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Philosophia Mathematica Advance Access originally published online on March 13, 2007
Philosophia Mathematica 2007 15(2):166-192; doi:10.1093/philmat/nkm001
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Copyright © The Author 2007. Published by Oxford University Press.

Falsification of Propensity Models by Statistical Tests and the Goodness-of-Fit Paradox

Christian Hennig*

* Department of Statistical Science, University College London WC1E 6BT, U.K.

Correspondence: chrish{at}stats.ucl.ac.uk

Gillies introduced a propensity interpretation of probability which is linked to experience by a falsifying rule for probability statements. The present paper argues that general statistical tests should qualify as falsification rules. The ‘goodness-of-fit paradox’ is introduced: the confirmation of a probability model by a test refutes the model's validity.

An example is given in which an independence test introduces dependence. Several possibilities to interpret the paradox and to deal with it are discussed. It is concluded that the propensity interpretation properly reflects statistical practice, but it is not as objective as some adherents claim.


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