1[2 {"id": "C1", "text": "The estimated programme effect is 0.961 points (difference in student-weighted arm means).", "results_keys": ["tau_hat", "mean_score_treated", "mean_score_control"], "status": "supported", "caveat": "Causal interpretation assumes random assignment of schools."},3 {"id": "C2", "text": "With school-clustered (CR1, t(39)) inference, H0: tau = 0 is not rejected at the 5% level: p = 0.195, 95% CI [-0.513, 2.436]; the data do not support a non-zero effect at 5%.", "results_keys": ["se_cluster", "p_value", "tau_ci_low", "tau_ci_high", "effect_significant_5pct", "cluster_t_df"], "status": "supported", "caveat": "Non-rejection is not evidence of zero effect; CI allows effects up to about 2.4 points."},4 {"id": "C3", "text": "The naive iid SE (0.282) understates uncertainty by a factor of about 2.58 and would wrongly suggest significance (p = 0.0007).", "results_keys": ["se_iid", "baseline_p_value_iid", "design_effect_se_ratio"], "status": "supported", "caveat": ""},5 {"id": "C4", "text": "The residual intraclass correlation is about 0.24, consistent with the observed SE inflation via the Moulton factor.", "results_keys": ["icc_hat", "design_effect_se_ratio", "students_per_school"], "status": "supported", "caveat": "ANOVA ICC estimator; balanced design."},6 {"id": "C5", "text": "A two-sample t-test on school means gives the same conclusion (SE 0.738, p 0.201).", "results_keys": ["robust_school_mean_ttest_se", "robust_school_mean_ttest_p"], "status": "supported", "caveat": ""}7]8