When research data are measured on at least an ordinal scale and the assumptions required in the theory underlying parametric statistical methods are in question, nonparametric procedures based on the ranks provide a sound approach to statistical analysis. Biomedical investigations, especially clinical trials, typically involve multivariate response and therefore multivariate statistical methods are called for in the interpretation of results. We discuss applications of the nonparametric multivariate rank test for completely randomized designs. Large sample theory can be used to support these statistical methods for assessing group differences in location. In small samples, randomization tests provide a basis for inferences. The execution of the procedure is facilitated by a computer program developed by the authors.