Information About ™Manova |
| CATEGORIES ABOUT MANOVA | |
| analysis of variance | |
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Where sums of squares appear in univariate analysis of variance, in multivariate analysis of variance certain Positive-definite Matrices (see Matrix (mathematics) ) appear. The diagonal entries are the same kinds of sums of squares that appear in univariate ANOVA. The off-diagonal entries are corresponding sums of products. Under normality assumptions about Error distributions, the counterpart of the sum of squares due to error has a Wishart Distribution . Analogous to ANOVA, MANOVA is based on the product of model variance matrix and error variance matrix inverse. Invariance considerations imply the MANOVA statistic should be a measure of Magnitude of the Singular Value Decomposition of this matrix product, but there is no unique choice owing to the multi- Dimension al nature of the alternative hypothesis. The most common statistics are Samuel Stanley Wilks ' lambda (Λ), the Pillai- M. S. Bartlett trace (see Trace Of A Matrix ), the Lawley- Hotelling trace and Roy's Greatest Root . Discussion continues over the merits of each, though the greatest root leads only to a bound on significance which is not generally of practical interest. A further complication is that the distribution of these statistics under the Null Hypothesis is not straightforward and can only be approximated except in a few low-dimensional cases. The best-known Approximation for Wilks' lambda was derived by C. R. Rao . In the case of two groups all the statistics are equivalent and the test reduces to Hotelling's T-square . EXTERNAL LINK |
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