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

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4.2. Balanced and Unbalanced Data

When the design is balanced in the sense that each group has the same number of measurements or certain orthogonality conditions are met (Searle, 1971), the analysis is relatively much simpler with respect to the computations as well as interpretations. In this case for a given response variable, the (univariate) ANOVA partitioning (Searle, 1971) of the corrected total sums of squares into various sources of variation specified by the model is unique. This simplicity is unfortunately lost as soon as the underlying design becomes unbalanced. The partitioning of the corrected total sums of squares is no longer unique in that it depends on the model and the various submodels of it as specified by the order in which ...

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