Check your understanding
Quiz
You have built the full observational-causal toolkit: matching and propensity scores, inverse-probability weighting and doubly-robust estimation, difference-in-differences and its staggered-rollout trap, regression discontinuity, instrumental variables, synthetic control, uplift modeling, double machine learning, sensitivity analysis, and mediation. Running through all of them is one discipline: state the assumption, then stress-test it. This quiz checks what stuck. The last two steps are live R you can run.
Question 1 of 12
Why a naive comparison misleads
In an observational study, people who chose a treatment are compared to those who did not, and the treated group did better. Why can this gap not be read as the causal effect?
Correct: E[Y|T=1] − E[Y|T=0] = ATT + (E[Y(0)|T=1] − E[Y(0)|T=0]). The second term is selection bias, nonzero whenever the groups would have differed untreated.
Measurement error is a separate problem. Even perfectly measured outcomes give a biased gap when the groups self-selected.