# Contract (P0)

Question. With few clusters, how reliable are cluster-robust 95% CIs for a population mean? Monte Carlo study over 9 cells (G in {5,10,30} x ICC in {0,0.2,0.5}), unequal cluster sizes (pattern 8,16,32,64 repeated).

Estimands (per cell x procedure CR0, CR1, WCB): (a) actual coverage of the nominal 95% CI for mu (=0); (b) for CR0/CR1, E[V_hat]/Var(ybar) with exact Var(ybar) = [ICC*sum n_g^2 + (1-ICC)N]/N^2; (c) MC SE sqrt(p(1-p)/R); (d) failure regimes: coverage < 0.90. Also "nominal-consistent": |p-0.95| <= 2 MCSE. Meaningful under the stated Gaussian random-effects DGP only.

Procedures exactly as specified: CR0 with z=1.96; CR1 = G/(G-1) CR0 with t_{G-1}; WCB unrestricted Rademacher bootstrap-t with B=399, q = 0.95 empirical quantile of |t*|, interval ybar +- q sqrt(V_CR1).

Outputs: out/table1.csv (27 rows: estimator,cell_id,G,icc,coverage,mc_se_coverage,rel_bias_var (empty for wcb),mean_ci_halfwidth,R); out/results.json (task_id,R,B,n_cells,coverage,mc_se_coverage,rel_bias_var,failure_cells,n_failure_cells,nominal_cells,best_procedure_small_G,feasibility,feasibility_reason,data_issues,n_input_rows,n_analysed,random_seed); out/figure1.png; out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues); out/analysis.py; out/claims.json.

Information rules: use only data/design.csv; R=2000, B=399, per-cell seeds; do not change grid.

Invalidity: changing R/B/grid/seeds, deviating from the procedure definitions, inconsistent design rows (sizes not summing to N, wrong G), non-deterministic script, runtime > 10 min.