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":"Causal interpretation assumes as-good-as-random school assignment; synthetic data."},3 {"id":"C2","text":"At the 5% level, with school-clustered uncertainty, the data do not support a non-zero programme effect (p≈0.195; 95% CI ≈ [-0.51, 2.44]).","results_keys":["effect_significant_5pct","p_value","tau_ci_low","tau_ci_high","se_cluster"],"status":"supported","caveat":"Failure to reject is not evidence of zero effect; effects up to ~2.4 points remain plausible. CR1 with t(G-1), G=40."},4 {"id":"C3","text":"The naïve iid standard error understates uncertainty by a factor of about 2.6 and would wrongly suggest significance (p≈0.0007).","results_keys":["se_iid","se_cluster","se_ratio_cluster_to_iid","p_value_iid"],"status":"supported","caveat":""},5 {"id":"C4","text":"About 23% of the residual score variance is between schools (ICC≈0.235), implying a design effect of about 6.6, consistent with the SE ratio.","results_keys":["icc_hat","design_effect_from_icc"],"status":"supported","caveat":"Moment estimator, imprecise with 40 schools."},6 {"id":"C5","text":"A t-test on school means gives the same conclusion (p≈0.20).","results_keys":["school_mean_ttest_p"],"status":"supported","caveat":""}7]8