# Verification checks (P4)

1. Clean re-run of out/analysis.py (results.json deleted first) → byte-identical results.json: PASS.
2. tau_hat equals raw difference of student-weighted means (0.961118): PASS.
3. CI [tau_ci_low, tau_ci_high] contains tau_hat: PASS.
4. se_iid > 0 and se_cluster > 0; se_cluster > se_iid as expected with positive ICC: PASS.
5. effect_significant_5pct == (p_value < 0.05): PASS.
6. icc_hat in [0,1]: PASS (0.235).
7. (se_cluster/se_iid)^2 = 6.68 vs design effect 1+(m−1)·ICC = 6.64 (rel. diff 0.6%): PASS — magnitudes coherent.
8. Sensitivity: school-means t-test p = 0.201 vs clustered p = 0.195 — same conclusion: PASS.
9. Counts: n_input_rows 1000 − 0 removed = n_analysed 1000; 40 schools, 20 treated: PASS.