Past exam of the mathematics course of the University of Cambridge 2026 iii Paper 207 1 e Solution Created 2026-09-24 Updated 2026-09-25
First inspect overlap and post-match balance using standardized mean differences, distributions, and interactions for every pre-treatment covariate. Material imbalance or UTCs outside the control support shows that the design is extrapolating and cannot justify conditional exchangeability on those variables.
Second perform a negative control outcome analysis using apprenticeship outcomes from before conversion, or another outcome that UTC status could not yet affect. A nonzero estimated effect indicates remaining selection or differential trends. Neither diagnostic proves absence of hidden confounding, so a quantitative sensitivity analysis for unmeasured confounding is also useful.