Table 3:

Empirical concentration (OPT) using the projection-based sample size procedure at a nominal level of 90 using a pilot study of size $n_0=200$ and $n_0=400$. We test whether the true value of the estimated regime is within $ϵ$ of the true value of the true optimal regime. The remaining columns give the mean, median, quartiles, and standard deviation of the estimated sample sizes across the 500 simulation repetitions.

$ϵ$	$n_0$	$\mathbb{E}\left(\widehat{n}\right)$	$\mathrm{Q}1\left(\widehat{n}\right)$	$\mathrm{Med}\left(\widehat{n}\right)$	$\mathrm{Q}3\left(\widehat{n}\right)$	$\mathrm{SD}\left(\widehat{n}\right)$	OPT
0.30	200	1844.93	1561.50	1796.00	2060.00	365.42	100.00
0.50	200	754.27	663.50	748.00	836.00	128.73	100.00
0.70	200	431.14	387.00	426.00	473.00	65.13	100.00
0.30	400	1319.70	1191.50	1294.50	1451.75	193.43	100.00
0.50	400	543.24	500.00	526.50	586.00	69.92	100.00
0.70	400	320.63	293.25	319.00	345.75	37.88	100.00