Multivariate analysis of variance: Difference between revisions

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* the [[K. C. Sreedharan Pillai]]–[[M. S. Bartlett]] [[trace of a matrix|trace]], <math>\Lambda_\text{Pillai} = \sum_{1,\ldots,p}(\lambda_p/(1 + \lambda_p)) = \operatorname{tr}(A(I + A)^{-1})</math><ref>{{cite web|url=http://www.real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/manova-basic-concepts/|title=MANOVA Basic Concepts – Real Statistics Using Excel|website=www.real-statistics.com|access-date=5 April 2018}}</ref>

* the Lawley–[[Harold Hotelling|Hotelling]] trace, <math>\Lambda_\text{LH} = \sum_{1,\ldots,p}(\lambda_{p}) = \operatorname{tr}(A)</math>

* [[Roy's greatest root]] (also called ''Roy's largest root''), <math>\Lambda_\text{Roy} = \max_p(\lambda_p) = \|A\|_\infty </math>

Discussion continues over the merits of each,<ref name="Warne2014" /> although the greatest root leads only to a bound on significance which is not generally of practical interest. A further complication is that, except for the Roy's greatest root, the distribution of these statistics under the [[null hypothesis]] is not straightforward and can only be approximated except in a few low-dimensional cases.<ref>Camo http://www.camo.com/multivariate_analysis.html</ref>