P-values and probability
In all kinds of hypothesis test, p-values are equally likely anywhere between 0 and 1 when the null hypothesis holds. Small p-values are therefore possible, though unlikely, even under the null hypothesis.
A simulation illustrates the distribution of the p-value, both when the null and alternative hypotheses hold.
Interpretation of p-value
We now describe a way to interpret p-values that can be applied to any hypothesis test.