
APPENDICES

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Reviews

"I found many of the ideas in this book interesting and compelling... this book presents an interesting modernization of certain classical nonparametric tests in terms of contingency tables. The authors have made a valuable contribution to the statistical literature..."
-Biometrics, December 2001

"Although its subject is highly technical, the book somehow maintains a good balance between theories and application. The excellent Appendix is self-contained and very easy to read…Overall, this book is an excellent addition to the statistical literature…"
-Technometrics, February 2003