1[2 {"id":"C1","text":"The unadjusted OLS slope of productivity growth on training hours is negative, about -0.132 pp/hour with 95% CI [-0.160, -0.103].","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 (robust SE 0.0098, 95% CI [0.234, 0.273]); conclusion positive_effect.","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 the sole confounder; untestable."},4 {"id":"C3","text":"The sign reversal is explained by skill_index being positively correlated with training and negatively related to growth.","results_keys":["skill_index_coefficient","corr_skill_training","naive_estimate","effect_estimate"],"status":"supported","caveat":"Mechanical omitted-variable-bias explanation within the linear model."},5 {"id":"C4","text":"The adjusted model fits much better (RMSE 1.98 vs 3.86 pp).","results_keys":["model_metric","baseline_metric"],"status":"supported","caveat":"In-sample fit; not evidence of causality."},6 {"id":"C5","text":"The result is robust to keeping the 12 negative-hour rows and to adding quadratic/interaction terms.","results_keys":["sensitivity_incl_negative_effect_estimate","sensitivity_incl_negative_effect_se","spec_check_nonlinear_terms_joint_pvalue","data_issues","n_analysed"],"status":"supported","caveat":"Limited power against heterogeneity; does not address unobserved confounding."}7]8