Nonparametric rank based main effects test procedures for the two-way layout in the presence of interaction
In spite of an extensive literature dealing with rank approaches to testing for main effects when an additive model is assumed, virtually no consideration has been given to developing nonparametric main effects test procedures that adjust for the possible presence of interaction in a non-additive model. This problem has been briefly discussed in Iman (1974), but has otherwise been ignored in the literature.
In this paper, we approach the two-way layout setting through an arbitrary non-additive model. We propose a technique for adjusting the data to account for the possible presence of interaction prior to conducting a rank test for either of the main effects. These adjustments involve both alignment and ranking of the data and utilize the basic properties of Latin squares. We discuss the results of a Monte Carlo simulation study of the relative powers of this new procedure and other nonparametric procedures designed only for an additive model.
Journal of Nonparametric Statistics