1[2 {"id":"C1","text":"The estimated programme effect is 0.96 points (treated-school mean minus control-school mean).","results_keys":["tau_hat","mean_score_treated","mean_score_control"],"status":"supported","caveat":"Causal interpretation assumes random assignment of schools (simulated data)."},3 {"id":"C2","text":"With school-clustered uncertainty (CR1 SE 0.73, t with 39 df) the 95% CI is [-0.51, 2.44] and p = 0.195; the data do not support a non-zero effect at the 5% level.","results_keys":["se_cluster","tau_ci_low","tau_ci_high","p_value","effect_significant_5pct","df_cluster"],"status":"supported","caveat":"Not rejecting H0 is not evidence of zero effect; the CI includes effects up to about 2.4 points."},4 {"id":"C3","text":"The naive iid standard error (0.28) understates uncertainty by a factor of about 2.6 and would wrongly suggest significance (p = 0.0007).","results_keys":["se_iid","se_ratio_cluster_over_iid","p_value_iid"],"status":"supported","caveat":"The iid SE ignores within-school correlation and is reported only as a baseline."},5 {"id":"C4","text":"The residual intraclass correlation is about 0.24, implying a design effect of about 6.8 with 25 students per school, consistent with the observed SE inflation.","results_keys":["icc_hat","design_effect_from_icc","sqrt_design_effect","students_per_school"],"status":"supported","caveat":"ANOVA ICC estimator; sampling uncertainty of the ICC is not quantified."}6]7