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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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Sum of squares decomposition: Intuitively, why should the cross term be zero?
The sum of squares decomposition produces this bit of algebra:
$$\sum (y_i - \bar{y})^2 = \sum(y_i - \hat{y}_i)^2 + \sum(\hat{y}_i - \bar{y})^2 + 2 \sum (y_i - \hat{y}_i)(\hat{y}_i - \bar{y}).$$
The …
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Multifactor ANOVA- What is the connection between sample size and orthogonality?
It is commonly stated that "balanced" designs in multifactor ANOVA (equal sample sizes in each group) have "orthogonal" factors. … But for ANOVA, I'm at a loss. I can't figure out how factors in ANOVA correspond to some kind of geometric objects that are orthogonal. …
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What does the intercept correspond in the Anova() function in R?
The Anova function from car calculates this in a somewhat backwards way because it's easiest to grab numbers that are available to it from the lm object. … All I can do at the moment is reproduce how Anova calculates it. …