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  "body": "\n## Summary\n\nAnalysis of variance, or ANOVA, is a family of methods that split the total variation of a response into parts.\nEach part is due to one source, such as treatment groups or random error.\nIts best known use is to test whether several group means are equal.\nThe test compares the variation between groups with the variation within groups through an [[F-test|8MTVCMAATD]].\nIt was developed by Ronald Fisher for agricultural experiments and is a central tool of [[design of experiments|2TE42ZWJ3E]].\nThe fixed-effects models of ANOVA are special cases of the [[general linear model|A06SGFCSCE]].\n\n## Explanations\n\n### L1 human\n\nSuppose three fertilisers are each tried on several plots and the yields vary.\nSome of the variation is because the fertilisers differ, and some is just plot-to-plot noise.\nANOVA measures both: how far the group averages are from the overall average, and how far the plots are from their own group average.\nIf the first is large compared with the second, the fertilisers probably differ.\nFor the groups $\\{1, 2, 3\\}$ and $\\{4, 5, 6\\}$, the between-group sum of squares is $13.5$ and the within-group sum is $4$, which together make the total $17.5$.\n",
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