ABSTRACT
For all the statistical tests that we have studied up to this point, the populations from which the data were sampled were assumed to be either normally distributed or ap‐ proximately so. In fact, this property is necessary for the tests to be valid. Since the forms of the underlying distributions are assumed to be known and only the values of certain parameters—such as the means and the standard deviations—are not, these tests are said to be parametric. If the data do not conform to the assumptions made by such traditional techniques, nonparametric methods of statistical inference should be used in‐ stead. Nonparametric techniques make fewer assumptions about the nature of the un‐ derlying distributions. As a result, they are sometimes called distribution‐free methods. Nonparametric tests of hypotheses follow the same general procedure as the para‐ metric tests that we have already studied. We begin by making some claim about the underlying populations in the form of a null hypothesis; we then calculate the value of a test statistic using the data contained in a random sample of observations. Depending on the magnitude of this statistic, we either reject or do not reject the null hypothesis.
