Rank-based tests for interactions in a two-way design when there are ties

Among the non-parametric approaches to defining and testing the hypothesis of no interactions in a two-way design, the method by Patel and Heel is app ealing because it is a function of the ranks and therefore invariant under monotonic increasing transformations of the data, and it does not require t he assumption of no main effects fur the approach to be valid, Recently, Wi lcox compared three different methods for implementing their method, each m ethod differing in how the appropriate standard error is estimated. In term s of Type I errors, only one of the methods gave satisfactory results in si mulations, but it assumes there are no tied values. Cliff has considered th e problem of tied values in detail, and his results are easily extended to the problem considered by Wilcox. This paper describes this extension and c ompares it to the method recommended by Wilcox.