Abstract

The aim of the article is to propose a way to determine to what extent a hypothesis H is confirmed if it has successfully passed a classical significance test. Bayesians have already raised many serious objections against significance testing, but in doing so they have always had to rely on epistemic probabilities and a further Bayesian analysis, which are rejected by classical statisticians. Therefore, I will suggest a purely frequentist evaluation procedure for significance tests that should also be accepted by a classical statistician. This procedure likewise indicates some additional problems of significance tests. In some situations, such tests offer only a weak incremental support of a hypothesis, although an absolute confirmation is necessary, and they overestimate positive results for small effects, since the confirmation of H is often rather marginal in these cases. In specific cases, for example, in cases of ESP-hypotheses, such as precognition, this phenomenon leads too easily to a significant confirmation and can be regarded as a form of the probabilistic falsification fallacy.