1[2 {"id":"C1","text":"The estimated programme effect is 0.96 points (treated minus control student-weighted mean score).","results_keys":["tau_hat","mean_treated","mean_control"],"status":"supported","caveat":"Point estimate only; imprecise given 40 schools."},3 {"id":"C2","text":"With school-clustered standard errors the effect is not statistically different from zero at the 5% level (p≈0.195; 95% CI −0.51 to 2.44).","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 no effect; the CI includes effects up to ~2.4 points."},4 {"id":"C3","text":"The naive iid OLS 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_over_iid","p_value_iid"],"status":"supported","caveat":"The iid SE is reported only as a baseline and is invalid for this design."},5 {"id":"C4","text":"About 24% of residual score variance lies between schools (ICC≈0.24), implying a design effect of about 6.8 with 25 students per school.","results_keys":["icc_hat","design_effect_from_icc","school_size"],"status":"supported","caveat":"ANOVA estimator; ICC estimated from 40 clusters is itself uncertain."},6 {"id":"C5","text":"The conclusion is robust to analysing school means with a two-sample t-test (p≈0.20).","results_keys":["sens_school_means_se","sens_school_means_p"],"status":"supported","caveat":"Equivalent to cluster inference in this balanced design."}7]8