A nonparametric test statistic for the general linear model

Puri and Sen (1969,1985) presented a nonparametric test statistic based on a general linear model approach that is appropriate for testing a wide class of hypotheses. The two forms of this statistic, pure- and mixed-rank, differ according to whether the original predictor values or their ranks are used. Both forms permit the use of standard statistical packages to perform the analyses. The applicability of these statistics in testing a number of hy-potheses is highlighted, and an example of their use is given. A simulation study for the multivariate-multiple-regression case is used to examine the distributional behavior of the pure- and mixed-rank statistics and an im-portant competitor, the rank transformation of Conover and Iman (1981). The results suggest that the pure- and mixed-rank statistics are superior with respect to minimizing liberal Type I error rates, whereas the Conover and Iman statistic produces larger power values. The use of nonparametric tests in educational and psychological research is typically limited to a small number of univariate between- and within-subjects designs and analyses. In this paper nonparametric tests are distin-guished from other procedures by their lack of a normality assumption on the relevant score distribution. In contrast to their multivariate-parametric (i.e., normal-theory) counterparts, the availability in the literature of multivariate-nonparametric procedures is fairly recent (e.g., Katz & McSweeney, 1980; Serlin & Marascuilo, 1983; Zwick, 1985). Hence, re-searchers may not be familiar with these procedures and their application to design and analysis problems. The difficulty of checking the normality assumption, and the likelihood of nonnormal data in educational and psy-chological research (Micceri, 1989), makes a nonparametric alternative attractive. The authors are indebted to the editor for a number of suggestions that were of great value in structuring the paper