Probabilities of sign errors as calibrated p-values

What is it about?

A sign error occurs whenever the estimated direction of an effect is mistaken. For example, a sign error occurs when a study concludes that an effect of a treatment is positive when it is actually negative or zero. This paper proposes a simple way to use a p-value and a prior probability to estimate the posterior probability of a sign error.

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Why is it important?

This paper's proposed calibration of the p-value reduces to standard Bayesian calibrations at one extreme and standard frequentist p-values at the other extreme. The two extremes are high and low values of the prior probability of the null hypothesis with a spectrum of compromises for medium values of the prior probability.

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