Table 2.

Estimated α-levels for the Gumbel approximation for different parameters, corresponding to five nominal α-levels.

					Nominal alpha
Number of cases	Maximum circle size	Region	Probability Model	Number of Monte Carlo replicates	0.00001	0.0001	0.001	0.01	0.05
6	50%	NE counties	Poisson	99	0.000003	0.00004	0.0006	0.008	0.051
				999	0.000001	0.00002	0.0004	0.007	0.048
				9999	0.000001	0.00002	0.0004	0.007	0.047
600	50%	NE counties	Poisson	99	0.000013	0.00012	0.0012	0.011	0.054
				999	0.000006	0.00008	0.0009	0.010	0.051
				9999	0.000006	0.00007	0.0008	0.010	0.050
600	50%	NE counties	Bernoulli	99	0.000014	0.00013	0.0012	0.011	0.053
				999	0.000007	0.00008	0.0009	0.010	0.050
				9999	0.000007	0.00008	0.0008	0.010	0.047
600	50%	US 3 digit zip codes	Poisson	99	0.000014	0.00013	0.0012	0.011	0.054
				999	0.000007	0.00008	0.0009	0.010	0.052
				9999	0.000006	0.00008	0.0009	0.010	0.051
600	1 county	NE counties	Poisson	99	0.000033	0.00022	0.0016	0.012	0.053
				999	0.000020	0.00016	0.0012	0.011	0.051
				9999	0.000018	0.00015	0.0018	0.011	0.050
6000	50%	NE counties	Poisson	99	0.000013	0.00012	0.0011	0.011	0.053
				999	0.000007	0.00008	0.0009	0.010	0.051
				9999	0.000006	0.00007	0.0008	0.010	0.050
60000	50%	NE counties	Poisson	99	0.000013	0.00012	0.0011	0.011	0.054
				999	0.000006	0.00007	0.0009	0.010	0.051
				9999	0.000006	0.00007	0.0008	0.009	0.050