# Contract (P0)

• Question: average effect of a school-level programme on student test score, with design-valid uncertainty; decide at 5% two-sided whether effect != 0.
• Estimand tau: difference in student-weighted mean score, treated minus control schools = OLS coef of score on treated (with intercept). Meaningful as causal effect under random (or as-good-as-random) assignment of schools; inference assumes independence across schools, arbitrary dependence within a school.
• Main SE: cluster-robust (by school_id) SE; naive iid OLS SE as baseline. p-value and 95% CI from cluster SE (t with G-1 df). icc_hat: share of residual variance (after removing arm means) between schools.
• 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, plus out/exclusions.csv, out/state/*.
• Information rule: only data/schools.csv.
• Invalidating: treatment varying within school, too few clusters, missing/duplicate data, using iid SE for inference.