ANOVA sum of squares decomposition
Proposition taught in Analysis of variance, part of Statistical inference
ANOVA sum of squares decomposition
| Type | Proposition |
| Taught in | Analysis of variance |
| Part | Statistical inference |
With
\mathrm{SS}_{\mathrm{total}}=\sum_{j=1}^k\sum_{i=1}^{n_j}(Y_{ij}-\overline Y_{\cdot\cdot})^2, \qquad \mathrm{SS}_{\mathrm{treatment}}=\sum_{j=1}^k n_j(\overline Y_{\cdot j}-\overline Y_{\cdot\cdot})^2, \qquad \mathrm{SS}_{\mathrm{error}}=\sum_{j=1}^k\sum_{i=1}^{n_j}(Y_{ij}-\overline Y_{\cdot j})^2,
the total sum of squares splits as \mathrm{SS}_{\mathrm{total}}=\mathrm{SS}_{\mathrm{treatment}}+\mathrm{SS}_{\mathrm{error}}.
Used in
- Taught in Analysis of variance, where the derivation and examples are.
- All 6 questions on Analysis of variance
See also
One-way analysis of variance · ANOVA F distribution · Contrast · Tukey intervals · Randomised block design