Nonparametric Statistical Tests : A Computational Approach

This book provides a modern and accessible overview of computationally intensive nonparametric statistical methods. It presents detailed information on the use of permutation and bootstrap methods to assess the significance of a statistic in a hypothesis test. The text includes numerous real examples to illustrate the methods and uses SAS programs throughout to apply the methods. In addition, a significant portion of the book is devoted to recent nonparametric tests for comparing independent groups with potentially unequal variances.

Nonparametric Statistical Tests: A Computational Approach describes classical nonparametric tests, as well as novel and little-known methods such as the Baumgartner-Weiss-Schindler and the Cucconi tests. The book presents SAS and R programs, allowing readers to carry out the different statistical methods, such as permutation and bootstrap tests. The author considers example data sets in each chapter to illustrate methods. Numerous real-life data from various areas, including the bible, and their analyses provide for greatly diversified reading.

The book covers:

• Nonparametric two-sample tests for the location-shift model, specifically the Fisher-Pitman permutation test, the Wilcoxon rank sum test, and the Baumgartner-Weiss-Schindler test
• Permutation tests, location-scale tests, tests for the nonparametric Behrens-Fisher problem, and tests for a difference in variability
• Tests for the general alternative, including the (Kolmogorov-)Smirnov test, ordered categorical, and discrete numerical data
• Well-known one-sample tests such as the sign test and Wilcoxon’s signed rank test, a modification suggested by Pratt (1959), a permutation test with original observations, and a one-sample bootstrap test are presented.
• Tests for more than two groups, the following tests are described in detail: the Kruskal-Wallis test, the permutation F test, the Jonckheere-Terpstra trend test, tests for umbrella alternatives, and the Friedman and Page tests for multiple dependent groups
• The concepts of independence and correlation, and stratified tests such as the van Elteren test and combination tests
• The applicability of computer-intensive methods such as bootstrap and permutation tests for non-standard situations and complex designs

Although the major development of nonparametric methods came to a certain end in the 1970s, their importance undoubtedly persists. What is still needed is a computer assisted evaluation of their main properties. This book closes that gap.