Design causal measurement without randomization

Assume a product group released an in-app notification feature on 2025-02-10. Because marketing controlled the rollout rather than random assignment, you need an observational approach to estimate the feature’s causal effect on 7-day retention. Design a study that compares two candidate methods: propensity score matching (PSM) and difference-in-differences (DiD). For each method, explain its key assumptions and justify when it would be appropriate. Your answer should…