. Author manuscript; available in PMC: 2010 Aug 16.

Published in final edited form as: Behav Genet. 2009 Jun 14;39(5):580–595. doi: 10.1007/s10519-009-9281-0

Table 4.

Empirical power for tests of equality of two means

Test	Error distribution	n per group	α = 0.05	α = 0.01	α = 0.001
t-test (Y)	Normal	5	0.10939	0.02733	0.00322
t-test (Blom)	Normal	5	0.11653^¥	0.04071^¥	0
Permutation test (Y)	Normal	5	0.10446	0.02162	0
Permutation test (Ranks)	Normal	5	0.03204	0.02162	0
t-test (Y)	LaPlace	5	0.12052	0.02851	0.00314
t-test (Blom)	LaPlace	5	0.14028^¥	0.05539^¥	0
Permutation test (Y)	LaPlace	5	0.12864	0.03139	0
Permutation test (Ranks)	LaPlace	5	0.09391	0.03139	0
t-test (Y)	$χ_{(1)}^{2}$	5	0.18244	0.05897	0.01084
t-test (Blom)	$χ_{(1)}^{2}$	5	0.26666^¥	0.13369^¥	0
Permutation test (Y)	$χ_{(1)}^{2}$	5	0.23624	0.09799	0
Permutation test (Ranks)	$χ_{(1)}^{2}$	5	0.19199	0.09799	0
t-test (Y)	Weibull (1, 0.5)	5	0.34973	0.18931	0.07927
t-test (Blom)	Weibull (1, 0.5)	5	0.43828^¥	0.31499^¥	0
Permutation test (Y)	Weibull (1, 0.5)	5	0.44622	0.29085	0
Permutation test (Ranks)	Weibull (1, 0.5)	5	0.36267	0.29085	0
t-test (Y)	LaPlace	25	0.42706	0.20808	0.05924
t-test (Blom)	LaPlace	25	0.47360	0.24784	0.07972
Kruskal–Wallis (Ranks)	LaPlace	25	0.50998	0.26034	0.07448
t-test (Y)	$χ_{(1)}^{2}$	25	0.46456	0.25234	0.08722
t-test (Blom)	$χ_{(1)}^{2}$	25	0.87178	0.68580	0.38978
Kruskal–Wallis (Ranks)	$χ_{(1)}^{2}$	25	0.86978	0.68242	0.37654
t-test (Y)	Weibull (1, 0.5)	25	0.58656	0.39310	0.20444
t-test (Blom)	Weibull (1, 0.5)	25	0.98630	0.93680	0.77968
Kruskal–Wallis (Ranks)	Weibull (1, 0.5)	25	0.99022	0.95642	0.82032
t-test (Y)*	Weibull (1, 0.5)	*25	0.08972	0.02034	0.00206
t-test (Blom)*	Weibull (1, 0.5)	*25	0.62910	0.37776	0.14214
Kruskal–Wallis (Ranks)*	Weibull (1, 0.5)	*25	0.60964	0.35880	0.12734

Note: 100,000 simulations

Population mean difference = 0.5 within group standard deviations, except * where Population mean difference = 0.125 within group standard deviations (last three rows). Kruskal–Wallis is the large-sample approximate test of the Wilcoxon–Mann–Whitney

^¥

Demonstrated significantly inflated Type 1 error rate (see Table 1)