ANOVA Notation

For one-way ANOVA, $y_{ij}$ denotes the $j$-th observation from treatment $i$, where $i = 1, \dots, k$ and $j = 1, \dots, n_i$.

The treatment mean is

$$ \bar{y}_{i\cdot} = \frac{1}{n_i}\sum_{j=1}^{n_i} y_{ij}, $$

and the grand mean is

$$ \bar{y}_{\cdot\cdot} = \frac{1}{N}\sum_{i=1}^{k}\sum_{j=1}^{n_i} y_{ij}, \quad N = \sum_{i=1}^{k} n_i. $$

This notation is the foundation for the ANOVA identity, sums of squares, and ANOVA table.