Table 1. Simulated Type I error rates based on 10,000 datasets.

Significance level	Optimal Omnibus-Fisher	Omnibus-Fisher	Usual Fisher
Independent G, M and E with binary traits
0.05	0.0521	0.0516	0.0522
0.01	0.0100	0.0109	0.0108
0.001	0.0015	0.0015	0.0015
Independent G, M and E with continuous traits
0.05	0.0483	0.0472	0.0478
0.01	0.0088	0.0095	0.0095
0.001	0.0007	0.0009	0.0009
G and E correlated with binary traits
0.05	0.0488	0.0526	0.0675
0.01	0.0089	0.0107	0.0161
0.001	0.0010	0.0015	0.0029
G and E correlated with continuous traits
0.05	0.0525	0.0509	0.0655
0.01	0.0093	0.0096	0.0166
0.001	0.0005	0.0011	0.0029