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  "body": "\n## Summary\n\nThe false discovery rate of a multiple testing procedure is the expected proportion of false rejections among all rejections.\nControlling it is less strict than controlling the [[family-wise error rate|GQCY1N8JZT]], so it allows more discoveries when many hypotheses are tested.\nThe Benjamini–Hochberg procedure is a simple step-up rule on the ordered [[p-values|0GGKJGZF6D]] that controls the false discovery rate under independence.\n\n## Explanations\n\n### L1 human\n\nIn a study with thousands of tests, such as gene screens, a few false alarms are acceptable if most discoveries are real.\nThe false discovery rate is the average fraction of false alarms in the list of discoveries.\nThe Benjamini–Hochberg procedure sorts the p-values and compares the $i$-th smallest with $i q/m$.\nIt rejects all hypotheses up to the last p-value below its threshold.\nWith $q = 0.1$, on average at most about one discovery in ten is false.\n",
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