TABLE 1.

Type I error rates of GBJ, GHC, MinP and OMNI tests at significance level of α = 0.05, 0.01, 10⁻³ and10⁻⁴ based on 1×10³, 1×10⁴, 1×10⁵ and 1×10⁶ replications respectively. The correlation matrix is exchangeable with off-diagonal element equal to ρ.

ρ	α	K = 2				K = 4				K = 10
		GBJ	GHC	MinP	OMNI	GBJ	GHC	MinP	OMNI	GBJ	GHC	MinP	OMNI
0.1	0.05	0.047	0.048	0.047	0.047	0.052	0.050	0.058	0.051	0.046	0.052	0.063	0.055
0.3		0.051	0.054	0.051	0.051	0.047	0.044	0.046	0.045	0.033	0.035	0.042	0.037
0.5		0.052	0.047	0.052	0.048	0.056	0.054	0.064	0.057	0.032	0.033	0.050	0.038
0.1	0.01	0.010	0.010	0.010	0.010	0.009	0.009	0.009	0.010	0.012	0.012	0.012	0.011
0.3		0.011	0.011	0.011	0.011	0.010	0.010	0.010	0.011	0.010	0.010	0.010	0.011
0.5		0.011	0.010	0.011	0.010	0.008	0.008	0.009	0.008	0.006	0.007	0.010	0.008
0.1	1×10−3	7.8×10−4	7.9×10−4	7.8×10−4	7.8×10−4	9.6×10−4	9.7×10−4	9.5×10−4	1.0×10−3	1.2×10−3	9.6×10−4	9.4×10−4	1.1×10−3
0.3		9.1×10−4	9.0×10−4	9.1×10−4	9.1×10−4	1.0×10−3	1.0×10−3	1.0×10−3	1.0×10−3	1.1×10−3	1.1×10−3	1.1×10−3	1.2×10−3
0.5		1.1×10−3	1.1×10−3	1.1×10−3	1.1×10−3	8.9×10−4	9.8×10−4	1.0×10−3	9.7×10−4	7.6×10−4	9.8×10−4	1.0×10−3	9.8×10−4
0.1	1×10−4	1.0×10−4	1.2×10−4	9.4×10−5	9.6×10−5	1.1×10−4	1.2×10−4	1.2×10−4	1.2×10−4	1.3×10−4	9.8×10−5	9.8×10−5	1.2×10−4
0.3		9.3×10−5	1.0×10−4	1.0×10−4	1.0×10−4	1.0×10−4	1.1×10−4	1.1×10−4	1.2×10−4	1.3×10−4	1.0×10−4	1.0×10−4	1.2×10−4
0.5		9.6×10−5	1.1×10−4	1.1×10−4	1.1×10−4	9.0×10−5	9.3×10−5	9.3×10−5	9.9×10−5	1.1×10−4	8.1×10−5	8.4×10−5	9.9×10−5