MANOVA for Nested Designs with Unequal Cell Sizes and Unequal Cell Covariance Matrices

Table 2

Empirical sizes and powers of the two tests for nested effects for 3-variate two-factor multivariate nested designs [𝑎=3,𝑏₁=8,𝑏₂=10,𝑏₃=12, (𝚺₁₁,𝚺₁₂,…,𝚺_𝑎𝑏𝑎)=𝟏^𝑇₁₀⊗(𝐈₃,diag(𝝀),(1−𝜌)𝐈₃+𝜌𝟏₃𝟏^𝑇₃)].

(𝝀,𝜌)	𝐧	𝛿=0		𝛿=0.6		𝛿=1.2		𝛿=1.8
		AHT	PB	AHT	PB	AHT	PB	AHT	PB
(𝝀1,𝜌1)	𝐧1	0.052	0.054	0.099	0.103	0.369	0.353	0.840	0.815
	𝐧2	0.056	0.041	0.164	0.152	0.705	0.691	0.994	0.991
	𝐧3	0.092	0.041	0.302	0.194	0.944	0.891	1.000	1.000
	𝐧4	0.096	0.044	0.288	0.185	0.927	0.847	1.000	1.000
(𝝀2,𝜌2)	𝐧1	0.054	0.049	0.181	0.213	0.756	0.860	0.997	1.000
	𝐧2	0.055	0.048	0.335	0.422	0.985	0.997	1.000	1.000
	𝐧3	0.090	0.050	0.629	0.519	1.000	1.000	1.000	1.000
	𝐧4	0.089	0.061	0.522	0.545	0.999	1.000	1.000	1.000
(𝝀3,𝜌3)	𝐧1	0.049	0.050	0.271	0.194	0.727	0.852	0.995	1.000
	𝐧2	0.052	0.056	0.308	0.427	0.978	0.998	1.000	1.000
	𝐧3	0.094	0.060	0.593	0.519	1.000	0.999	1.000	1.000
	𝐧4	0.098	0.057	0.486	0.551	0.999	1.000	1.000	1.000
	ARE	46.67	10.83

(𝝀₁,𝜌₁)=(1₃,0), (𝝀₂,𝜌₂)=(1,15,0.1,0.1), and (𝝀₃,𝜌₃)=(1,10,0.1,0.5). 𝐧₁=(10,10,10)₁₀, 𝐧₂=(15,15,15)₁₀, 𝐧₃=(10,20,40)₁₀, and 𝐧₄=(40,20,10)₁₀.