Table 1. Parameters defining weighted sampling and empirical false positive rate of the present method for computing significance of overlap among three sets from weighted sampling.

Weight(w)	Population Size (n)
	1000	2000	3000	4000	5000	6000	7000	8000	9000	10000
1.0	0.036	0.04	0.01	0.009	0.018	0.026	0.01	0.005	0.033	0.024
1.1	0.05	0.035	0.014	0.018	0.015	0.039	0.015	0.01	0.038	0.026
1.2	0.054	0.035	0.023	0.018	0.015	0.038	0.014	0.004	0.03	0.02
1.3	0.052	0.035	0.018	0.024	0.018	0.025	0.017	0.006	0.04	0.021
1.4	0.067	0.053	0.024	0.02	0.013	0.028	0.007	0.006	0.042	0.023
1.5	0.078	0.04	0.021	0.014	0.019	0.027	0.011	0.01	0.036	0.023
1.6	0.084	0.047	0.022	0.02	0.022	0.029	0.012	0.003	0.037	0.024
1.7	0.102	0.062	0.015	0.019	0.013	0.029	0.008	0.009	0.03	0.033
1.8	0.137	0.057	0.029	0.027	0.017	0.033	0.014	0.007	0.041	0.024
1.9	0.157	0.063	0.03	0.021	0.028	0.029	0.013	0.008	0.038	0.031
2.0	0.178	0.078	0.035	0.029	0.022	0.041	0.014	0.008	0.028	0.027

The rate of false positive was calculated as the fraction of simulations with P value < 0.05 in 1000 repeated simulations. In each simulation, we sampled independently three sets of sizes 200, 300 and 400, from a population of size n. In each population, 100 elements had a sampling probability weight of w over the rest of the elements: all elements in the population were equally likely to be sampled (i.e. unbiased sampling) if w = 1, while 100 of the elements had twice the chance to be sampled compared with the others if w = 2.