Comparing nonparametric tests of equality of means for randomized block designs

A number of nonparametric tests are compared empirically for a randomized block layout. We assess tests appropriate for when the data are not consistent with normality or when outliers invalidate traditional analysis of variance (ANOVA) tests. The objective is to assess, within this setting, tests that use ranks within blocks, the rank transform procedure that ranks the complete sample and continuous analogs of the Cochran-Mantel-Haenszel tests. The usual linear model is assumed, and our primary foci are tests of equality of means and component tests that assess linear and quadratic trends in the means. These tests include the traditional Page and Friedman tests. We conclude that the rank transform tests have competitive power and warrant greater use than is currently apparent.