. Author manuscript; available in PMC: 2015 Jan 1.

Published in final edited form as: Genet Epidemiol. 2014 Jan;38(1):51–59. doi: 10.1002/gepi.21778

Table II.

Comparison of empirical Type I error/power between one step tests and two-step tests in four simulated scenarios adjusting for a covariate. PB:Parametric Bootstrap; LR:Linear Regression; KW:Kruskal-Wallis; FK:Fligner-Killeen.

A. QTL is correlated with the covariate (confounder).

Simulated effects	one-step tests					two-step tests
Simulated effects	LRT_MV	LRT_MV(PB)	LRT_M	LRT_V	LR	Lepage	KW	FK	Levene
No effect	0.047	0.049	0.053	0.061	0.049	0.026	0.029	0.058	0.055
Mean	0.624	0.619	0.730	0.048	0.736	0.551	0.578	0.040	0.040
Variance	0.736	0.726	0.051	0.822	0.055	0.749	0.031	0.756	0.764
Mean & var	0.951	0.948	0.707	0.829	0.747	0.948	0.560	0.775	0.782

B. QTL is independent of the covariate.

Simulated effects	one-step tests					two-step tests
Simulated effects	LRT_MV	LRT_MV(PB)	LRT_M	LRT_V	LR	Lepage	KW	FK	Levene
No effect	0.057	0.053	0.048	0.045	0.051	0.044	0.048	0.046	0.043
Mean	0.779	0.780	0.866	0.046	0.869	0.844	0.857	0.044	0.047
Variance	0.722	0.718	0.040	0.823	0.059	0.751	0.047	0.762	0.767
Mean & var	0.978	0.979	0.811	0.845	0.853	0.983	0.833	0.786	0.795