On the Interpretation of P-Values

Suppose that the p-value for an hypothesis test has a Uniform [0,1] distribution when the null hypothesis is true. This paper proposes a ”rough and ready” rule for the interpretation of the evidence corresponding to such p-values. The rule is to use B̄∗(p) = 1/{epln(1/p)} as an upper bound on the Bayes factor against the null hypothesis for p ≤ 1/e = 0.368 . The rule is found to work well for two-sided z-tests, one-sided z-tests, and two-sided t-tests with degrees of freedom at least in the teens. The rule is plausible for Chi-squared tests. If the prior distribution under the alternative is chosen so that the median p-value is between .05 and .01, then (3/4)B̄∗(p) is found to be a good ballpark estimate of the Bayes factor in these situations when the p-value is between .05 and .001.