ABSTRACT
In spite of the robust nature of the t and F tests there are situations where their use is inappropriate. When samples are small, and very different in size, we find the t test and F test quite sensitive to violations of the assumptions on which they are based, that is, sampling from normal populations with identical variances. Under these circumstances, or when we clearly have less than interval measurement, we should make use of nonparametric or distribution-free tests of significance. While nonparametric tests are usually distribution-free, the terms are not synonymous. When a test is nonparametric, it means that it does not involve inferences about the parameters of some population; if it is distribution-free it means that we need not make any assumptions about the shape of the population being sampled. Nonparametric tests are widely used in behavioral research. They can be calculated easily. The logical basis of many of them is easy to understand. Unfortunately they are not as powerful as the t test and the F test and, of course, none of them can reveal the subtle interaction effects for which the ANOVA is so well-suited. Of the nonparametric tests we shall discuss, the first two are used when we require a matched pairs test but cannot meet the assumptions for a matched pairs t test.
