Table 3.

Simulation results for $H_0:p=0.2$ and $H_1:p=0.4$ with Simon’s optimal sample size.

Data	($n_1$, $n_2$)	Par	Simon	logit(0.2)	logit(0.3)	logit(0.4)
$H_0$	(5, 31)	$\widehat{p}$	0.32 (0.08)	0.21 (0.07)	0.22 (0.08)	0.22 (0.08)
		FPR	0.01	0.08	0.08	0.08
		PET	0.99	0.59	0.57	0.56
		ESS	5.21	17.79	18.32	18.79
	(15, 21)	$\widehat{p}$	0.24 (0.07)	0.21 (0.07)	0.21 (0.07)	0.21 (0.07)
		FPR	0.07	0.08	0.08	0.08
		PET	0.65	0.56	0.55	0.54
		ESS	22.39	24.28	24.51	24.69
	(20, 16)	$\widehat{p}$	0.23 (0.07)	0.22 (0.07)	0.22 (0.07)	0.22 (0.07)
		FPR	0.09	0.09	0.09	0.09
		PET	0.41	0.56	0.55	0.55
		ESS	29.42	26.98	27.14	27.25
	(10, 26)	$\widehat{p}$	0.26 (0.07)	0.21 (0.07)	0.21 (0.07)	0.21 (0.07)
		FPR	0.03	0.08	0.08	0.08
		PET	0.88	0.58	0.57	0.56
		ESS	13.14	20.95	21.27	21.57
$H_1$	(5, 31)	$\widehat{p}$	0.47 (0.08)	0.40 (0.09)	0.41 (0.09)	0.41 (0.09)
		Power	0.09	0.84	0.84	0.85
	(15, 21)	$\widehat{p}$	0.43 (0.08)	0.40 (0.09)	0.40 (0.09)	0.40 (0.09)
		Power	0.60	0.89	0.89	0.90
	(20, 16)	$\widehat{p}$	0.41 (0.08)	0.40 (0.09)	0.40 (0.09)	0.40 (0.09)
		Power	0.85	0.90	0.90	0.90
	(10, 26)	$\widehat{p}$	0.40 (0.08)	0.40 (0.09)	0.40 (0.09)	0.40 (0.09)
		Power	0.89	0.90	0.90	0.90

FPR = false positive rate; PET = probability of early termination; ESS=expected sample size