Rank tests for patterned alternatives in two-way non-parametric analysis of variance |
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| Institution: | 1. Fondation FondaMental, Créteil, France;2. INSERM U955, Translational Psychiatry team, Créteil, France;3. Pôle Psychiatrie Universitaire, CHU Sainte-Marguerite, F-13274 Marseille Cedex 09, France;4. Centre Hospitalier Charles Perrens, Université de Bordeaux, F-33076 Bordeaux, France;5. Hôpitaux Universitaires de Strasbourg, Université de Strasbourg, INSERM U1114, Fédération de Médecine Translationnelle de Strasbourg, Strasbourg, France;6. Service Universitaire de Psychiatrie Adulte, Hôpital la Colombière, CHRU Montpellier, Université Montpellier 1, Inserm 1061, Montpellier, France.;7. CMP B, CHU, EA 7280 Faculté de Médecine, Université d''Auvergne, BP 69, 63003 Clermont-Ferrand Cedex 1, France.;8. INSERM U1028, CNRS UMR5292, Centre de Recherche en Neurosciences de Lyon, Université Claude Bernard Lyon 1, Equipe PSYR2, Centre Hospitalier Le Vinatier, Pole Est, 95 bd Pinel, BP 30039, 69678 Bron Cedex, France.;9. AP-HP, Department of Psychiatry, Louis Mourier Hospital, Colombes, Inserm U894, Université Paris Diderot, Sorbonne Paris Cité, Faculté de médecine, France.;10. Centre Référent de Réhabilitation Psychosociale, CH Alpes Isère, Grenoble, France.;11. Assistance Publique des Hôpitaux de Marseille (AP-HM), pôle universitaire de psychiatrie, Marseille, France.;12. Service Universitaire de psychiatrie d''adulte, Centre Hospitalier de Versailles, Laboratoire EA4047 HandiRESP, Université Versailles Saint-Quentin-en-Yvelines, Le Chesnay, France;13. Inserm, Neurocentre Magendie, Physiopathologie de la Plasticité Neuronale, U862, F-33000 Bordeaux, France;14. CNRS UMR 5287-INCIA, France;15. Sorbonne Universités, UPMC Univ Paris 06, INSERM, UMR_S 1136, Institut Pierre Louis d''Epidémiologie et de Santé Publique, F-75013 Paris, France;p. Paris Est University, DHU Pe-PSY, Pôle de Psychiatrie des Hôpitaux Universitaires H Mondor, Créteil, France;1. Sonoma State University, Rohnert Park, CA, USA;2. Old Dominion University, Norfolk, VA, USA |
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| Abstract: | We consider the problem of testing against trend and umbrella alternatives, with known and unknown peak, in two-way layouts with fixed effects. We consider the non-parametric two-way layout ANOVA model of Akritas and Arnold (J. Amer. Statist. Assoc. 89 (1994) 336), and use the non-parametric formulation of patterned alternatives introduced by Akritas and Brunner (Research Developments in Probability and Statistics: Festschrift in honor of Madan L. Puri, VSP, Zeist, The Netherlands, 1996, pp. 277–288). The hypotheses of no main effects and of no simple effects are both considered. New rank test statistics are developed to specifically detect these types of alternatives. For main effects, we consider two types of statistics, one using weights similar to Hettmansperger and Norton (J. Amer. Statist. Assoc. 82 (1987) 292) and one with weights which maximize the asymptotic efficacy. For simple effects, we consider in detail only statistics to detect trend or umbrella patterns with known peaks, and refer to Callegari (Ph.D. Thesis, University of Padova, Italy) for a discussion about possible statistics for umbrella alternatives with unknown peaks. The null asymptotic distributions of the new statistics are derived. A number of simulation studies investigate their finite sample behaviors and compare the achieved alpha levels and power with some alternative procedures. An application to data used in a clinical study is presented to illustrate how to utilize some of the proposed tests for main effects. |
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