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  "body": "\n## Summary\n\nThe Bonferroni correction is the simplest way to test many hypotheses at once: test each of $m$ hypotheses at level $\\alpha/m$.\nBy [[Boole's inequality|0EGSEE9J9R]], the [[family-wise error rate|GQCY1N8JZT]] is then at most $\\alpha$.\nIt needs no assumption on the dependence between the tests, but it loses power when $m$ is large.\n\n## Explanations\n\n### L1 human\n\nIf you look at many results, some will look surprising just by chance.\nThe Bonferroni correction makes each single test stricter by dividing the threshold by the number of tests.\nWith $20$ tests and an overall level of $5\\%$, each p-value must be below $0.0025$ to count.\nThen the chance of even one false alarm in the whole family is at most $5\\%$.\n",
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