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**Randomization tests.
3rd ed., rev. and expanded.**
*(English)*
Zbl 0893.62036

Statistics: Textbooks and Monographs. 147. New York, NY: Marcel Dekker. xxii, 409 p. (1995).

This is an updated and enlarged third edition of a useful and valuable book presenting special statistical techniques, called randomization tests, for analyzing data obtained from nonrandom samples, and for which random assignment is the only random element occurring in the problem; for a review of the second edition from 1987 see Zbl 0629.62003, and for the first edition from 1980 see Zbl 0439.62030. The validity of numerous techniques of statistical inference depends upon drawing a random sample from a population which in many situations (e.g. medicine, education, biology, psychology, etc.) may not be feasible and the investigator is forced to rely on data collected from nonrandom samples. Since the use of a randomization test involves a great deal of computation, appropriate computer programs for a number of practical applications of randomization tests are presented throughout the book. The current edition differs from the previous one in that two chapters, 13 and 14, are entirely new, additional factorial designs are presented, and material on “theory” and on single-subject randomization tests has been reorganized and supplemented.

Of the 16 chapters, the first three deal with topics such as advantages of using randomization test procedures, random assignment, and obtaining significance values when randomization tests are performed by a computer. An interesting historical background of the development of randomization procedures is presented in Section 1.13. The next two chapters are set aside for the applications of these tests to data obtained by using one-way analysis of variance, and for determining significance for repeated-measures analysis of variance. Completely randomized factorial and randomized block designs are covered in Chapters 6 and 7, respectively, (as opposed to the last edition which covered these under one chapter). Randomization tests as applied to multivariate designs, correlations, point-biserial correlation, and Kendall’s rank correlation are discussed in the next two chapters. Chapter 10 is on trend tests which deal with testing a null hypothesis of no treatment effects using a test statistic which is sensitive to a certain type of expected trend. It is demonstrated in Chapter 11 that for randomization tests, random selection of treatment levels permits a different type of test, in which sensitivity of a test can be significantly increased. Single subject randomization tests are discussed at great length in Chapter 12, which has undergone an extensive revision. The problems of testing null hypotheses of specified amount or type of treatment effects by using randomization tests are taken up in Chapters 13 and 14 (entirely new chapters). Next, Chapter 15 provides a sound theoretical foundation for developing randomization tests, and presents also a detailed analysis of the relationship among the following: The random assignment procedure, the null hypothesis, and the data permutation for calculating significance levels. The final Chapter 16 is on general guidelines for making effective use of randomization tests.

A new appendix lists sources of free and commercial software for carrying out permutation tests, and also includes computing algorithms which can speed up permutation tests considerably. Each chapter ends with a useful list of references, and has a combined subject-author index. A detailed account of the differences between permutation tests and randomization tests is also presented.

The author, presents a clear account of the applications of randomzation tests through numerous illustrative examples drawn from various field. It is a valuable source and a handy reference of programs and techniques for applying randomization tests. To read it, one needs only an introductory statistics course, and does not require much mathematical sophistication. It illustrates in an easy-to-understand style the relationship of randomization tests with topics in parametric and nonparametric statistics. With the exponential growth of computing facilities and the absence of the assumption of random sampling of data, researchers and experimenters are going to turn more and more to the use of randomization tests. The lack of any set of exercises in the book diminishes its value as a text book for classroom use. Overall, it is an excellent addition to the academic market, and researchers working in many fields as well as advanced undergraduate and graduate students will benefit a lot from it.

Of the 16 chapters, the first three deal with topics such as advantages of using randomization test procedures, random assignment, and obtaining significance values when randomization tests are performed by a computer. An interesting historical background of the development of randomization procedures is presented in Section 1.13. The next two chapters are set aside for the applications of these tests to data obtained by using one-way analysis of variance, and for determining significance for repeated-measures analysis of variance. Completely randomized factorial and randomized block designs are covered in Chapters 6 and 7, respectively, (as opposed to the last edition which covered these under one chapter). Randomization tests as applied to multivariate designs, correlations, point-biserial correlation, and Kendall’s rank correlation are discussed in the next two chapters. Chapter 10 is on trend tests which deal with testing a null hypothesis of no treatment effects using a test statistic which is sensitive to a certain type of expected trend. It is demonstrated in Chapter 11 that for randomization tests, random selection of treatment levels permits a different type of test, in which sensitivity of a test can be significantly increased. Single subject randomization tests are discussed at great length in Chapter 12, which has undergone an extensive revision. The problems of testing null hypotheses of specified amount or type of treatment effects by using randomization tests are taken up in Chapters 13 and 14 (entirely new chapters). Next, Chapter 15 provides a sound theoretical foundation for developing randomization tests, and presents also a detailed analysis of the relationship among the following: The random assignment procedure, the null hypothesis, and the data permutation for calculating significance levels. The final Chapter 16 is on general guidelines for making effective use of randomization tests.

A new appendix lists sources of free and commercial software for carrying out permutation tests, and also includes computing algorithms which can speed up permutation tests considerably. Each chapter ends with a useful list of references, and has a combined subject-author index. A detailed account of the differences between permutation tests and randomization tests is also presented.

The author, presents a clear account of the applications of randomzation tests through numerous illustrative examples drawn from various field. It is a valuable source and a handy reference of programs and techniques for applying randomization tests. To read it, one needs only an introductory statistics course, and does not require much mathematical sophistication. It illustrates in an easy-to-understand style the relationship of randomization tests with topics in parametric and nonparametric statistics. With the exponential growth of computing facilities and the absence of the assumption of random sampling of data, researchers and experimenters are going to turn more and more to the use of randomization tests. The lack of any set of exercises in the book diminishes its value as a text book for classroom use. Overall, it is an excellent addition to the academic market, and researchers working in many fields as well as advanced undergraduate and graduate students will benefit a lot from it.

Reviewer: D.V.Chopra (Wichita)

### MSC:

62G10 | Nonparametric hypothesis testing |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62K99 | Design of statistical experiments |

62-04 | Software, source code, etc. for problems pertaining to statistics |