1[2 {"id":"C1","text":"The estimated programme effect is 0.961 points (treated minus control schools).","results_keys":["tau_hat"],"status":"supported","caveat":"Causal reading assumes random assignment of schools."},3 {"id":"C2","text":"At the 5% level, using the school-clustered SE, the data do not support a non-zero programme effect (p=0.195; 95% CI -0.513 to 2.436).","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 includes effects up to ~2.4 points."},4 {"id":"C3","text":"The naive iid SE understates uncertainty by a factor of about 2.6, consistent with a residual ICC of 0.235 and 25 students per school, and would wrongly suggest significance.","results_keys":["se_iid","se_cluster","se_ratio_cluster_to_iid","icc_hat","design_effect_from_icc","p_value_iid"],"status":"supported","caveat":"ICC from ANOVA estimator on OLS residuals."},5 {"id":"C4","text":"A school-means t-test gives the same conclusion as the cluster-robust analysis.","results_keys":["check_se_school_means","check_p_school_means_pooled_t"],"status":"supported","caveat":""}6]7