Falsification or choice among alternatives: The unsolved dilemma of hypothesis testing

Summary The scientific attitude towards statistical method has always pursued two basic objectives: identifying false assumptions and selecting, amongst the likely assertions, those which are most consistent with a given system. The methodological demarcation between rejection of a statistical statement, because it is ?false?, or exclusion, because it is ?least probable?, lies in the fundamental premises of inferential procedures. In the first class we find the methods proposed by Fisher, Neyman and Pearson; in the second one, the Bayesian techniques. Even if different inferential theories may coexist, any particular solution has a limit of validity strictly bouded, to the conventional procedural rules on which it is based. Invited paper at the Conference on ?Statistical Tests: Methodology and Econometric Applications?, held in Bologna, Italy, 27–28 May 1993.