Abstract
Distribution-free methods are considered for comparing k 1 treatments to k 2 controls in the one-way layout. Using normal scores statistics, one-sided tests are developed for k 1 treatment versus k 2 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 k 1 and k 2 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.
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Solorzano, E. Nonparametric comparisons with k 2 > 2 controls using normal scores and savage statistics. Computational Statistics 21, 463–472 (2006). https://doi.org/10.1007/s00180-006-0006-z
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DOI: https://doi.org/10.1007/s00180-006-0006-z