1[2{"id":"C1","text":"The unadjusted association between training hours and productivity growth is negative (-0.132 pp/h, 95% CI excludes zero).","results_keys":["naive_estimate","naive_ci_low","naive_ci_high"],"status":"supported","caveat":"Association only; confounded by skill_index."},3{"id":"C2","text":"Adjusting for pre-programme skill_index, one extra training hour raises next-year productivity growth by about 0.254 pp, 95% CI [0.234, 0.273].","results_keys":["effect_estimate","effect_se","effect_ci_low","effect_ci_high","conclusion"],"status":"supported","caveat":"Causal only under selection on observables with skill_index as sole confounder and linear homogeneous effect."},4{"id":"C3","text":"The sign flip is explained by confounding: skill is positively correlated with training and strongly negatively related to growth.","results_keys":["skill_index_coefficient","corr_skill_training","naive_estimate","effect_estimate"],"status":"supported","caveat":"Omitted-variable-bias direction argument; relies on linear model."},5{"id":"C4","text":"The estimate is robust to excluding/including the 12 negative-hours rows and to a quadratic skill term.","results_keys":["sensitivity_all_rows_effect","sensitivity_quadratic_skill_effect","n_analysed"],"status":"supported","caveat":"Does not address unobserved confounding."},6{"id":"C5","text":"Adding skill_index halves residual RMSE (3.86 to 1.98 pp).","results_keys":["baseline_metric","model_metric"],"status":"supported","caveat":"In-sample fit, not a causal validity check."}7]8