Definition

P-value

The probability of observing data at least as extreme as yours if the null hypothesis were true. It is not the probability that the hypothesis is true.

A p-value answers a narrow, conditional question: assuming there is really no effect (the null hypothesis), how surprising is data like mine? Small p-values mean the data would be rare under the null — which is evidence against it, by convention "significant" below 0.05.

What it is not: the probability the null is true, the probability the finding replicates, or a measure of importance. A tiny effect in a huge sample can have p < .001; a large effect in a small sample can miss .05. This is why journals increasingly require effect sizes and confidence intervals alongside p-values.