permutation-p-value-add-one-correction
IN premise — summaries/2026/08/24/aristotelian-2026-sR-references-chunk-2.md
Created 2026-08-24T17:10:51+00:00
The permutation p-value is computed as p = (1 + #{null_scores ≥ s_obs}) / (K+1), where the +1 ensures p never equals zero and guarantees super-uniformity under exchangeability
Summary
The +1 adjustment in a permutation p-value is a small but essential fix that guarantees the result can never be exactly zero and keeps the test from rejecting the null hypothesis more often than its stated significance level allows. Without this correction, the test would be anti-conservative, meaning it would produce false positives at a rate higher than intended, undermining the validity of every downstream conclusion built on that p-value.