Table 3.

Simulation results for two communities (the true parameter S₁₂ = 120; simulation trials = 2000), ${\widehat{S}}_{12}$: the original lower bound; ${\tilde{S}}_{12}$: the bias-corrected form

Cases	Average of observed shared	Estimator	Average estimate	Sample SE	Average estimated SE	Sample RMSE	Coverage of 95% CI
I vs. I	92.5	${\widehat{S}}_{12}$	122.1	11.32	11.14	11.50	0.93
		${\tilde{S}}_{12}$	119.8	10.63	11.16	10.63	0.96
I vs. II	100.5	${\widehat{S}}_{12}$	119.0	8.47	8.85	8.53	0.96
		${\tilde{S}}_{12}$	117.1	7.84	7.95	8.36	0.96
I vs. III	95.8	${\widehat{S}}_{12}$	116.9	10.02	9.84	10.51	0.94
		${\tilde{S}}_{12}$	114.3	9.01	8.84	10.66	0.91
I vs. IV	98.5	${\widehat{S}}_{12}$	121.6	9.61	9.56	9.74	0.94
		${\tilde{S}}_{12}$	119.5	8.87	9.20	8.88	0.96
I vs. V	69.9	${\widehat{S}}_{12}$	115.7	20.65	19.36	21.09	0.93
		${\tilde{S}}_{12}$	110.4	17.66	18.24	20.10	0.93
II vs. II	111.5	${\widehat{S}}_{12}$	116.6	5.56	5.32	6.50	0.89
		${\tilde{S}}_{12}$	115.2	4.62	4.14	6.67	0.83
II vs. III	103.7	${\widehat{S}}_{12}$	112.1	6.73	6.08	10.39	0.84
		${\tilde{S}}_{12}$	111.2	6.35	5.49	10.85	0.80
II vs. IV	106.5	${\widehat{S}}_{12}$	117.6	6.59	6.69	7.02	0.95
		${\tilde{S}}_{12}$	116.2	6.06	5.92	7.13	0.94
II vs. V	75.8	${\widehat{S}}_{12}$	110.4	16.26	15.81	18.88	0.90
		${\tilde{S}}_{12}$	107.9	15.45	14.63	19.64	0.87
III vs. III	104.0	${\widehat{S}}_{12}$	113.4	7.81	7.44	10.20	0.85
		${\tilde{S}}_{12}$	111.2	6.47	6.17	10.94	0.79
III vs. IV	101.8	${\widehat{S}}_{12}$	115.5	7.94	7.66	9.14	0.93
		${\tilde{S}}_{12}$	113.6	7.15	6.77	9.61	0.90
III vs. V	72.2	${\widehat{S}}_{12}$	108.6	16.74	16.94	20.23	0.90
		${\tilde{S}}_{12}$	104.7	15.23	15.19	21.60	0.85
IV vs. IV	105.0	${\widehat{S}}_{12}$	120.5	7.94	7.94	7.95	0.95
		${\tilde{S}}_{12}$	118.5	7.08	7.49	7.25	0.96
IV vs. V	75.7	${\widehat{S}}_{12}$	114.1	17.83	18.04	18.78	0.94
		${\tilde{S}}_{12}$	109.1	15.68	16.31	19.08	0.92
V vs. V	57.5	${\widehat{S}}_{12}$	106.9	27.90	26.21	30.81	0.88
		${\tilde{S}}_{12}$	98.0	21.95	23.22	31.06	0.87