A Contingency Table Approach to Nonparametric Testing

A Contingency Table Approach to Nonparametric Testing

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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.show more

Product details

  • Hardback | 264 pages
  • 158.5 x 245.9 x 19.6mm | 539.78g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 20 black & white illustrations, 68 black & white tables
  • 1584881615
  • 9781584881612

Review quote

"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 readOverall, this book is an excellent addition to the statistical literature" -Technometrics, February 2003show more

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 APPENDICESshow more