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ANOVA stands for ANalysis Of VAriance, a statistical model and set of procedures for comparing multiple group means. The independent variables in an ANOVA model are categorical, but an ANOVA table can be used to test continuous variables as well.
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What is the variance decomposition method?
I think it is related to ANOVA or factor analysis, but I could not find something which looks applicable in my particular setting, because I only have observations $x_{ij}$. …