Table 4 Type I error rates of five tests based on simulation set 1 for qualitative traits.

Number of Subpopulations	Test	Alpha	Un-corrected	GC	PC-linear	Biased Perm	PC-nonp
2	Single Variant	0.01	0.02914	0.00648	0.01124	0.0065	0.0107
	Single Variant	0.001	0.00592	0.00034	0.00094	0.00056	0.00094
	Regional	0.01	0.04066	0.00924	0.01168	0.0103	0.01192
	Regional	0.001	0.0093	0.0009	0.00144	0.001	0.00146
10	Single Variant	0.01	0.0428	0.01106	0.0106	0.00672	0.0103
	Single Variant	0.001	0.01172	0.00124	0.00162	0.00078	0.00138
	Regional	0.01	0.04862	0.00984	0.0105	0.01034	0.01062
	Regional	0.001	0.01174	0.00134	0.00128	0.0008	0.0012
20	Single Variant	0.01	0.02022	0.01244	0.01734	0.02296	0.01072
	Single Variant	0.001	0.00414	0.00138	0.00354	0.00458	0.00132
	Regional	0.01	0.04014	0.01068	0.03468	0.02694	0.01034
	Regional	0.001	0.00952	0.00172	0.00746	0.0051	0.00152

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