Nonparametric comparisons with k2 > 2 controls using normal scores and savage statistics

Distribution-free methods are considered for comparing k1 treatments to k2 controls in the one-way layout. Using normal scores statistics, one-sided tests are developed for k1 treatment versus k2 control comparisons of medians. Using Savage statistics, analogous results are developed for comparing scale parameters of the treatments to the controls with non-negative data. Upper bounds for the Type I error probabilities are established for general k1 and k2 using the concept of partitions and a union–intersection algorithm. The code for the computations in this manuscript is available at http ://wsbe.unh.edu/WSBE_FacultyStaff / Faculty_Staff.cfm under the author’s name. Asymptotic relative efficiencies of these tests relative to their competitors are identical to their two-sample counterparts.