Table 2.

Empirical Type 1 error rates for tests of equality of three means with total sample size of N = 400, allele frequency of P = 0.50 (n_GG = 100, n_Gg = 200, n_gg = 100), negative (upper-half), and positive (lower-half) pairing of sample sizes and variances

Test	Error distribution	(GG Gg gg) σ2 per group	α = 0.05	α = 0.01	α = 0.001
F-test (Y)	Normal	2.0 1.0 2.0	0.07802¥	0.01982¥	0.00286¥
F-test (Blom)	Normal		0.07189¥	0.01763¥	0.00249¥
Welch test (Y)	Normal		0.05021	0.00982	0.00093
Welch test (Blom)	Normal		0.04709	0.00896	0.00083
F-test (Y)	LaPlace	2.0 1.0 2.0	0.07735¥	0.01970¥	0.00272¥
F-test (Blom)	LaPlace		0.06774¥	0.01587¥	0.00196¥
Welch test (Y)	LaPlace		0.04897	0.00951	0.00090
Welch test (Blom)	LaPlace		0.04918	0.00947	0.00087
F-test (Y)	${\chi }_{\left(1\right)}^2$	2.0 1.0 2.0	0.07641¥	0.01890¥	0.00251¥
F-test (Blom)	${\chi }_{\left(1\right)}^2$		0.97045¥	0.89414¥	0.70173¥
Welch test (Y)	${\chi }_{\left(1\right)}^2$		0.06122¥	0.01718¥	0.00358¥
Welch test (Blom)	${\chi }_{\left(1\right)}^2$		0.96537¥	0.87953¥	0.66590¥
F-test (Y)	Weibull (1, 0.5)	2.0 1.0 2.0	0.07067¥	0.01461¥	0.00169¥
F-test (Blom)	Weibull (1, 0.5)		0.99981¥	0.99869¥	0.98711¥
Welch test (Y)	Weibull (1, 0.5)		0.08008¥	0.02698¥	0.00684¥
Welch test (Blom)	Weibull (1, 0.5)		0.99976¥	0.99820¥	0.98406¥
F-test (Y)	Normal	1.0 2.0 1.0	0.02975	0.00462	0.00042
F-test (Blom)	Normal		0.02721	0.00395	0.00028
Welch test (Y)	Normal		0.05043	0.01000	0.00096
Welch test (Blom)	Normal		0.04655	0.00881	0.00082
F-test (Y)	LaPlace	1.0 2.0 1.0	0.02943	0.00475	0.00030
F-test (Blom)	LaPlace		0.03297	0.00524	0.00038
Welch test (Y)	LaPlace		0.04889	0.00969	0.00086
Welch test (Blom)	LaPlace		0.04815	0.00936	0.00084
F-test (Y)	${\chi }_{\left(1\right)}^2$	1.0 2.0 1.0	0.03114	0.00568	0.00067
F-test (Blom)	${\chi }_{\left(1\right)}^2$		0.96098¥	0.87231¥	0.65804¥
Welch test (Y)	${\chi }_{\left(1\right)}^2$		0.05264	0.01136	0.00145
Welch test (Blom)	${\chi }_{\left(1\right)}^2$		0.96551¥	0.88077¥	0.66728¥
F-test (Y)	Weibull (1, 0.5)	1.0 2.0 1.0	0.03460	0.00808	0.00100
F-test (Blom)	Weibull (1, 0.5)		0.99982¥	0.99750¥	0.98304¥
Welch test (Y)	Weibull (1, 0.5)		0.05359	0.01076	0.00091
Welch test (Blom)	Weibull (1, 0.5)		0.99985¥	0.99775¥	0.98388¥

Note: 100,000 simulations

^¥Indicates significantly greater than nominal α level at the 95% confidence level