A class of rank tests for interaction in two-way layouts

A class of aligned rank order tests for interaction in two-way layouts is considered. The technique is based on application of the existing nonparametric techniques for one-way layouts to the transformed observations. It is shown that the asymptotic properties of these techniques are preserved after alignment. Furthermore, asymptotic relative efficiency comparisons are made with some of the competing tests. Finally, we demonstrate that our technique can be used to test for higher-order interactions in general multi-factor layouts.