Table 2.

The null distribution of the test statistic for WCR-MO procedure using 100,000 replicates of 50 unequal size families given in Figure 2. 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	67,318	32,682	3,023	0.0449
	0.01	67,318	32,682	1,730	0.0257
	0.001	67,318	32,682	1,092	0.0162
	0.0001	67,318	32,682	788	0.0117
1 df test using Z-scores	0.05	68,220	31,780	2,199	0.0292
	0.01	68,220	31,780	1,303	0.0175
	0.001	68,220	31,780	740	0.0109
	0.0001	68,220	31,780	541	0.0077
2 df test using Z-scores	0.05	64,747	35,253	2,161	0.0334
	0.01	64,747	35,253	1,280	0.0198
	0.001	64,747	35,253	817	0.0126
	0.0001	64,747	35,253	581	0.0090