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A note on p-values interpreted as plausibilities
P-values are a mainstay in statistics but are often misinterpreted. We
propose a new interpretation of p-value as a meaningful plausibility, where
this is to be interpreted formally within the inferential model framework. We
show that, for most practical hypothesis testing problems, there exists an
inferential model such that the corresponding plausibility function, evaluated
at the null hypothesis, is exactly the p-value. The advantages of this
representation are that the notion of plausibility is consistent with the way
practitioners use and interpret p-values, and the plausibility calculation
avoids the troublesome conditioning on the truthfulness of the null. This
connection with plausibilities also reveals a shortcoming of standard p-values
in problems with non-trivial parameter constraints.Comment: 13 pages, 1 figur
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