What a p-value actually is

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Define a p-value precisely, state what it does and does not tell you, and list the common misinterpretations. Where does this matter in a quant research pipeline?

Accepted Answer

Definition. A p-value is the probability, assuming the null hypothesis is true, of observing data at least as extreme as what you actually saw: p = P\big(	ext{test statistic as or more extreme than observed} \mid H0\big). It measures how surprising your data would be under the null. A small p-value means the observed result would be unusual if nothing were going on, so it is evidence against the null. What it is not. The p-value is a statement about the data given the hypothesis, not the hypothesis given the data. Common misreadings: - It is not P(H0 	ext{ is true} \mid 	ext{data}). That i…

What a p-value actually is

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