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A statistical test can be seen as a procedure to produce a decision based onobserved data, where some decisions consist of rejecting a hypothesis (yieldinga significant result) and some do not, and where one controls the probabilityto make a wrong rejection at some pre-specified significance level. Whereastraditional hypothesis testing involves only two possible decisions (to rejector not a null hypothesis), Kaiser's directional two-sided test as well as themore recently introduced Jones and Tukey's testing procedure involve threepossible decisions to infer on unidimensional parameter. The latter procedureassumes that a point null hypothesis is impossible (e.g. that two treatmentscannot have exactly the same effect), allowing a gain of statistical power.There are however situations where a point hypothesis is indeed plausible, forexample when considering hypotheses derived from Einstein's theories. In thisarticle, we introduce a five-decision rule testing procedure, which combinesthe advantages of the testing procedures of Kaiser (no assumption on a pointhypothesis being impossible) and of Jones and Tukey (higher power), allowingfor a non-negligible (typically 20%) reduction of the sample size needed toreach a given statistical power to get a significant result, compared to thetraditional approach.

A five-decision testing procedure to infer on unidimensional parameter