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P Values and replication: the problem is not what you think

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Abstract It has been claimed that there is a crisis of replication in science. Prominent amongst the many factors that have been fingered as being responsible is the humble and ubiquitous P-value. One journal has even gone so far as to ban all inferential statistics. However, it is one thing to banish measures of uncertainty and another to banish uncertainty from your measures. I shall claim that the apparent discrepancy between P-values and posterior probabilities is as much a discrepancy between two approaches to Bayesian inference as it is between frequentist and Bayesian frameworks and that a further problem has been misunderstandings regarding predictive probabilities. I conclude that banning P-values won’t make all published results repeatable and that it is possible undesirable that it should.

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