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Bayesian Philosophy of Science$
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Jan Sprenger and Stephan Hartmann

Print publication date: 2019

Print ISBN-13: 9780199672110

Published to Oxford Scholarship Online: October 2019

DOI: 10.1093/oso/9780199672110.001.0001

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Hypothesis Tests and Corroboration

Hypothesis Tests and Corroboration

(p.227) Variation 9: Hypothesis Tests and Corroboration
Bayesian Philosophy of Science

Jan Sprenger

Stephan Hartmann

Oxford University Press

According to Popper and other influential philosophers and scientists, scientific knowledge grows by repeatedly testing our best hypotheses. However, the interpretation of non-significant results—those that do not lead to a “rejection” of the tested hypothesis—poses a major philosophical challenge. To what extent do they corroborate the tested hypothesis or provide a reason to accept it? In this chapter, we prove two impossibility results for measures of corroboration that follow Popper’s criterion of measuring both predictive success and the testability of a hypothesis. Then we provide an axiomatic characterization of a more promising and scientifically useful concept of corroboration and discuss implications for the practice of hypothesis testing and the concept of statistical significance.

Keywords:   Hypothesis testing, null hypothesis significance tests (NHST), non-significant results, frequentist statistics, Bayes factors, Bayesian confirmation, corroboration, Karl R. Popper

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