A Contingency Table Approach to Nonparametric Testing: 1st Edition (Hardback) book cover

A Contingency Table Approach to Nonparametric Testing

1st Edition

By J.C.W. Rayner, D.J. Best

Chapman and Hall/CRC

264 pages | 20 B/W Illus.

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Hardback: 9781584881612
pub: 2000-12-07
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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.

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

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

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MAT029010
MATHEMATICS / Probability & Statistics / Bayesian Analysis