P-value

A p-value is the probability of obtaining data at least as extreme as the observed data, assuming the null hypothesis and every other model assumption is correct. It is derived from a test statistic and runs from 0 to 1. The 0.05 threshold traces back to Fisher and has no special mathematical status. In 2016 the American Statistical Association issued a formal statement, the first of its kind in its history, setting out six principles. Among them: a p-value does not measure the probability that the hypothesis is true, it does not measure effect size or importance, and scientific conclusions should not rest on whether a value passes a threshold. The standard misinterpretations are well documented. A value of 0.03 does not mean a 3% chance the finding is a fluke. A value above 0.05 does not establish that no effect exists, since absence of evidence is not evidence of absence. Two studies landing on opposite sides of 0.05 are not in conflict when their confidence intervals overlap heavily. The practical failure mode is selective analysis. Testing many outcomes, subgroups or cut-points until one crosses 0.05 pushes the false positive rate far above 5%. Nutrition and longevity trials measuring dozens of biomarkers are exposed, which is why preregistered primary endpoints matter.

Last reviewed: August 25, 2026

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