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  "body": "\n## Summary\n\nMultivariate analysis of variance, or MANOVA, tests whether several groups have the same mean vector when each observation consists of several measurements.\nIt extends the [[analysis of variance|M9AQ5HKGP4]] from one response variable to a vector of responses.\nIt compares a between-group and a within-group matrix of sums of squares and cross-products.\nCommon test statistics are Wilks' lambda, Pillai's trace, the Hotelling–Lawley trace and Roy's largest root.\n\n## Explanations\n\n### L1 human\n\nThree teaching methods may be compared by both reading scores and writing scores of the pupils.\nRunning two separate comparisons ignores that the two scores are correlated.\nMANOVA asks one question about both scores at once: do the groups differ in their average pair of scores?\nIt weighs how far apart the group averages are against how much the pupils vary inside each group.\n",
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