. 2020 Nov 24;30(3):687–701. doi: 10.1177/0962280220970228

Table 4.

Multiple contrast test results of the protein abundance trial.

	Interaction						Region						Group
	Chang ( $z_{95 %} = 3.10)$			Randomization ( $z_{95 %} = 3.76$ )			Chang ( $z_{95 %} = 3.10)$			Rand. ( $z_{95 %} = 3.75$ )			Chang ( $z_{95 %} = 3.09)$			Rand. $(z_{95 %} = 3.88)$
$ℓ =$	${\hat{δ}}_{ℓ}$	$T_{ℓ}$	95%-L	95%-U	95%-L	95%-U	${\hat{δ}}_{ℓ}$	$T_{ℓ}$	95%-L	95%-U	95%-L	95%-U	${\hat{δ}}_{ℓ}$	$T_{ℓ}$	95%-L	95%-U	95%-L	95%-U
1	−0.65	−1.20	−2.32	1.03	−2.67	1.37	1.35	2.50	−0.32	3.03	−0.68	3.38	0.39	0.41	−2.57	3.36	−3.32	4.11
2	−0.53	−1.00	−2.17	1.11	−2.50	1.44	2.49	4.71	0.85	4.13	0.51	4.48	0.51	0.69	−1.77	2.80	−2.35	3.38
3	1.09	1.37	−1.37	3.55	−1.88	4.05	−2.38	−3.00	−4.84	0.07	−5.36	0.59	2.13	1.93	−1.28	5.55	−2.15	6.42
4	−0.04	−0.10	−1.41	1.32	−1.69	1.60	−2.40	−5.43	−3.77	−1.03	−4.06	−0.74	1.00	1.06	−1.92	3.91	−2.66	4.66
5	−0.01	−0.02	−1.39	1.37	−1.67	1.66	−0.68	−1.53	−2.06	0.70	−2.36	0.99	1.04	1.03	−2.08	4.15	−2.87	4.94
6	0.14	0.28	−1.41	1.70	−1.74	2.02	1.62	3.23	0.06	3.18	−0.26	3.51	1.18	1.20	−1.85	4.21	−2.62	4.99
7	−0.22	−0.72	−1.15	0.71	−1.34	0.91	0.18	0.58	−0.76	1.11	−0.95	1.30	−0.61	−1.84	−1.64	0.41	−1.90	0.68
8	−0.68	−2.50	−1.53	0.16	−1.71	0.34	−1.85	−6.75	−2.70	−1.00	−2.88	−0.82	−1.08	−2.90	−2.23	0.07	−2.53	0.36
9	0.15	0.74	−0.49	0.80	−0.63	0.94	−0.10	−0.50	−0.75	0.54	−0.89	0.68	−0.24	−0.89	−1.09	0.60	−1.30	0.82
10	0.20	0.98	−0.43	0.83	−0.56	0.96	−1.97	−9.69	−2.60	−1.34	−2.74	−1.21	−0.20	−0.85	−0.91	0.52	−1.10	0.70
11	0.24	1.41	−0.28	0.75	−0.39	0.86	1.10	6.58	0.58	1.62	0.47	1.73	−0.16	−0.61	−0.98	0.66	−1.19	0.87
12	0.31	2.42	−0.09	0.71	−0.17	0.79	2.65	20.58	2.25	3.05	2.17	3.13	−0.09	−0.77	−0.43	0.25	−0.51	0.34
13	0.46	1.44	−0.53	1.45	−0.74	1.66	2.62	8.18	1.63	3.62	1.42	3.83	0.59	1.66	−0.51	1.69	−0.79	1.97
14	−0.07	−0.31	−0.79	0.64	−0.93	0.79	3.73	16.17	3.02	4.45	2.87	4.60	0.06	0.24	−0.70	0.82	−0.90	1.02
15	−0.23	−0.29	−2.67	2.21	−3.18	2.72	−6.67	−8.45	−9.12	−4.23	−9.63	−3.71	−0.10	−0.09	−3.37	3.17	−4.20	4.00
16	−0.41	−1.80	−1.13	0.30	−1.27	0.45	−3.98	−17.27	−4.69	−3.26	−4.84	−3.11	−0.28	−0.62	−1.70	1.14	−2.07	1.50
17	0.24	0.55	−1.11	1.59	−1.39	1.87	1.46	3.34	0.11	2.81	−0.18	3.10	0.37	0.98	−0.80	1.54	−1.10	1.84
18	0.01	0.04	−0.91	0.94	−1.10	1.13	2.83	9.47	1.90	3.75	1.71	3.95	0.14	0.45	−0.84	1.13	−1.09	1.38
19	−0.57	−1.11	−2.14	1.01	−2.47	1.34	−1.78	−3.49	−3.36	−0.20	−3.69	0.13	−0.86	−1.41	−2.74	1.02	−3.22	1.49
20	−1.08	−1.89	−2.86	0.69	−3.22	1.05	−0.50	−0.88	−2.28	1.27	−2.65	1.64	−1.38	−1.83	−3.70	0.94	−4.29	1.53
21	0.54	1.62	−0.49	1.56	−0.70	1.77	0.58	1.75	−0.44	1.61	−0.66	1.82	0.24	0.76	−0.74	1.23	−0.99	1.48
22	−0.17	−0.56	−1.14	0.79	−1.34	0.99	−3.14	−10.09	−4.10	−2.17	−4.30	−1.97	−0.47	−1.52	−1.42	0.48	−1.66	0.72
23	0.72	1.35	−0.93	2.37	−1.27	2.71	1.05	1.97	−0.60	2.70	−0.95	3.05	0.43	0.62	−1.70	2.55	−2.24	3.09
24	0.57	2.32	−0.19	1.32	−0.35	1.48	3.79	15.52	3.03	4.55	2.87	4.71	0.27	0.86	−0.70	1.25	−0.95	1.49
25	0.45	1.16	−0.75	1.65	−1.00	1.90	3.31	8.52	2.11	4.52	1.85	4.77	−0.16	−2.19	−0.39	0.07	−0.45	0.13
26	0.30	0.72	−1.00	1.61	−1.27	1.88	2.80	6.63	1.49	4.11	1.21	4.38	−0.31	−2.55	−0.69	0.07	−0.78	0.16
27	−0.92	−1.93	−2.39	0.56	−2.70	0.86	−2.17	−4.56	−3.65	−0.70	−3.96	−0.38	−1.53	−2.05	−3.84	0.78	−4.43	1.37
28	−0.76	−1.40	−2.44	0.92	−2.78	1.26	−5.50	−10.16	−7.18	−3.83	−7.54	−3.47	−1.37	−1.54	−4.13	1.38	−4.83	2.08
29	0.59	2.64	−0.10	1.28	−0.25	1.43	2.05	9.18	1.36	2.75	1.21	2.89	−0.02	−0.08	−0.95	0.90	−1.18	1.13
30	0.33	0.86	−0.87	1.53	−1.11	1.78	−0.49	−1.26	−1.68	0.71	−1.94	0.96	−0.28	−0.39	−2.50	1.93	−3.07	2.50
31	0.11	0.52	−0.55	0.78	−0.69	0.92	0.45	2.08	−0.22	1.11	−0.36	1.26	0.40	1.87	−0.26	1.06	−0.43	1.23
32	−0.22	−0.93	−0.94	0.50	−1.09	0.65	1.07	4.59	0.35	1.79	0.20	1.94	0.07	0.37	−0.51	0.65	−0.66	0.80
33	0.31	0.96	−0.69	1.31	−0.89	1.52	−2.18	−6.77	−3.18	−1.18	−3.40	−0.97	0.60	1.52	−0.62	1.82	−0.93	2.12
34	0.22	0.81	−0.61	1.05	−0.79	1.22	−3.10	−11.54	−3.93	−2.27	−4.11	−2.09	0.51	1.60	−0.47	1.48	−0.72	1.73
35	−0.43	−1.81	−1.16	0.31	−1.32	0.46	0.85	3.59	0.12	1.59	−0.04	1.75	−0.14	−0.50	−1.00	0.72	−1.22	0.94
36	0.01	0.06	−0.41	0.42	−0.49	0.51	2.91	21.80	2.50	3.33	2.41	3.41	0.30	2.02	−0.16	0.75	−0.27	0.86
	$T_{0} = 2.63$						$T_{0} = 21.80$						$T_{0} = 2.90$

Here, $ℓ = 1, \dots, 36$ corresponds to each of the 36 contrasts tested by the hypothesis of no interaction, region or group as given in Equation (2) or Equation (16), respectively. In addition, ${\hat{δ}}_{ℓ}$ is the estimated contrast, $T_{ℓ}$ the value of the t-test type statistic and 95%-L or 95%-U the 95% lower or upper bound of the 95% simultaneous confidence intervals. The estimated quantiles $z_{95 %} (\max)$ are given in the headers. Different test decisions between the competing methods are marked boldface.