Can p-values be interpreted as continuous measures of evidence for an effect?

Note also the blog post by Daniel Lakens on the same topic here. Update March 23, 2022: a more concise / slightly modified version of these thoughts was published as a letter in TREE, co-authored together with Fred Barraquand. Background Criticism of p-values has been rampant in recent years, as were predictions of their imminent…

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Is the p-value a conditional probability?

A comment by Deborah Mayo on a recent post by Andre Gelman started a heated and surprisingly subtle discussion on the correct (frequentist) definition of the p-value that currently continues on Larry Wasserman blog. Read for yourself – I for myself am still happy to write p(D>d|H0) ;).