---
tag: 8J3B7N8CAT
kind: concept
name: Multivariate analysis of variance
msc: [62H15, 62J10]
specializes: [M9AQ5HKGP4]
sources:
  - url: https://en.wikipedia.org/wiki/Multivariate_analysis_of_variance
same_as:
  wikidata: Q929408
  wikipedia: Multivariate analysis of variance
---

## Summary

Multivariate analysis of variance, or MANOVA, tests whether several groups have the same mean vector when each observation consists of several measurements.
It extends the [[analysis of variance|M9AQ5HKGP4]] from one response variable to a vector of responses.
It compares a between-group and a within-group matrix of sums of squares and cross-products.
Common test statistics are Wilks' lambda, Pillai's trace, the Hotelling–Lawley trace and Roy's largest root.

## Explanations

### L1 human

Three teaching methods may be compared by both reading scores and writing scores of the pupils.
Running two separate comparisons ignores that the two scores are correlated.
MANOVA asks one question about both scores at once: do the groups differ in their average pair of scores?
It weighs how far apart the group averages are against how much the pupils vary inside each group.