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

Table 3

Empirical sizes and powers of the two tests for nested effects for 10-variate two-factor multivariate nested designs [𝑎=3,𝑏₁=3,𝑏₂=5,𝑏₃=7, (𝚺₁₁,𝚺₁₂,…,𝚺_𝑎𝑏𝑎)=𝟏^𝑇₁₀⊗(𝐈₃,diag(𝝀),diag(𝜼))].

(𝝀,𝜼)	𝐧	𝛿=0		𝛿=1		𝛿=2		𝛿=3
		AHT	PB	AHT	PB	AHT	PB	AHT	PB
(𝝀1,𝜼1)	𝐧1	0.046	0.042	0.438	0.415	0.999	0.998	1.000	1.000
	𝐧2	0.052	0.050	0.937	0.932	1.000	1.000	1.000	1.000
	𝐧3	0.062	0.046	0.788	0.762	1.000	1.000	1.000	1.000
	𝐧4	0.058	0.056	0.871	0.846	1.000	1.000	1.000	1.000
(𝝀2,𝜼2)	𝐧1	0.052	0.044	0.842	0.635	1.000	1.000	1.000	1.000
	𝐧2	0.052	0.047	1.000	0.996	1.000	1.000	1.000	1.000
	𝐧3	0.067	0.049	0.995	0.965	1.000	1.000	1.000	1.000
	𝐧4	0.059	0.046	0.999	0.972	1.000	1.000	1.000	1.000
(𝝀3,𝜼3)	𝐧1	0.049	0.042	0.066	0.101	0.115	0.401	0.235	0.877
	𝐧2	0.050	0.054	0.090	0.236	0.255	0.930	0.660	1.000
	𝐧3	0.071	0.045	0.089	0.145	0.183	0.622	0.442	0.982
	𝐧4	0.055	0.047	0.095	0.236	0.260	0.961	0.662	1.000
	ARE	13.78	8.67

𝝀₁=(1₁₀)₅, 𝜼₁=(1₁₀)₅; 𝝀₂=(12₃,1₃,24₃,1)₅, 𝜼₂=(1₃,0.1₃,2₂,24,21)₅; and 𝝀₃=(1₃,3₃,9₃,20)₅, 𝜼₃=(5₃,15₃,45₃,100)₅. 𝐧₁=(25₃)₅, 𝐧₂=(50₃)₅, 𝐧₃=(25,35,50)₅, and 𝐧₄=(70,40,35)₅.