Table 1.

The ratio of the observed type I error rates of the set-valued (SV), logistic regression (LG and oLG), and the usual ordered Probit (oPRB) methods over the given significance levels α using SVsimu data generation method and random sampling scheme.

n	p A	0.05				0.01				1×10−5				1×10−6
		LG	SV	oLG	oPRB	LG	SV	oLG	oPRB	LG	SV	oLG	oPRB	LG	SV	oLG	oPRB
150	0.05	0.8	1.02	0.96	1	0.37	0.9	0.77	0.86	0	0.4	57	1.3	0	0.26	560	11
150	0.2	0.98	1.06	1.02	1.04	0.84	1.1	0.98	1	0.07	1.10	0.4	0.7	0.1	1.1	0.2	0.48
2500	0.0025	0.66	0.9	0.88	0.9	0.2	0.69	0.79	0.69	0	0.16	190	0.16	0	0.07	1900	0.068
5000	0.0025	0.9	0.96	0.96	0.96	0.64	0.88	0.83	0.88	0	0.4	0.8	0.35	0	0.3	4.3	0.12
1000	0.0075	0.76	0.98	0.92	0.96	0.31	0.81	0.73	0.8	0	0.26	55	0.22	0	0.1	550	0.19
2000	0.0075	0.9	1	0.98	1	0.70	0.95	0.88	0.94	0.01	0.42	0.4	0.4	0	0.3	0.5	0.34
1000	0.01	0.84	0.98	0.94	0.98	0.50	0.89	0.79	0.88	0	0.34	4.50	0.29	0	0.2	43	0.18
2000	0.01	0.92	1	0.98	1	0.77	0.96	0.92	0.95	0.04	0.58	0.54	0.57	0	0.4	0.5	0.44
1000	0.05	0.98	1	1	1	0.92	1	0.99	0.99	0.39	0.86	0.71	0.81	0.2	0.8	0.6	0.74
2000	0.05	1	1	1.02	1	0.97	1	1	1	0.69	0.94	0.86	0.92	0.5	0.8	0.8	0.8
1000	0.2	1	1	1.02	1	0.97	1	1	1	0.77	1	0.93	0.96	0.7	0.9	0.7	0.78
2000	0.2	1	1	1.02	1	0.99	1	1	1	0.85	1.10	1	1.1	0.7	1	0.9	0.98

n is the number of individuals sampled from the population; p_A is minor allele frequency of SNP; LG stands for logistic regression model on the regrouped binary outcome (recoding as 0 or greater than 0); SV stands for the set-valued method; oLG stands for ordered logistic regression method; oPRB stands for the usual ordered probit model with the traditional IRWLS algorithm. Values in bold means inflated type I error rates.