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. Modelling Ties. Tests on One-Way Layout Data: Extensions to the Median and Kruska-Wallis Tests. Tests Based on a Product Multinomial Model: Yates´ Test and Its Extensions. Further Tests Based on a Product Multinomial Model: Order in the Sign Test and Ordinal Categorical Data with a Factorial Response. Tests on Complete Randomised Blocks: Extensions to the Friedman and Cochran Tests. Further Tests on Randomised Blocks: Extensions to Durbin's Test. Extensions to a Nonparametric Correlation Test: Spearman's Test. One and S-Sample Smooth Tests of Goodness of Fit. Conclusion. Appendices.
"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