Nonparametric Statistics for the Behavioral Sciences

Sidney Siegel (January 4, 1916–November 29, 1961) was a psychologist trained at Stanford University. He spent nearly his entire career as a professor at Pennsylvania State University. He is known for his contribution to nonparametric statistics, including the development with John Tukey of the Siegel–Tukey test—a test for differences in scale between groups. Arguably, he is most well known for his book, Nonparametric Statistics for the Behavioral Sciences, the first edition of which was published by McGraw-Hill in 1956. After Siegel’s death, a second edition was published (1988) adding N. John Castellan Jr. as coauthor. Nonparametric Statistics for the Behavioral Sciences is the first text to provide a practitioner’s introduction to nonparametric statistics. By its copious use of examples and its straightforward “how to” approach to the most frequently used nonparametric tests, this text was the first accessible introduction to nonparametric statistics for the nonmathematician. In that sense, it represents an important step forward in the analysis and presentation of non-normal data, particularly in the field of psychology.

The organization of the book is designed to assist the researcher in choosing the correct nonparametric test. After the introduction, the second chapter introduces the basic principles of hypothesis testing, including the definitions of: the null and alternative hypothesis, the size of the test, Type I and Type II errors, power, sampling distributions, and the decision rule. Chapter 3 describes the factors that influence the choice of correct test. After explaining some common parametric assumptions and the circumstances under which [Page 1083]nonparametric tests should be used, the text gives a basic outline of how the proper statistical test should be chosen. Tests are distinguished from one another in two important ways: First, tests are distinguished by their capability of analyzing data of varying levels of measurement. For example, the ${\chi }^2$ goodness-of-fit test can be applied to nominal data, whereas the Kolmogorov–Smirnov requires at least the ordinal level of measurement. Second, tests are distinguished in terms of the type of samples to be analyzed. For example, two-sample paired tests are distinguished from tests applicable to $K$ independent samples, which are distinguished tests of correlation, and so on. Tests included in the text include the following: the binomial test, the sign test, the signed-rank test, tests for data displayed in two-way tables, the Mann–Whitney $U$test, the Kruskal–Wallis test, and others. Also included are extensive tables of critical values for the various tests discussed in the text.

Because nonparametric tests make fewer assumptions than parametric tests, they are generally less powerful than the parametric alternatives. The text compares the various tests presented with their parametric analogues in terms of power efficiency. Power efficiency is defined to be the percent decrease in sample size required for the parametric test to achieve the same power as that of the nonparametric test when the test is performed on data that do, in fact, satisfy the assumptions of the parametric test.

This work is important because it seeks to present nonparametric statistics in a way that is “completely intelligible to the reader whose mathematical training is limited to elementary algebra” (Siegel, 1956, p. 4). It is replete with examples to demonstrate the application of these tests in contexts that are familiar to psychologists and other social scientists. The text is organized so that the user, knowing the specific level of measurement and type(s) of samples being analyzed, can immediately identify several nonparametric tests that might be applied to his or her data.

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