1[2 {"id":"C1","text":"The estimated programme effect is 0.96 points (treated minus control student means).","results_keys":["tau_hat"],"status":"supported","caveat":"Causal interpretation assumes random school assignment."},3 {"id":"C2","text":"Using the school-clustered SE, the programme does not have a statistically significant non-zero effect at the 5% level (p = 0.195; 95% CI -0.51 to 2.44 contains 0).","results_keys":["effect_significant_5pct","p_value","se_cluster","tau_ci_low","tau_ci_high"],"status":"supported","caveat":"Non-rejection is not evidence of zero effect; CI is wide."},4 {"id":"C3","text":"The naive iid SE understates uncertainty by a factor of about 2.6 and would wrongly indicate significance (p = 0.0007).","results_keys":["se_iid","se_cluster","diagnostics.se_ratio_cluster_over_iid","diagnostics.p_value_iid"],"status":"supported","caveat":"iid SE is invalid under the clustered design; reported only as baseline."},5 {"id":"C4","text":"About 24% of residual score variance is between schools (ICC 0.24), implying a design effect of about 6.8 that explains the SE inflation.","results_keys":["icc_hat","diagnostics.design_effect_moulton","diagnostics.sqrt_design_effect"],"status":"supported","caveat":"ANOVA ICC estimator; design effect formula assumes equal cluster sizes (true here)."}6]7