A statistical inference strategy (FOSTIS): A non-confounded hybrid theory

Due to the many misconceptions surrounding the common significance tests, a catalogue of demands to be satisfied by statistical induction is developed. The result of such criteria is a four step hybrid theory of statistical inference (FOSTIS), which is organized hierarchicalry: starting with a planning phase (Neyman-Pearson), going on with a loglikelihood-test (Bayes, Fisher, wald), coming to a maximum likelihood-test (Edwards), and ending with an effect qualification. strengths and weaknesses of this approach are discussed. Generally, there is something to be learned: the more meaningful statistical induction should be the more precise theoretical deduction must be.