644 CHAPTER 13 Nonparametric Tests Misleading Terminology The term distribution-free test correctly indicates that a test does not require a particular distribution. The term nonparametric tests is misleading in the sense that it suggests that the tests are not based on a parameter, but there are some nonparametric tests that are based on a parameter such as the median. Due to the widespread use of the term nonparametric test, we use that terminology, but we define it to be a test that does not require a particular distribution. Advantages and Disadvantages Advantages of Nonparametric Tests 1. Because nonparametric tests have less rigid requirements than parametric tests, they can be applied to a wider variety of situations. 2. Nonparametric tests can be applied to more data types than parametric tests. For example, nonparametric tests can be used with data consisting of ranks, and they can be used with categorical data, such as genders of survey respondents. Disadvantages of Nonparametric Tests 1. Nonparametric tests tend to waste information because exact numerical data are often reduced to a qualitative form. For example, with the nonparametric sign test (Section 13-2), weight losses by dieters are recorded simply as negative signs, and the actual magnitudes of the weight losses are ignored. 2. Nonparametric tests are not as efficient as parametric tests, so a nonparametric test generally needs stronger evidence (such as a larger sample or greater differences) in order to reject a null hypothesis. 13-7 Runs Test for Randomness • Develop the ability to use the runs test for randomness to determine whether sample data occur in a random sequence. This chapter introduces methods of nonparametric tests, which do not have the stricter requirements of corresponding parametric tests, which are based on samples from populations with specific parameters such as m or s. 13-1 Basics of Nonparametric Tests DEFINITIONS Parametric tests have requirements about the distribution of the populations involved; nonparametric (or distribution-free) tests do not require that samples come from populations with normal distributions or any other particular distributions.
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