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Keywords:

  • Distribution-free test;
  • One-way classification;
  • Sample allocation;
  • Treatment versus control;
  • Two-way classification

Abstract  In this paper we propose distribution-free treatments versus control tests for the one- and two-way classifications. The null distribution properties are shown to be equivalent to those of well-known statistics for which critical values have been extensively tabled. Asymptotic relative efficiencies with respect to corresponding normal theory competitors are derived and optimal designs for the allocation of experimental units to the treatments and control are obtained.