Equivariance and Generalized Inference in Two-Sample Location-Scale Families

Table 7

Powers for 𝛿 (normal case with unequal sample sizes & scale parameters).

Sizes (𝑚,𝑛)	(𝛿,𝜎1,𝜎2)	Power		(𝛿,𝜎1,𝜎2)	Power
		Welch	GTV		Welch	GTV
(5,10)	(−2,2,1)	0.5472	0.550	(−102,200,2)	0.2462	0.2488
	(−1,2,1)	0.2274	0.2296	(−12,200,2)	0.0572	0.0608
	(0,2,1)	0.0578	0.0464	(0,200,2)	0.0542	0.0504
	(1,2,1)	0.0082	0.0066	(8,200,2)	0.046	0.037
(10,5)	(−2,2,1)	0.7712	0.7791	(−102,200,2)	0.438	0.4402
	(−1,2,1)	0.3216	0.3304	(−12,200,2)	0.066	0.0678
	(0,2,1)	0.045	0.0458	(0,200,2)	0.0524	0.049
	(1,2,1)	0.0016	0.002	(8,200,2)	0.0448	0.042
(5,100)	(−2,2,1)	0.5714	0.5804	(−102,200,2)	0.2414	0.2496
	(−1,2,1)	0.2322	0.2409	(−12,200,2)	0.0592	0.0688
	(0,2,1)	0.0542	0.0508	(0,200,2)	0.047	0.0486
	(1,2,1)	0.0044	0.004	(8,200,2)	0.0448	0.0486
(50,100)	(−2,2,1)	1	1	(−102,200,2)	0.9712	0.9726
	(−1,2,1)	0.9522	0.9534	(−12,200,2)	0.110	0.116
	(0,2,1)	0.052	0.0488	(0,200,2)	0.047	0.049
	(1,2,1)	0	0	(8,200,2)	0.029	0.0252
(100,50)	(−2,2,1)	1	1	(−102,200,2)	0.9984	0.999
	(−1,2,1)	0.992	0.9932	(−12,200,2)	0.1378	0.156
	(0,2,1)	0.0512	0.0492	(0,200,2)	0.051	0.0486