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    $\begingroup$ You could say that more than formalizing it, Bayes allows it to happen. Without Bayesian thinking, quantities such as a p-value (P(data more impressive than mine if the null hypothesis is true)) are at most indirect measures of evidence. Frequentism deals with the probability of making an assertion and Bayes deals with the probability that a made assertion is true. hbiostat.org/bbr/md/alpha.html $\endgroup$ Commented Apr 2, 2022 at 14:29