Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 30 / 2 / c

Index chocolate by $a\in \{A,B,C,D\}$, day by $d$ in the three observed categories, and replicate by $r\in \{1,2\}$. The additive two-factor normal linear model isHere $Y_{adr}$ is the board count, $\mu$ is the mean for the reference chocolate and reference day, and ${\alpha }_a,{\gamma }_d$ are chocolate and day fixed effects. With corner-point constraints, set ${\alpha }_A=0$ and ${\gamma }_{d_0}=0$, where $d_0$ is the first level in the day factor. The printed coefficient-free output does not determine that factor ordering; the model is unchanged by a different reference category. There is no chocolate–day interaction term in this fit. The six free mean statistical parameters consist of one baseline, three chocolate contrasts and two day contrasts; the common error variance supplies a further statistical parameter.