Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 37 / 3 / c / Solution

Compare the species-only model against the additive day-and-species model. The null hypothesis is $H_0:d_2=d_3=0$, with the alternative that at least one is nonzero. The likelihood-ratio statistic is the reduction in residual deviance,Under the null hypothesis, regular binomial likelihood asymptotics give $G^2\stackrel{\mathrm{approx}}{\sim }{\chi }_2^2$, because the larger model has two additional parameters. For this chi-squared distribution the upper-tail probability is $\exp (-0.341/2)\simeq 0.843$. There is no evidence of a day effect after controlling for species, and the species-only model is a reasonable simpler choice. The sequential day-only statistic 0.273 from the preceding table answers a different question and must not replace this comparison.