Distribution-Free Tests for Main Effects in Multifactor Designs

This article concerns distribution-free tests for main effects in M . 1 factor designs when the factors are crossed.A single test statistic using Wilcoxon type scores is introduced that can be used for designs with any value of M.We illustrate that the properties of the test statistic, such as limiting distribution and asymptotic relative efficiency (ARE), can be obtained from known properties of test statistics proposed for two-factor designs.Large-sample properties are found based on cell sizes tending to infinity and based on the number of levels of the other factors tending to infinity.It is also shown that the Kruskal.Wallis and Friedman test statistics are special cases.