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  "body": "\n## Summary\n\nThe Wilcoxon signed-rank test is a [[hypothesis test|087P03NEND]] for the centre of a symmetric distribution, most often applied to the differences within matched pairs.\nIt ranks the absolute values of the observations and adds the ranks of the positive ones.\nUnlike the [[sign test|NBK6G2VB7A]], it uses how far each observation lies from the hypothesised centre.\nSo it is usually more powerful, but it assumes that the distribution is symmetric.\nIt is the rank-based counterpart of the one-sample $t$-test.\n\n## Explanations\n\n### L1 human\n\nSuppose you measure each patient before and after a treatment and take the differences.\nIf the treatment does nothing, positive and negative differences of each size should be equally likely.\nSort the differences by size, ignoring the sign, and number them $1, 2, 3, \\dots$ from smallest to largest.\nAdd up the numbers that belong to positive differences.\nA total near the maximum means that the large differences are mostly positive, which is evidence of an effect.\n",
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