Table 2.

Simulation results (1000 simulated datasets, each with n patients) showing empirical rejection probabilities of the proposed resampling tests for a classification Random Forest. For all variables the information is given whether or not $H_0^{(1)}$ and $H_0^{(2)}$ is true. Thereby, $H_0^{(1)}$ is considered to be true for variables that are independent to all variables $X_i$ with non-zero regression coefficient ($X_3,X_4,X_5$) and $H_0^{(2)}$ is considered to be true when the variable’s regression coefficient is zero ($X_4$, $X_5$, Z)

Variable			Rejection probability of ${\mathbf{H}}_{\mathbf{0}}^{(\mathbf{1})}$			Rejection probability of ${\mathbf{H}}_{\mathbf{0}}^{(\mathbf{2})}$
Z=	${\mathbf{H}}_{\mathbf{0}}^{(\mathbf{1})}=$	${\mathbf{H}}_{\mathbf{0}}^{(\mathbf{2})}=$	n=500	n=1000	n=5000	n=500	n=1000	n=5000
$X_1$	false	false	0.300	0.571	1.000	0.797	0.969	1.000
$X_2$	false	false	0.303	0.561	0.999	0.776	0.963	1.000
$X_3$	true	false	0.000	0.000	0.000	0.866	0.985	1.000
$X_4$	true	true	0.000	0.000	0.002	0.061	0.058	0.066
$X_5$	true	true	0.000	0.002	0.001	0.063	0.050	0.074
Z	false	true	0.154	0.226	0.572	0.045	0.065	0.063