Faut-il contrôler l’erreur de type I dans le cas de comparaisons de moyennes multiples? Must we over-control the type I error rate in post anova multiple comparison procedures?

Abstract

Almost since the creation of analysis of variance by Fisher in the years 1920’s, interpretation of its results and the multiple comparisons of means it entailed have raised the problem of the type I error rate (α) and its control. Fisher himself, then Tukey and many others have contributed to the question, finally stockpiling a plethora of principles, methods and suggestions, all aimed at keeping the effective α level within prescribed bounds, and all equally attractive to the naïve user. We revisit this controversial question, from the standpoint of the empirical researcher, and propose a severe stripping down of statistical-probabilistic complications, in order to give back to the researcher just what he needs to drive out and appraise the significant results in his data.