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The most common<ref>{{cite web|last=Garson|first=G. David|title=Multivariate GLM, MANOVA, and MANCOVA|url=http://faculty.chass.ncsu.edu/garson/PA765/manova.htm|accessdate=2011-03-22}}</ref><ref>{{cite web|last=UCLA: Academic Technology Services, Statistical Consulting Group.|title=Stata Annotated Output -- MANOVA|url=http://www.ats.ucla.edu/stat/stata/output/Stata_MANOVA.htm|accessdate=2011-03-22}}</ref> statistics are summaries based on the roots (or [[eigenvalues]]) <math>\lambda_p</math> of the <math>A</math> matrix:
* [[Samuel Stanley Wilks]]' <math>\Lambda_{Wilks} = \prod _{1...p}(1/(1 + \lambda_{p})) = \det(I + A)^{-1} = \det(\Sigma_{res})/\det(\Sigma_{res} + \Sigma_{model})</math>
* the Pillai-[[M. S. Bartlett]] [[trace of a matrix|trace]], <math>\Lambda_{Pillai} = \sum _{1...p}(\lambda_{p}/(1 + \lambda_{p})) = \mathrm{tr}((I + A)^{-1})</math><ref>http://www.real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/manova-basic-concepts/</ref>
* the Lawley-[[Harold Hotelling|Hotelling]] trace, <math>\Lambda_{LH} = \sum _{1...p}(\lambda_{p}) = \mathrm{tr}(A)</math>
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