1st Edition

A Contingency Table Approach to Nonparametric Testing

By J.C.W. Rayner, D.J. Best Copyright 2001
    264 Pages 20 B/W Illustrations
    by Chapman & Hall

    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.

    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

    Biography

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

    "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