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Nonparametric Statistical Tests: A Computational Approach

Markus Neuhäuser
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
[Reviewed by
Robert W. Hayden
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This book might well be titled “recent advances in elementary nonparametric tests.” The main part is less than 200 pages, and much of that is computer code, so that coverage is narrow: approximately the tests in a typical first course. On the borderline, we see that regression and most confidence intervals are not covered, while analysis of variance and chi-squared techniques (including McNemar’s test) are. Two chapters (of 13) offer miscellaneous more complex applications.

The subtitle “A Computational Approach” seems justified in three ways. First, there are substantial amounts of SAS code in the body of the work, and a briefer account of R code in an appendix. (A disk or website holding all the code and the the data used for examples would be welcome.) While many standard statistical software packages include the classic non-parametric procedures, this volume presents many recent ones that have not found their way into most software yet, hence the need to include code for these techniques. Another computer feature is the inclusion of a variety of resampling techniques such as permutation tests and the bootstrap, which are similar to traditional nonparametric tests but differ in some respects as well. Historically, some of the older techniques were offered as simplified shortcuts compared to parametric alternatives, while resampling methods are very computationally intensive, so their inclusion constitutes a second way in which this book offers a computational approach. Finally, many recommendations are offered on the merits of the various techniques, usually based on computationally intensive simulation studies, often conducted by the author.

The history of the study of the limitations of classical techniques, and possible alternatives, has had it ups and downs. In his article “Student” and small-sample theory (Statist. Sci. Volume 14, Number 4 (1999), 418-426), E. L. Lehmann reports on letters from Gosset to Fisher in the early 1920s. begging him to investigate these issues, while Fisher brushes this off as not the job of the theorist. E. S. Pearson began using simulation studies to address these issues in the late 1920s. Initially, the parametric procedures appeared to be very robust. In recent years, however, more detailed research has revealed problems. To give an example relevant to the book at hand, early studies asked if nominal 95% confidence intervals actually captured the population parameter 95% of the time. Often they did. Later studies looked at the width of those intervals, and found that alternative methods might provide 95% coverage as well, but offer much narrower intervals for non-normal populations. These are therefore more powerful tests, or, to put it yet another way, they allow equal precision of estimates with much smaller samples. This book addresses both the coverage and power issues.

In many ways this book seems like an interim status report. It is not a textbook in that it includes no exercises. Coverage is variable in its completeness, though this may simply reflect the current state of knowledge. For example, the nonparametric tests may (or may not) be compared to competing parametric tests, or to one another. In some chapters a number of tests are simply given with an example and no guide as to what the best approach might be. Many formulae are given but little in the way of derivations (because the issue is usually how well proposed tests work in practice rather than their theoretical justification).

The writing is clear and concise with only an occasional clue that English might not have been the original language. There are 24 pages of references at the end of the work for anyone who wishes to explore the material in greater depth. There are more references to works from Germany than we usually see, which adds to our knowledge base. The work is more free than most recent works from the kinds of errors spell checkers do not find.

Highly recommended to anyone familiar with the classic nonparametric tests who wants an update (and extensive bibliography) concerning recent results.

After a few years in industry, Robert W. Hayden ([email protected]) taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He now teaches statistics online at and does summer workshops for high school teachers of Advanced Placement Statistics. He contributed the chapter on evaluating introductory statistics textbooks to the MAA's Teaching Statistics.

Introduction and Overview
Nonparametric tests for the location problem
Tests in case of heteroscedasticity
Tests for the general alternative
Ordered categorical and discrete data
The conservativeness of permutation tests
Further examples for the comparison of two groups
One-sample tests and tests for paired data
Tests for more than two groups
Independence and correlation
Stratified studies and combination of p-values
Estimation and confidence intervals
Appendix. Nonparametric tests in R