1[2 {"id": "C1", "text": "The estimated programme effect is about 0.96 points (treated minus control student-weighted mean score).", "results_keys": ["tau_hat"], "status": "supported", "caveat": "Point estimate only; imprecise given 40 schools."},3 {"id": "C2", "text": "At the 5% level, the data do not support a non-zero programme effect once uncertainty accounts for school-level clustering (p = 0.195; 95% CI -0.51 to 2.44).", "results_keys": ["p_value", "tau_ci_low", "tau_ci_high", "effect_significant_5pct", "se_cluster"], "status": "supported", "caveat": "Failure to reject is not evidence of no effect; a modest positive effect remains compatible with the data."},4 {"id": "C3", "text": "The naive iid standard error understates uncertainty by a factor of about 2.6, which would wrongly suggest a significant effect.", "results_keys": ["se_iid", "se_cluster"], "status": "supported", "caveat": "The iid SE is invalid for this design and is reported only as a baseline."},5 {"id": "C4", "text": "About 23% of residual score variance lies between schools (ICC about 0.235), implying a design effect of about 6.6.", "results_keys": ["icc_hat"], "status": "supported", "caveat": "ANOVA estimator of the ICC; sampling uncertainty of the ICC itself not quantified."}6]7