1[2 {"id": "C1", "text": "The estimated programme effect is 0.961 points (treated minus control student-weighted mean score).", "results_keys": ["tau_hat", "mean_score_treated", "mean_score_control"], "status": "supported", "caveat": "Causal reading requires as-if-random assignment of schools."},3 {"id": "C2", "text": "With school-clustered (CR1, t with 39 df) uncertainty, H0: tau = 0 is not rejected at the 5% level (p = 0.195; 95% CI -0.513 to 2.436); the data do not support a non-zero effect.", "results_keys": ["se_cluster", "p_value", "tau_ci_low", "tau_ci_high", "effect_significant_5pct", "df_cluster"], "status": "supported", "caveat": "Non-rejection is not evidence of zero effect; CI is wide."},4 {"id": "C3", "text": "The naive iid standard error (0.282) understates uncertainty by a factor of about 2.58 and would wrongly indicate significance (p = 0.00068).", "results_keys": ["se_iid", "se_ratio_cluster_to_iid", "baseline_p_value_iid", "baseline_ci_iid_low", "baseline_ci_iid_high"], "status": "supported", "caveat": "Baseline shown only for contrast; it is invalid under the design."},5 {"id": "C4", "text": "The residual intraclass correlation is about 0.24, implying a design effect of about 6.8 consistent with the observed SE inflation.", "results_keys": ["icc_hat", "design_effect_from_icc", "se_ratio_cluster_to_iid"], "status": "supported", "caveat": "ANOVA ICC estimator; sampling uncertainty of ICC not quantified."},6 {"id": "C5", "text": "A Welch t-test on the 40 school means gives nearly the same SE and p-value as the cluster-robust analysis.", "results_keys": ["school_means_welch_se", "school_means_welch_p", "se_cluster", "p_value"], "status": "supported", "caveat": ""},7 {"id": "C6", "text": "All 1000 students in 40 schools (20 treated) were analysed with no exclusions or data issues.", "results_keys": ["n_analysed", "n_schools", "n_treated_schools", "n_input_rows", "data_issues"], "status": "supported", "caveat": ""}8]9