Table 3.

Empirical Type 1 error rates for tests of equality of three means with total sample size of n = 400, allele frequency of P = 0.25 (n_GG = 25, n_Gg = 150, n_gg = 225), 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 1.5 1.0	0.10030¥	0.03034¥	0.00533¥
F-test (Blom)	Normal		0.09252¥	0.02647¥	0.00421¥
Welch test (Y)	Normal		0.05001	0.01039	0.00116
Welch test (Blom)	Normal		0.04878	0.01048	0.00125
F-test (Y)	LaPlace	2.0 1.5 1.0	0.09985¥	0.03036¥	0.00556¥
F-test (Blom)	LaPlace		0.08025¥	0.02078¥	0.00299¥
Welch test (Y)	LaPlace		0.04827	0.00907	0.00077
Welch test (Blom)	LaPlace		0.04954	0.01068	0.00131
F-test (Y)	${\chi }_{\left(1\right)}^2$	2.0 1.5 1.0	0.09544¥	0.02847¥	0.00620¥
F-test (Blom)	${\chi }_{\left(1\right)}^2$		0.94547¥	0.85131¥	0.65849¥
Welch test (Y)	${\chi }_{\left(1\right)}^2$		0.08964¥	0.03948¥	0.01687¥
Welch test (Blom)	${\chi }_{\left(1\right)}^2$		0.88016¥	0.68898¥	0.37710¥
F-test (Y)	Weibull (1, 0.5)	2.0 1.5 1.0	0.08504¥	0.02861¥	0.00867
F-test (Blom)	Weibull (1, 0.5)		0.99859¥	0.99177¥	0.96038
Welch test (Y)	Weibull (1, 0.5)		0.14157¥	0.08047¥	0.04306
Welch test (Blom)	Weibull (1, 0.5)		0.99407¥	0.96715	0.84900
F-test (Y)	Normal	1.0 1.5 2.0	0.02446	0.00378¥	0.00034¥
F-test (Blom)	Normal		0.02388	0.00353¥	0.00037¥
Welch test (Y)	Normal		0.05037	0.00986¥	0.00121¥
Welch test (Blom)	Normal		0.04831	0.00935¥	0.00108¥
F-test (Y)	LaPlace	1.0 1.5 2.0	0.02492	0.00380	0.00034
F-test (Blom)	LaPlace		0.02883	0.00451	0.00042
Welch test (Y)	LaPlace		0.04814	0.00848	0.00084
Welch test (Blom)	LaPlace		0.04910	0.00943	0.00106
F-test (Y)	${\chi }_{\left(1\right)}^2$	1.0 1.5 2.0	0.02611	0.00508	0.00048
F-test (Blom)	${\chi }_{\left(1\right)}^2$		0.80479¥	0.57026¥	0.27504¥
Welch test (Y)	${\chi }_{\left(1\right)}^2$		0.07594¥	0.02862¥	0.00938¥
Welch test (Blom)	${\chi }_{\left(1\right)}^2$		0.90466¥	0.72989¥	0.41380¥
F-test (Y)	Weibull (1, 0.5)	1.0 1.5 2.0	0.03269	0.00801	0.00135
F-test (Blom)	Weibull (1, 0.5)		0.98888¥	0.94116¥	0.77915¥
Welch test (Y)	Weibull (1, 0.5)		0.10358¥	0.04449¥	0.01593¥
Welch test (Blom)	Weibull (1, 0.5)		0.99897¥	0.99093¥	0.93403¥

Note: 100,000 simulations

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