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  "body": "\n## Summary\n\nThe Cramér–von Mises criterion measures how far an [[empirical distribution function|A05WR6TEK5]] is from a hypothesised [[cumulative distribution function|0H8H7ZTHW2]] by an integrated squared difference.\nIt gives a goodness-of-fit [[hypothesis test|087P03NEND]] that, like the [[Kolmogorov–Smirnov test|YZYHWC6C5F]], has the same null law for every continuous hypothesised distribution.\nWhere the Kolmogorov–Smirnov statistic looks at the single largest gap, this criterion adds up the squared gaps over the whole line.\nA two-sample version compares two empirical distribution functions.\n\n## Explanations\n\n### L1 human\n\nPicture the staircase of the data and the curve of the expected distribution on one graph.\nInstead of looking for the single widest gap, square the gap at every point and average these squares along the curve.\nA large average means that the data and the curve disagree over a wide range, not only at one place.\nFor one observation at $0.5$ tested against the uniform law on $[0, 1]$, the statistic is $1/12$.\n",
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