What a p-value actually means

Question

Define the p-value precisely, and list the most common ways it is misinterpreted.

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Definition. Fix a null hypothesis H0 and a test statistic T. The p-value is p = \mathbb{P}\big(T 	ext{ as or more extreme than the observed value} \;\big\; H0 	ext{ true}\big). It is the probability, computed under the assumption that the null is true, of seeing data at least as extreme as what you got. That is all it is: a tail probability of the data given H0, in the direction the alternative points. Common misconceptions. 1. "The p-value is the probability that H0 is true." False, and it is the central error. The p-value is \mathbb{P}(	ext{data} \mid H0), not \mathbb{P}(H0 \mid 	ext{da…

What a p-value actually means

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