Calibration of p values for testing precise null hypotheses

P values are the most commonly used tool to measure evidence against a hypo thesis or hypothesized model. Unfortunately, they are often incorrectly vie wed as an error probability for rejection of the hypothesis or, even worse, as the posterior probability that the hypothesis is true. The fact that th ese interpretations can be completely misleading when testing precise hypot heses is first reviewed, through consideration of two revealing simulations . Then two calibrations of a p value are developed, the first being interpr etable as odds and the second as either a (conditional) frequentist error p robability or as the posterior probability of the hypothesis.