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  "body": "\n## Summary\n\nWhen several [[hypothesis tests|087P03NEND]] are done together, the family-wise error rate is the probability of at least one [[type I error|03N8C8ZR4B]] among them.\nControlling it at level $\\alpha$ protects against any false rejection in the whole family.\nThe [[Bonferroni correction|8GRD2TMJRR]] is the simplest procedure that controls it.\n\n## Explanations\n\n### L1 human\n\nIf you run $20$ independent tests at level $5\\%$ and all null hypotheses are true, the chance of at least one false alarm is $1 - 0.95^{20}$, about $64\\%$.\nThe family-wise error rate is this chance of at least one false alarm.\nA multiple testing procedure that controls it keeps this chance below a chosen level, such as $5\\%$.\n",
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