Table 1.

Estimated type I errors of two testing methods based on structures S1–S6 for quantitative traits.

	Structure	$t_{kj}^2=0.05$		$t_{kj}^2=0.15$		$t_{kj}^2=0.35$
ρkj	No.	S	M	S	M	S	M
–	S1	0.0099	0.0100	0.0099	0.0100	0.0099	0.0100
	S2	0.0096	0.0096	0.0085	0.0092	0.0101	0.0097
	S3	0.0088	0.0095	0.0092	0.0091	0.0081	0.0089
	S4	0.0098	0.0095	0.0095	0.0098	0.0092	0.0093
	S5	0.0095	0.0091	0.0094	0.0091	0.0098	0.0099
	S6	0.0090	0.0093	0.0091	0.0091	0.0070	0.0085
0.2	S1	0.0090	0.0097	0.0090	0.0097	0.0090	0.0097
	S2	0.0100	0.0101	0.0094	0.0097	0.0094	0.0097
	S3	0.0101	0.0101	0.0092	0.0096	0.0084	0.0096
	S4	0.0095	0.0099	0.0101	0.0102	0.0087	0.0102
	S5	0.0099	0.0100	0.0092	0.0101	0.0085	0.0095
	S6	0.0093	0.0092	0.0080	0.0092	0.0078	0.0096
−0.2	S1	0.0095	0.0097	0.0095	0.0097	0.0095	0.0097
	S2	0.0102	0.0101	0.0095	0.0097	0.0094	0.0097
	S3	0.0104	0.0089	0.0098	0.0096	0.0093	0.0096
	S4	0.0098	0.0096	0.0094	0.0097	0.0103	0.0102
	S5	0.0090	0.0096	0.0095	0.0097	0.0093	0.0097
	S6	0.0093	0.0091	0.0094	0.0096	0.0078	0.0097

‘S’ and ‘M’ denote the single-trait and multiple-trait tests, respectively. ρ_kj= –, 0.2, and −0.2 represent the case of no extraneous variables, and the cases of having extraneous variables that result in positive and negative correlations among traits, respectively. The nominal significance level is 0.01.