Treatment Effects with BH-Adjusted p-values and E-values
E-values indicate robustness to unmeasured confounding
Wave	Model	Estimate	SE	p-value1	p-value (BH)1,2	E-value3	E-value (CI)4	95% CI	N
Feeling Thermometer (W1)
Wave 1	Unweighted (no adjustment)	5.194	1.206	1.706102e-05	0.000***	1.60	1.39	[2.831, 7.557]	2,681
Wave 1	Unweighted with Lin adjustment	4.091	0.817	5.786268e-07	0.000***	1.50	1.36	[2.491, 5.692]	2,681
Wave 1	ATT weighted	3.930	1.172	0.000000e+00	0.000***	1.49	1.27	[1.634, 6.275]	2,681
Wave 1	ATT weighted with Lin adjustment	3.864	0.798	0.000000e+00	0.000***	1.48	1.34	[2.246, 5.443]	2,681
Wave 1	ATE weighted	4.033	1.181	0.000000e+00	0.000***	1.50	1.28	[1.697, 6.413]	2,681
Wave 1	ATE weighted with Lin adjustment	3.981	0.796	0.000000e+00	0.000***	1.49	1.35	[2.388, 5.547]	2,681
Wave 1	Attrition ATE weighted	4.706	1.192	0.000000e+00	0.000***	1.56	1.35	[2.376, 7.086]	2,681
Wave 1	Attrition ATE weighted with Lin adjustment	4.084	0.794	0.000000e+00	0.000***	1.50	1.36	[2.498, 5.659]	2,681
Wave 1	Double robust (ATT weighted with all covariates)	3.805	0.795	0.000000e+00	0.000***	1.48	1.34	[2.233, 5.436]	2,679
Wave 1	Double robust (ATE weighted with all covariates)	3.936	0.795	0.000000e+00	0.000***	1.49	1.35	[2.414, 5.529]	2,679
Wave 1	Double robust (Attrition ATE weighted with all covariates)	3.927	0.793	0.000000e+00	0.000***	1.49	1.35	[2.394, 5.516]	2,679
Wave 1	Regression adjustment only (no weights)	3.929	0.807	1.201535e-06	0.000***	1.49	1.35	[2.347, 5.512]	2,679
Behavioral Intentions (W1)
Wave 1	Unweighted (no adjustment)	0.277	0.050	3.038025e-08	0.000***	1.73	1.53	[0.179, 0.375]	2,681
Wave 1	Unweighted with Lin adjustment	0.238	0.039	8.461987e-10	0.000***	1.65	1.49	[0.162, 0.314]	2,681
Wave 1	ATT weighted	0.240	0.050	0.000000e+00	0.000***	1.65	1.45	[0.138, 0.33]	2,681
Wave 1	ATT weighted with Lin adjustment	0.238	0.040	0.000000e+00	0.000***	1.65	1.48	[0.154, 0.313]	2,681
Wave 1	ATE weighted	0.234	0.050	0.000000e+00	0.000***	1.64	1.43	[0.13, 0.326]	2,681
Wave 1	ATE weighted with Lin adjustment	0.232	0.040	0.000000e+00	0.000***	1.63	1.47	[0.15, 0.308]	2,681
Wave 1	Attrition ATE weighted	0.254	0.049	0.000000e+00	0.000***	1.68	1.48	[0.151, 0.346]	2,681
Wave 1	Attrition ATE weighted with Lin adjustment	0.232	0.039	0.000000e+00	0.000***	1.63	1.47	[0.15, 0.307]	2,681
Wave 1	Double robust (ATT weighted with all covariates)	0.234	0.039	0.000000e+00	0.000***	1.64	1.48	[0.153, 0.309]	2,679
Wave 1	Double robust (ATE weighted with all covariates)	0.231	0.039	0.000000e+00	0.000***	1.63	1.47	[0.151, 0.306]	2,679
Wave 1	Double robust (Attrition ATE weighted with all covariates)	0.226	0.038	0.000000e+00	0.000***	1.62	1.47	[0.148, 0.3]	2,679
Wave 1	Regression adjustment only (no weights)	0.226	0.037	1.070375e-09	0.000***	1.62	1.47	[0.154, 0.299]	2,679
Attitudes (W1)
Wave 1	Unweighted (no adjustment)	0.127	0.043	2.994494e-03	0.006**	1.46	1.23	[0.043, 0.21]	2,681
Wave 1	Unweighted with Lin adjustment	0.095	0.034	5.517471e-03	0.006**	1.38	1.18	[0.028, 0.162]	2,681
Wave 1	ATT weighted	0.090	0.043	3.400000e-02	0.036*	1.37	1.08	[0.005, 0.172]	2,681
Wave 1	ATT weighted with Lin adjustment	0.088	0.035	6.000000e-03	0.007**	1.36	1.15	[0.021, 0.159]	2,681
Wave 1	ATE weighted	0.090	0.043	3.600000e-02	0.036*	1.36	1.08	[0.005, 0.172]	2,681
Wave 1	ATE weighted with Lin adjustment	0.088	0.035	6.000000e-03	0.006**	1.36	1.15	[0.021, 0.16]	2,681
Wave 1	Attrition ATE weighted	0.108	0.043	4.000000e-03	0.007**	1.41	1.16	[0.022, 0.191]	2,681
Wave 1	Attrition ATE weighted with Lin adjustment	0.091	0.035	4.000000e-03	0.006**	1.37	1.16	[0.024, 0.163]	2,681
Wave 1	Double robust (ATT weighted with all covariates)	0.089	0.033	2.000000e-03	0.007**	1.36	1.16	[0.026, 0.156]	2,679
Wave 1	Double robust (ATE weighted with all covariates)	0.088	0.033	0.000000e+00	0.000***	1.36	1.16	[0.025, 0.157]	2,679
Wave 1	Double robust (Attrition ATE weighted with all covariates)	0.089	0.033	2.000000e-03	0.007**	1.36	1.16	[0.023, 0.156]	2,679
Wave 1	Regression adjustment only (no weights)	0.092	0.032	4.412885e-03	0.007**	1.37	1.18	[0.029, 0.155]	2,679
Latent Support (W1)
Wave 1	Unweighted (no adjustment)	0.285	0.058	7.880294e-07	0.000***	1.66	1.46	[0.172, 0.398]	2,681
Wave 1	Unweighted with Lin adjustment	0.231	0.037	7.186469e-10	0.000***	1.57	1.43	[0.158, 0.304]	2,681
Wave 1	ATT weighted	0.226	0.056	0.000000e+00	0.000***	1.56	1.35	[0.115, 0.335]	2,681
Wave 1	ATT weighted with Lin adjustment	0.223	0.038	0.000000e+00	0.000***	1.55	1.42	[0.154, 0.295]	2,681
Wave 1	ATE weighted	0.225	0.057	0.000000e+00	0.000***	1.56	1.35	[0.115, 0.332]	2,681
Wave 1	ATE weighted with Lin adjustment	0.223	0.038	0.000000e+00	0.000***	1.55	1.42	[0.151, 0.297]	2,681
Wave 1	Attrition ATE weighted	0.256	0.057	0.000000e+00	0.000***	1.61	1.41	[0.144, 0.365]	2,681
Wave 1	Attrition ATE weighted with Lin adjustment	0.226	0.038	0.000000e+00	0.000***	1.56	1.42	[0.156, 0.298]	2,681
Wave 1	Double robust (ATT weighted with all covariates)	0.220	0.037	0.000000e+00	0.000***	1.55	1.42	[0.152, 0.293]	2,679
Wave 1	Double robust (ATE weighted with all covariates)	0.221	0.037	0.000000e+00	0.000***	1.55	1.42	[0.154, 0.295]	2,679
Wave 1	Double robust (Attrition ATE weighted with all covariates)	0.219	0.037	0.000000e+00	0.000***	1.55	1.41	[0.149, 0.292]	2,679
Wave 1	Regression adjustment only (no weights)	0.221	0.036	9.656578e-10	0.000***	1.55	1.42	[0.15, 0.291]	2,679
Feeling Thermometer (W2)
Wave 2	Unweighted (no adjustment)	3.776	1.839	4.023575e-02	0.201	1.48	1.08	[0.172, 7.38]	1,155
Wave 2	Unweighted with Lin adjustment	1.615	1.300	2.141999e-01	0.214	1.27	1.00	[-0.932, 4.163]	1,155
Wave 2	Wave 2-only ATT weighted	1.516	1.889	4.140000e-01	0.436	1.26	1.00	[-2.18, 5.194]	1,155
Wave 2	Wave 2-only ATT weighted with Lin adjustment	1.499	1.326	2.660000e-01	0.416	1.26	1.00	[-0.958, 4.235]	1,155
Wave 2	Wave 2-only ATE weighted	1.526	1.936	4.360000e-01	0.436	1.26	1.00	[-2.449, 5.31]	1,155
Wave 2	Wave 2-only ATE weighted with Lin adjustment	1.445	1.335	2.860000e-01	0.416	1.25	1.00	[-0.95, 4.304]	1,155
Wave 2	Sequential ATT weighted	1.639	2.077	4.120000e-01	0.436	1.28	1.00	[-2.507, 5.522]	1,155
Wave 2	Sequential ATT weighted with Lin adjustment	1.749	1.460	2.260000e-01	0.416	1.29	1.00	[-0.771, 4.759]	1,155
Wave 2	Doubly robust with Sequential ATT weights	1.660	1.426	2.220000e-01	0.416	1.28	1.00	[-0.805, 4.689]	1,155
Wave 2	Sequential ATE weighted	1.648	2.084	4.060000e-01	0.436	1.28	1.00	[-2.633, 5.576]	1,155
Wave 2	Sequential ATE weighted with Lin adjustment	1.832	1.467	1.980000e-01	0.214	1.30	1.00	[-0.688, 4.821]	1,155
Wave 2	Doubly robust with Sequential ATE weights	1.707	1.433	2.140000e-01	0.214	1.28	1.00	[-0.742, 4.698]	1,155
Wave 2	Sequential Attrition ATE weighted	2.010	2.101	3.260000e-01	0.435	1.31	1.00	[-2.118, 5.982]	1,155
Wave 2	Sequential Attrition ATE weighted with Lin adjustment	1.819	1.476	1.960000e-01	0.214	1.29	1.00	[-0.777, 4.888]	1,155
Wave 2	Doubly robust with Sequential Attrition ATE weights	1.570	1.437	2.500000e-01	0.416	1.27	1.00	[-0.989, 4.501]	1,155
Wave 2	Regression adjustment only (no weights)	1.525	1.291	2.375359e-01	0.416	1.26	1.00	[-1.004, 4.055]	1,155
Behavioral Intentions (W2)
Wave 2	Unweighted (no adjustment)	0.144	0.077	6.156194e-02	0.308	1.45	1.00	[-0.007, 0.295]	1,155
Wave 2	Unweighted with Lin adjustment	0.063	0.060	2.924754e-01	0.490	1.26	1.00	[-0.054, 0.18]	1,155
Wave 2	Wave 2-only ATT weighted	0.054	0.080	4.900000e-01	0.603	1.24	1.00	[-0.104, 0.212]	1,155
Wave 2	Wave 2-only ATT weighted with Lin adjustment	0.054	0.064	3.720000e-01	0.603	1.24	1.00	[-0.075, 0.182]	1,155
Wave 2	Wave 2-only ATE weighted	0.070	0.080	3.940000e-01	0.603	1.28	1.00	[-0.096, 0.227]	1,155
Wave 2	Wave 2-only ATE weighted with Lin adjustment	0.067	0.063	2.660000e-01	0.603	1.27	1.00	[-0.059, 0.19]	1,155
Wave 2	Sequential ATT weighted	0.046	0.088	6.160000e-01	0.616	1.22	1.00	[-0.127, 0.221]	1,155
Wave 2	Sequential ATT weighted with Lin adjustment	0.050	0.068	4.560000e-01	0.603	1.23	1.00	[-0.086, 0.184]	1,155
Wave 2	Doubly robust with Sequential ATT weights	0.036	0.065	5.520000e-01	0.616	1.19	1.00	[-0.087, 0.164]	1,155
Wave 2	Sequential ATE weighted	0.045	0.088	6.040000e-01	0.616	1.21	1.00	[-0.13, 0.222]	1,155
Wave 2	Sequential ATE weighted with Lin adjustment	0.052	0.067	4.220000e-01	0.490	1.23	1.00	[-0.078, 0.184]	1,155
Wave 2	Doubly robust with Sequential ATE weights	0.043	0.064	4.900000e-01	0.490	1.21	1.00	[-0.083, 0.17]	1,155
Wave 2	Sequential Attrition ATE weighted	0.061	0.087	4.700000e-01	0.603	1.26	1.00	[-0.112, 0.23]	1,155
Wave 2	Sequential Attrition ATE weighted with Lin adjustment	0.054	0.066	3.960000e-01	0.490	1.24	1.00	[-0.074, 0.183]	1,155
Wave 2	Doubly robust with Sequential Attrition ATE weights	0.043	0.064	4.640000e-01	0.603	1.21	1.00	[-0.078, 0.169]	1,155
Wave 2	Regression adjustment only (no weights)	0.067	0.058	2.502452e-01	0.603	1.27	1.00	[-0.047, 0.18]	1,155
Attitudes (W2)
Wave 2	Unweighted (no adjustment)	0.186	0.065	4.490031e-03	0.022*	1.60	1.27	[0.058, 0.314]	1,155
Wave 2	Unweighted with Lin adjustment	0.118	0.051	2.106129e-02	0.053	1.44	1.14	[0.018, 0.219]	1,155
Wave 2	Wave 2-only ATT weighted	0.100	0.063	1.100000e-01	0.160	1.39	1.00	[-0.02, 0.223]	1,155
Wave 2	Wave 2-only ATT weighted with Lin adjustment	0.100	0.050	4.000000e-02	0.147	1.39	1.05	[0.005, 0.201]	1,155
Wave 2	Wave 2-only ATE weighted	0.100	0.066	1.140000e-01	0.160	1.39	1.00	[-0.029, 0.228]	1,155
Wave 2	Wave 2-only ATE weighted with Lin adjustment	0.097	0.051	4.600000e-02	0.147	1.38	1.00	[0.004, 0.203]	1,155
Wave 2	Sequential ATT weighted	0.083	0.071	2.300000e-01	0.230	1.34	1.00	[-0.057, 0.224]	1,155
Wave 2	Sequential ATT weighted with Lin adjustment	0.086	0.057	1.200000e-01	0.160	1.35	1.00	[-0.029, 0.2]	1,155
Wave 2	Doubly robust with Sequential ATT weights	0.084	0.056	1.320000e-01	0.162	1.35	1.00	[-0.023, 0.203]	1,155
Wave 2	Sequential ATE weighted	0.085	0.071	2.240000e-01	0.230	1.35	1.00	[-0.049, 0.227]	1,155
Wave 2	Sequential ATE weighted with Lin adjustment	0.091	0.057	1.140000e-01	0.116	1.36	1.00	[-0.019, 0.207]	1,155
Wave 2	Doubly robust with Sequential ATE weights	0.087	0.055	1.160000e-01	0.116	1.36	1.00	[-0.019, 0.204]	1,155
Wave 2	Sequential Attrition ATE weighted	0.106	0.072	1.460000e-01	0.167	1.40	1.00	[-0.035, 0.243]	1,155
Wave 2	Sequential Attrition ATE weighted with Lin adjustment	0.100	0.057	7.600000e-02	0.116	1.39	1.00	[-0.009, 0.215]	1,155
Wave 2	Doubly robust with Sequential Attrition ATE weights	0.084	0.055	1.200000e-01	0.160	1.35	1.00	[-0.021, 0.199]	1,155
Wave 2	Regression adjustment only (no weights)	0.100	0.050	4.584395e-02	0.147	1.39	1.04	[0.002, 0.199]	1,155
Latent Support (W2)
Wave 2	Unweighted (no adjustment)	0.230	0.089	1.001956e-02	0.050	1.56	1.22	[0.055, 0.404]	1,155
Wave 2	Unweighted with Lin adjustment	0.119	0.059	4.502779e-02	0.106	1.36	1.04	[0.003, 0.235]	1,155
Wave 2	Wave 2-only ATT weighted	0.104	0.090	2.380000e-01	0.272	1.33	1.00	[-0.077, 0.271]	1,155
Wave 2	Wave 2-only ATT weighted with Lin adjustment	0.103	0.060	7.600000e-02	0.192	1.32	1.00	[-0.013, 0.224]	1,155
Wave 2	Wave 2-only ATE weighted	0.111	0.092	2.180000e-01	0.272	1.34	1.00	[-0.074, 0.281]	1,155
Wave 2	Wave 2-only ATE weighted with Lin adjustment	0.107	0.060	6.200000e-02	0.192	1.33	1.00	[-0.007, 0.231]	1,155
Wave 2	Sequential ATT weighted	0.094	0.099	3.420000e-01	0.342	1.30	1.00	[-0.108, 0.285]	1,155
Wave 2	Sequential ATT weighted with Lin adjustment	0.099	0.065	1.180000e-01	0.192	1.32	1.00	[-0.021, 0.231]	1,155
Wave 2	Doubly robust with Sequential ATT weights	0.091	0.063	1.360000e-01	0.198	1.30	1.00	[-0.027, 0.224]	1,155
Wave 2	Sequential ATE weighted	0.095	0.099	3.240000e-01	0.342	1.31	1.00	[-0.113, 0.288]	1,155
Wave 2	Sequential ATE weighted with Lin adjustment	0.104	0.065	9.800000e-02	0.106	1.33	1.00	[-0.017, 0.236]	1,155
Wave 2	Doubly robust with Sequential ATE weights	0.096	0.063	1.060000e-01	0.106	1.31	1.00	[-0.022, 0.229]	1,155
Wave 2	Sequential Attrition ATE weighted	0.119	0.100	2.240000e-01	0.272	1.36	1.00	[-0.088, 0.31]	1,155
Wave 2	Sequential Attrition ATE weighted with Lin adjustment	0.110	0.065	7.800000e-02	0.106	1.34	1.00	[-0.01, 0.241]	1,155
Wave 2	Doubly robust with Sequential Attrition ATE weights	0.092	0.063	1.200000e-01	0.192	1.30	1.00	[-0.026, 0.224]	1,155
Wave 2	Regression adjustment only (no weights)	0.109	0.058	5.767706e-02	0.192	1.34	1.00	[-0.003, 0.222]	1,155
1 *p < 0.05, **p < 0.01, ***p < 0.001
2 Benjamini-Hochberg correction applied within each outcome type
3 E-values ≥ 2 (highlighted in green) suggest greater robustness to unmeasured confounding
4 E-value (CI) represents the E-value for the confidence interval lower bound