Abstract: Friedman’s test is a rank-based procedure that can be used to test for differences among t treatment distributions in a randomized complete block design. It is well-known that the test has reasonably good power under location-shift alternatives to the null hypothesis of no difference in the t treatment distributions. However the power of Friedman’s test when the alternative hypothesis consists of a non-location difference in treatment distributions can be poor. We develop the properties of an alternative rank-based test that has greater power than Friedman’s test in a variety of such circumstances. The test is based on the joint distribution of the t! possible permutations of the treatment ranks within a block (assuming no ties). We show when our proposed test will have greater power than Friedman’s test, and provide results from extensive numerical work comparing the power of the two tests under various configurations for the underlying treatment distributions.