The validity of many of the inference procedures presented in this book requires that various assumptions be met. Often, for instance, a normality assumption is required. In this chapter we have learned that, when the needed assumptions are not met, we must employ a nonparametric method. Such a method does not require any assumptions about the shape(s) of the distribution(s) of the sampled population(s).

We first presented the sign test, which is a hypothesis test about a population median. This test is useful when we have taken a sample from a population that may not be normally distributed. We next presented two nonparametric tests for comparing the locations of two populations. The first such test, the Wilcoxon rank sum test, is appropriate when an independent samples experiment has been carried out. The second, the Wilcoxon signed ranks test, is appropriate when a paired difference experiment has been carried out. Both of these tests can be used without assuming that the sampled populations have the shapes of any particular probability distributions. We then discussed the Kruskal-Wallis H test, which is a nonparametric test for comparing the locations of several populations by using independent samples. This test, which employs the chi-square distribution, can be used when the normality and/or equal variances assumptions for one-way analysis of variance do not hold. Finally, we presented a nonparametric approach for testing the significance of a population correlation coefficient. Here we saw how to compute Spearman's rank correlation coefficient, and we discussed how to use this quantity to test the significance of the population correlation coefficient.