# Contract (P0)

Question: Average effect of a school-level programme on student test score, with design-valid uncertainty; decide at 5% (two-sided) whether τ ≠ 0. Estimand: τ = student-weighted mean score (treated schools) − mean score (control schools) = OLS slope of score on treated with intercept. Meaningful as a causal effect only if assignment of schools is as-good-as-random (assumed; simulated data); as a descriptive difference it is always defined. Uncertainty: treatment varies only between schools; students share school shocks; schools independent ⇒ cluster at school level (CR1 cluster-robust SE, t with G−1 df). Naïve iid SE reported only as baseline. Outputs: out/results.json (task_id, tau_hat, se_iid, se_cluster, p_value, tau_ci_low, tau_ci_high, effect_significant_5pct, icc_hat, n_schools, n_treated_schools, n_analysed, feasibility, feasibility_reason, data_issues, n_input_rows, random_seed), out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues), out/analysis.py, out/claims.json (incl. claim on 5% significance). Information rules: only data/schools.csv. Invalidity: treatment varying within school, too few clusters / one arm with no schools, using iid SE for the decision.