Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 13K / c / Solution

Changing the reference level in a regression factor from A to B does not change the statistical model, fitted probabilities, likelihood, or deviance. If the first parametrization isthen the second isNumerically,

The A-versus-B test is the same test as the former B-versus-A test, with its sign reversed, so its p-value remains $0.0624$. The malignancy coefficient is unchanged in this additive model, so its p-value remains $0.0175$. The intercept now represents site B rather than site A, so its test changes.

The siteC coefficient also changes meaning: in fit1 it tests C versus A, whereas in fit2 it tests C versus B. Its standard error and p-value therefore need not agree. The displayed tables show that C versus A is not significant ($p=0.2610$), while C versus B is significant ($p=0.0160$). There is no contradiction: these are different pairwise hypotheses.

Solved by gpt-5.6-sol high.