anova is good for catergorical data and a good subsititue for linear modeling. It is a comparison of models.
| Source | Degrees of Freedom | Sum of Squares | Mean Square | F-ratio |
|---|---|---|---|---|
| Treatment | t − 1 | SSM | $MS_M = \frac{SS_M}{(t - 1)}$ | $F = \frac{MS_M}{MS_E}$ |
| Residual | (n − 1) − (t − 1) = n − t | SSE | $MS_E = \frac{SS_E}{(n - t)}$ | |
| Total | n − 1 | SST |
$SS_M = \sum _{j=1}^{t} \frac{Y_{j.}^2}{n_j} - \frac{Y_{..}^2}{N}$
$SS_E = {j=1}^{t} ( Y{jk} - )^2 S^2 $
$SS_T = \sum _{j=1}^{t} \sum _{k=1}^{n_j} Y_{jk}^2 - \frac{Y_{..}^2}{N}$
$Y_{.} `:=` \sum _{i=1}^{n} Y_{i}$, so means sum over the index.
This anova table can be different for different tests.
TODO