The effects of violations of assumptions underlying the test.

As psychologists who perform in a research capacity are well aware, psychological data too frequently have an exasperating tendency to manifest themselves in a form which violates one or more of the assumptions underlying the usual statistical tests of significance. Faced with the problem of analyzing such data, the researcher usually attempts to transform them in such a way that the assumptions are tenable, or he may look elsewhere for a statistical test. The latter alternative has become popular because of the proliferation of the so-called nonparametric or distribution-free methods. These techniques quite generally, however, couple their freedom from restricting assumptions with a disdain for much of the information contained within the data. For example, by classifying scores into groups above and below the median one ignores the fact that there are intracategory differences between the individual scores. As a result, tests which make no assumptions about the distribution from which one is sampling will tend not to reject the null hypothesis when it is actually false as often as will those tests which do make assumptions. This lack of power of the nonpara-