Table 1 Coverage relative frequencies of...

Table 1

Coverage relative frequencies of confidence regions at confidence level α = 95% for difference of location parameters μ_d with various combinations of sample sizes, ρ₁, ρ₂ and D₁, D₂ using Hotelling's T² as the pivotal quantity when Σ₁ and Σ₂ are equal but unknown

$(n_{1}, n_{2})$	$Σ = (\begin{matrix} 1 & ρ \\ ρ & 1 \end{matrix})$	$D_{1} = (\begin{matrix} 1 & 3 \\ 2 & - 5 \end{matrix})$		$D_{2} = (\begin{matrix} - 2 & 2 \\ 3 & 0 \end{matrix})$

		F-distribution	CSF-distribution	F-distribution	CSF-distribution
$(20,25)$	ρ = 0.2	0.9268	0.9495	0.9224	0.9524
	ρ = 0.5	0.9274	0.9511	0.9135	0.9502
	ρ = 0.8	0.9206	0.9504	0.9227	0.9520
$(40,45)$	ρ = 0.2	0.9025	0.9479	0.9008	0.9534
	ρ = 0.5	0.9118	0.9451	0.9095	0.9509
	ρ = 0.8	0.9036	0.9521	0.9016	0.9524
$(80,100)$	ρ = 0.2	0.8932	0.9527	0.9080	0.9479
	ρ = 0.5	0.8917	0.9463	0.8702	0.9470
	ρ = 0.8	0.9035	0.9483	0.8933	0.9448
$(200,250)$	ρ = 0.2	0.8824	0.9503	0.8883	0.9461
	ρ = 0.5	0.88920	0.9533	0.8956	0.9559
	ρ = 0.8	0.8998	0.9492	0.8852	0.9546

$(n_{1}, n_{2})$	$Σ = (\begin{matrix} 1 & ρ \\ ρ & 1 \end{matrix})$	$D_{1} = (\begin{matrix} 1 & 3 \\ 2 & - 5 \end{matrix})$		$D_{2} = (\begin{matrix} - 2 & 2 \\ 3 & 0 \end{matrix})$

		F-distribution	CSF-distribution	F-distribution	CSF-distribution
$(20,25)$	ρ = 0.2	0.9268	0.9495	0.9224	0.9524
	ρ = 0.5	0.9274	0.9511	0.9135	0.9502
	ρ = 0.8	0.9206	0.9504	0.9227	0.9520
$(40,45)$	ρ = 0.2	0.9025	0.9479	0.9008	0.9534
	ρ = 0.5	0.9118	0.9451	0.9095	0.9509
	ρ = 0.8	0.9036	0.9521	0.9016	0.9524
$(80,100)$	ρ = 0.2	0.8932	0.9527	0.9080	0.9479
	ρ = 0.5	0.8917	0.9463	0.8702	0.9470
	ρ = 0.8	0.9035	0.9483	0.8933	0.9448
$(200,250)$	ρ = 0.2	0.8824	0.9503	0.8883	0.9461
	ρ = 0.5	0.88920	0.9533	0.8956	0.9559
	ρ = 0.8	0.8998	0.9492	0.8852	0.9546

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