Analysis of Variance

Wed, 11 Nov 2026 14:00:00 +1100

analysis of variance compares the means of groups. it was born as its own subject, with its own tables and vocabulary, but once a categorical predictor is written as a block of indicator columns it is simply a linear gaussian model — the same \(\hat\beta = (\mathbf{X}^\top\mathbf{X})^{-1}\mathbf{X}^\top\mathbf{y}\), the same nested \(F\)-test from estimation & inference. what is genuinely new is the bookkeeping: how to code a factor so the design matrix has full rank, what the coefficients then mean, and how the total variation splits into a between-groups and a within-groups part. 𐃏

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Analysis of Variance