1[2 {"id":"C1","text":"The estimated programme effect is 0.96 points (treated minus control student-weighted mean score).","results_keys":["tau_hat"],"status":"supported","caveat":"Causal interpretation requires random assignment of schools, which the task describes but does not state explicitly."},3 {"id":"C2","text":"At the 5% level, with school-clustered uncertainty (CR1 SE 0.73, t with 39 df, p = 0.195, 95% CI [-0.51, 2.44]), the data do not support a non-zero programme effect.","results_keys":["se_cluster","p_value","tau_ci_low","tau_ci_high","effect_significant_5pct"],"status":"supported","caveat":"Failure to reject is not evidence of zero effect; only 40 clusters."},4 {"id":"C3","text":"The naive iid standard error (0.28) understates the design-valid standard error by a factor of about 2.6 and would wrongly indicate significance.","results_keys":["se_iid","se_cluster"],"status":"supported","caveat":"The naive p-value (about 0.0007) is reported only as a diagnostic."},5 {"id":"C4","text":"About 24% of residual score variance is between schools (ICC 0.24), implying a design effect of about 6.8 with 25 students per school.","results_keys":["icc_hat"],"status":"supported","caveat":"ANOVA estimator; the ICC is itself estimated with sampling error from only 40 schools."}6]7