ABSTRACT
In Chapter 9 we showed how to apply the t-test in assessing the probability that two sets of observations, with their observed means, were drawn from the same or different populations. In order to apply the t-test, some assumptions were made with respect to the distributions of the observations in the population, i.e., that the observations were normally distributed with homogeneous variances. In this chapter we will present some useful tests that do not assume that our sampled observations are either normally distributed and/or have homogeneous variances. These tests are part of the family of, so-called, distribution-free or nonparametric statistical tests. Distribution-free tests do not make specific assumptions about the distributions of the data in the populations from which the observations have been sampled. Since there is not an assumed distribution, then there are no parameters that characterise such a distribution (e.g., mean, variance), hence the name nonparametric tests. Nonparametric tests are attractive because they can be used to perform statistical analyses on data-sets that violate the assumptions underlying the use of the t-test. As stated in Chapter 9, the t-test is fairly robust; hence, violations of the underlying assumptions have a relatively small impact on the precision of the test. Nevertheless, if violations are severe, it may be useful to employ nonparametric tests. We will mainly describe two tests that can be used with matched samples and with independent samples. These are called the Wilcoxon matched-pairs signed-ranks test and the Wilcoxon rank-sum test, respectively. Both tests were devised by Frank Wilcoxon, hence their names.
