A General Approach to Hypothesis Testing for Nonparametric Tests
Researchers have preferred normal-theory tests over nonparametric procedures, despite evidence that the statistical properties of the latter are sometimes superior for variables and subject populations frequently encountered in educational and psychological research. Two ongoing concerns among researchers are that non parametric tests exist only in simple cases (e.g., univariate one-, two-, and /-sample tests) and that these tests are often not available in statistical computing programs. The nonparametric hypothesis-testing model of Puri and Sen (1969, 1985) cir cumvents these concerns by permitting a variety of statistical hypotheses to be tested using existing computing programs. The breadth and flexibility of this model is il lustrated with several examples. NORMAL-THEORY TESTS have been used more widely in educational and psychological research than nonparametric procedures. In this article, normal-theory tests will be identified by their reliance on a normality as sumption for the distribution of scores and nonparametric tests by a data transformation, e.g., replacing the original scores with ranks, whose sole purpose is to remove the normality requirement. Nonparametric analysis of qualitative data (i.e., contingency table analysis) is not considered. The im portance of evaluating the normality assumption underlying normal-theory tests has been reinforced by the work of Micceri (1989), whose results sug gest that the bulk of educational and psychological data are at least mod erately and sometimes strikingly nonnormal (e.g., polymodal). Under these conditions, data-analytic alternatives that are not dependent upon a nor mality assumption (e.g., nonparametric tests) deserve serious consideration. Why then do so many researchers prefer normal-theory tests? One reason is their supposed statistical power advantage over nonparametric tests. Despite theoretical and empirical evidence that nonparametric tests possess competitive power properties over a broad range of data conditions (Marascuilo & McSweeney, 1977, chpt. 4; Lehmann, 1975, pp. 69-81), many researchers remain skeptical that a test based on ranks can be more