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Incoming links: Orthogonal polynomial contrast
Past exam of the mathematics course of the University of Cambridge 2013 iii Paper 35 1 c iii Solution Created 2026-10-03 Updated 2026-10-07
The constant subspace has one statistical degree of freedom. Day contrasts have , and the within-block ANOVA stratum has . Because the orthogonal block design puts all four independent dose contrasts in that last ANOVA stratum, the residual has statistical degrees of freedom.
| Stratum | Source | Degrees of freedom |
|---|---|---|
| Mean | Grand mean | 1 |
| Between days | Days | 4 |
| Within days | Dose | 4 |
| Within days | Residual | 41 |
| Uncorrected total | All observations | 50 |
The corrected total has 49 statistical degrees of freedom; dose is tested against the within-day residual. The quantitative dose scale also permits the dose component to be split into linear, quadratic, cubic and quartic orthogonal polynomial contrasts, each with one statistical degree of freedom. This is optional and does not assume the response is linear in dose.