Distribution-Free and Computationally Intensive Methods
The statistical procedures described in the previous chapters have relied in the main for their validity on an underlying assumption of distributional normality. How well these procedures operate outside the confines of this normality constraint varies from setting to setting. Many people believe that in most situations, normal based methods are sufficiently powerful to make consideration of alternatives unnecessary. They may have a point; t tests and F tests, for example, have been shown to be relatively robust to departures from the normality assumption. Nevertheless, alternatives to normal based methods have been proposed and it is important for psychologists to be aware of these, because many are widely quoted in the psychological literature. One class of tests that do not rely on the normality assumptions are usually referred to as non parametric or distribution free. (The two labels are almost synonymous, and we shall use the latter here.) Distribution-free procedures are generally based on the ranks of the raw data and are usually valid over a large class of distributions for the data, although they do often assume distributional symmetry. Although slightly less efficient than their normal theory competitors when the underlying populations are normal, they are
often considerably more efficient when the underlying populations are not normal. A number of commonly used distribution-free procedures will be described in Sections 8.2-8.5.