In Chapter 9, several hypothesis tests that depended on the assumption of normality for population distributions were introduced. Frequently, the assumption of normality is reasonable. Moreover, by virtue of the central limit theorem, many of these test procedures remain approximately valid when applied to large samples even if the population distribution is not normal. However, it is often the case in practical applications that a normality assumption is not tenable. In these circumstances, it is desirable to base inference on tests that are valid over a wide range of distributions of the parent population. Such tests are called nonparametric, or distribution-free.
In this chapter, we describe nonparametric tests that are appropriate for analyzing some of the problems we have already met. Other nonparametric tests will be discussed in subsequent chapters. Although they do require certain assumptions, such as independent sample observations, nonparametric tests are generally valid whatever the population distribution. That is to say, tests can be developed that have the required significance levels, no matter what the distribution of the population members. It is not our intention here to attempt to describe the wide array of such tests that are available. Rather, our objective is the more modest one of providing a flavor of the methods used. In this chapter, we will discuss nonparametric procedures for testing the equality of the centers of two population distributions. These tests are nonparametric alternatives to the tests discussed in Section 9.6.
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