Testing for normality. (English) Zbl 1032.62040

Thode, Henry C. jun.

Statistics: Textbooks and Monographs. 164. New York, NY: Marcel Dekker. x, 479 p. (2002).

Normality is one of the most common assumptions made in the development and use of statistical procedures. A large number of methods for testing for normality are developed providing researchers with a wide range of choices (this can also result in a good deal confusion). This book, for example, deals with about forty formal testing procedures that are proposed to test univariate and multivariate normality, offering plotting methods, outlier and general goodness of fit tests, and power comparisons for detection of non-normality in specialized conditions. The objective of the book is to summarize the vast literature on tests of normality and to describe which of the many tests are effective and which are not. For example, such popular tests as the Kolmogorov-Smirnov or chi-squared goodness of fit tests have power so low that they should not be considered for testing normality, while the performance of moment tests and the Wilk-Shapiro test is so impressive that they are recommended for use in everyday practice.
The book consists of 13 Chapters and Appendices. Chapters 2-7 describe procedures for testing normality in complete samples. They describe plotting methods and regression and correlation tests, moment-type tests, other tests specifically derived for testing normality, general goodness of fit tests and their usefulness in testing specifically for normality, tests specifically designed to detect outliers, summarizing results of power studies and comparisons of the various univariate tests for normality. Chapter 8 also deals with univariate samples, but considers the case of censored data. Chapters 9 and 10 deal with testing normality in multivariate samples. They describe tests for multivariate normality and tests designed to detect multivariate outliers. Chapter 11 focuses on testing for mixtures of normal distributions in both univariate and multivariate cases. Chapter 12 presents basic methods for robust estimation which can be used in testing normality. Chapter 13 describes various computational issues in assessing normality. The appendices contain data sets used in examples presented in the text and tables of parameter and critical values for the described procedures.
Although some historical background and theory are provided for many of the tests, the emphasis in the book is on the calculation and performance of the tests.
This book is a good resource for all statisticians, quality control engineers, data analysts, as well as a text for graduate students in these disciplines.

Reviewer: Mikhail P.Moklyachuk (Kyïv)

MSC:

62G10	Nonparametric hypothesis testing
62F03	Parametric hypothesis testing
62-02	Research exposition (monographs, survey articles) pertaining to statistics
62H15	Hypothesis testing in multivariate analysis

Keywords:

Kolmogorov-Smirnov test; goodness of fit tests; plotting; outliers; chi-squared test; regression; correlation test; robust estimation; censored data; mixtures of normal distributions; multivariate normal distributions; univariate normal distributions; power of tests