How Strong is the Confirmation of a Hypothesis by Significant Data?

Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 47 (2):277-291 (2016)
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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.

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Thomas Bartelborth
Universität Leipzig

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Interpretations of probability.Alan Hájek - 2007 - Stanford Encyclopedia of Philosophy.
Resurrecting logical probability.James Franklin - 2001 - Erkenntnis 55 (2):277-305.
Do large probabilities explain better?Michael Strevens - 2000 - Philosophy of Science 67 (3):366-390.
A statistical paradox.D. V. Lindley - 1957 - Biometrika 44 (1/2):187-192.

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