Table 3.

The Monte Carlo Type I Errors and Powers of the EL ratio test statistics (3) and (7) for testing H₀: μ_x = 0 Based on Data Following the Hybrid Design (X_i ~ N(μ_x, 1), ${\epsilon }_i~N(0,{\sigma }_m^2)$. The pooling proportion α = 0.5; the expected significance level was 0.05).

Sample Size (N)	Pooling Group Size (p)	Parameters ${\sigma }_m^2$	ELR Test Statistic (3)			ELR Test Statistic (7)
			Type I Error	Power		Type I Error	Power
			μx =0	μx =0.5	μx =1.0	μx =0	μx =0.5	μx =1.0
N=100	p=2	0.4	0.0587	0.9919	1.0000	0.0580	0.9718	0.9990
		1.0	0.0558	0.9373	1.0000	0.0611	0.9230	0.9986
	p=5	0.4	0.0555	0.9989	1.0000	0.0530	0.9512	0.9992
		1.0	0.0587	0.9626	1.0000	0.0604	0.9446	0.9976
	p=10	0.4	0.0588	0.9995	1.0000	0.0595	0.9531	0.9999
		1.0	0.0556	0.9684	1.0000	0.0621	0.9680	0.9992
N=200	p=2	0.4	0.0495	0.9999	1.0000	0.0594	0.9990	0.9985
		1.0	0.0536	0.9991	1.0000	0.0593	0.9983	0.9995
	p=5	0.4	0.0540	1.0000	1.0000	0.0524	0.9952	0.9996
		1.0	0.0511	0.9997	1.0000	0.0543	0.9981	0.9999
	p=10	0.4	0.0549	1.0000	1.0000	0.0546	0.9950	0.9996
		1.0	0.0536	0.9999	1.0000	0.0551	0.9979	1.0000