Researchers should always test the assumptions of parametric tests. What should be done if the assumptions are violated? The data can be transformed, or a non-parametric test applied to the raw data. The reader is advised that if the data set with which he is working is fairly large, then he should transform it, fix the assumption violations, and apply a parametric test. With a computer, this can be done fairly efficiently, and will take less time than applying a non-parametric test, whose hand calculations can be cumbersome for large data sets. If the data set is small, however, the researcher may be better off applying a non-parametric test.

Non-parametric tests are distribution-free. That is, they do not make any assumptions about the distribution of the population from which the samples were collected. Hence, these tests can be applied to non-normal data. Non-parametric tests are so-called because their null hypothesis does not specify a value for the population's parameter. Hence, the null hypothesis will not be written in parametric notation. Rather, it will simply be stated as, for example, there is no treatment effect, or the samples were obtained from the same population, etc.

Non-parametric tests are particularly well suited for many social science situations in which the sample sizes are exceedingly small: a paleoanthropologist may have small samples of fossils, or an archaeologist may wish to compare a few projectile points from several sites.