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APPLIED MULTIVARIATE STATISTICS: WITH SAS® SOFTWARE by Dayanand N. Naik, Ravindra Khattree

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5.4. Factorial Designs

When the treatment combinations are made up of various levels of several factors, then both the multivariate and univariate approaches are generalized in a straightforward way. It is so because all these situations can still be dealt within the general framework of multivariate linear model. Also, the assumption of compound symmetry of covariance structure needed in the univariate analysis is on the error. Therefore, what design has been used for data collection does not affect the univariate approach. For the multivariate approach, the MANOVA partitioning of the total sums of squares and crossproduct matrix has been seen to be the straightforward generalization of the univariate ANOVA and therefore the multivariate approach ...

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