. 2019 May 10;29(6):1715–1727. doi: 10.1177/0962280219846146

Table 2.

Probability of stratified and unstratified randomization procedures to keep the 5% level for BSD(9), CR, EBC(0.67) and PBR(4) depending on the amount of selection $η = 0, 0.2$ and time-trend bias $Θ = 0, 0.2$ for different allocation ratios and analysis using weighted ( $w_{j}^{*}$ ), unweighted (w_j = 1) and unstratified (us) t test.

Allocation ratio	Θ	η	Randomization procedure	Stratified randomization			Unstratified randomization
Allocation ratio	Θ	η	Randomization procedure	$w_{j}^{*}$ test	w_j = 1 test	us-test	$w_{j}^{*}$ test	w_j = 1 test	us-test
$20 ⋮ 60$	0.2	0	BSD (9)	0.65	0.31	0.71	0.67	0.31	0.67
			CR	0.66	0.32	0.68	0.66	0.32	0.68
			EBC (0.67)	0.90	0.47	0.95	0.84	0.47	0.96
			PBR (4)	1.00	0.97	1.00	1.00	0.97	1.00
	0	0.2	BSD (9)	0.45	0.15	0.54	0.43	0.15	0.53
			CR	0.45	0.16	0.54	0.44	0.16	0.55
			EBC (0.67)	0.15	0.05	0.23	0.23	0.05	0.24
			PBR (4)	0.00	0.00	0.00	0.00	0.00	0.00
	0.2	0.2	BSD (9)	0.48	0.18	0.62	0.48	0.18	0.61
			CR	0.48	0.18	0.62	0.48	0.18	0.60
			EBC (0.67)	0.28	0.09	0.83	0.34	0.09	0.84
			PBR (4)	0.03	0.00	1.00	0.03	0.00	1.00
$40 ⋮ 40$	0.2	0	BSD (9)	0.66	0.36	0.75	0.66	0.36	0.65
			CR	0.67	0.36	0.67	0.67	0.36	0.67
			EBC (0.67)	0.89	0.60	0.97	0.82	0.60	0.96
			PBR (4)	1.00	1.00	1.00	1.00	1.00	1.00
	0	0.2	BSD (9)	0.45	0.22	0.53	0.45	0.22	0.54
			CR	0.44	0.21	0.54	0.45	0.21	0.54
			EBC (0.67)	0.15	0.05	0.24	0.22	0.05	0.25
			PBR (4)	0.00	0.00	0.00	0.00	0.00	0.00
	0.2	0.2	BSD (9)	0.48	0.25	0.67	0.48	0.25	0.61
			CR	0.48	0.25	0.62	0.47	0.25	0.61
			EBC (0.67)	0.27	0.11	0.86	0.33	0.11	0.84
			PBR (4)	0.01	0.00	1.00	0.01	0.00	1.00
8 × 10	0.2	0	BSD (2)	0.72	0.11	0.97	0.61	0.11	0.66
			CR	0.61	0.08	0.68	0.62	0.08	0.68
			EBC (0.67)	0.70	0.10	0.91	0.64	0.10	0.96
			PBR (2)	1.00	0.37	1.00	0.72	0.37	1.00
	0	0.2	BSD (2)	0.00	0.00	0.25	0.03	0.00	0.54
			CR	0.03	0.00	0.54	0.03	0.00	0.54
			EBC (0.67)	0.00	0.00	0.26	0.01	0.00	0.24
			PBR (2)	0.00	0.00	0.00	0.00	0.00	0.00
	0.2	0.2	BSD (2)	0.00	0.00	0.82	0.04	0.00	0.60
			CR	0.04	0.00	0.61	0.03	0.00	0.61
			EBC (0.67)	0.00	0.00	0.77	0.01	0.00	0.85
			PBR (2)	0.00	0.00	1.00	0.00	0.00	1.00

BSD: big stick design; EBC: Efron's biased coin design; PBR: permuted block randomization; CR: complete randomization.