The use of a vector of sign statistics as the basis of a nonparametric test for equality of distributions in one‐way layouts is considered. An important feature of this test is its ability to detect a broad range of alternatives, including scale and shape differences. In this scenario, the data consist of several independent measurements on each treatment or subject. Presented here are a finite sample and asymptotic distribution theory for the test statistics and a discussion of a follow‐up clustering procedure based on a mixture model approximation. Finally, the methods are illustrated using two examples from the literature.