Many ‘distribution‐free’ statistical tests using very different computational procedures can be viewed as special cases of two general tests based on the principle of analysis of variance by ranks. The first test, due to Bernard&Van Elteren (1953), is a general test for any differences among the samples. The second test evaluates trends and contrasts between the samples. The two general procedures embrace popular tests by Friedman, Kruskal, Cochran, Spearman, Wilcoxon, Mann&Whitney, Dixon&Mood, Page and Marascuilo&McSweeney as well as chi‐square tests for contingency tables whose dependent variable is in the form of dichotomous or rankable categories. The system can be used to generate convenient computational formulac for a range of new designs, to express popular procedures in a unified notation, as a teaching aid to illustrate the relationships among tests and as the basis for a simple computer program to analyse data from any design within the