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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

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

Jan Sprenger

Stephan Hartmann

Publisher:
Oxford University Press
DOI:10.1093/oso/9780199672110.003.0009

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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