Table 3.

The null distribution of the test statistic for WCR-MO procedure using 100,000 replicates of 100 equal size families (i.e. two siblings and both parents in the family). For each replicate we used 10,000 bootstrap samples.

Test Procedure	Nominal α-level	Total number of times the total variance estimate was positive	Number of times total variance was negative resulting in missing p-values	Number of times p-values less than given α-level	Type I error rate using only non-missing p-values
Testing β1 with 1 df test	0.05	71,223	28,777	4,576	0.06425
	0.01	71,223	28,777	2,552	0.03583
	0.001	71,223	28,777	1,529	0.02147
	0.0001	71,223	28,777	1,082	0.01519
1 df test using Z-scores	0.05	68,220	31,780	1,989	0.02916
	0.01	68,220	31,780	1,193	0.01749
	0.001	68,220	31,780	743	0.01089
	0.0001	68,220	31,780	528	0.00774
2 df test using Z-scores	0.05	72,578	27,422	3,064	0.04222
	0.01	72,578	27,422	1,904	0.02623
	0.001	72,578	27,422	1,239	0.01707
	0.0001	72,578	27,422	888	0.01223