Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 13J / a / iii / Solution

The additive model has four free coefficients: an intercept, two treatment contrasts, and one outcome contrast. The interaction model addstreatment-by-outcome interaction term, making six parameters for six cells. It is saturated, so the residual degrees of freedom fall from two to zero and the likelihood-ratio test has

The deviance reduction is $44.48$, with p-value $2.194\times 10^{-10}$. The analysis of deviance for nested generalized linear models therefore gives overwhelming evidence against a common outcome distribution across the three groups. The observed proportions and the negative treatment--Worse interactions show that both doses reduce the chance of worsening relative to Control, with a larger reduction for LD.

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