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

Table 1

Empirical sizes and powers of the two tests for nested effects for bivariate two-factor multivariate nested designs [𝑎=2,𝑏₁=16,𝑏₂=20, (𝚺₁₁,𝚺₁₂,…,𝚺_𝑎𝑏𝑎)=𝟏^𝑇₁₈⊗(𝐈₂,diag(𝝀))].

𝝀	𝐧	𝛿=0		𝛿=1		𝛿=2		𝛿=3
		AHT	PB	AHT	PB	AHT	PB	AHT	PB
𝝀1	𝐧1	0.056	0.046	0.210	0.162	0.831	0.793	0.999	0.999
	𝐧2	0.057	0.050	0.394	0.372	0.995	0.994	1.000	1.000
	𝐧3	0.070	0.052	0.295	0.232	0.957	0.930	1.000	1.000
	𝐧4	0.057	0.054	0.926	0.923	1.000	1.000	1.000	1.000
𝝀2	𝐧1	0.058	0.055	0.108	0.124	0.379	0.551	0.826	0.964
	𝐧2	0.068	0.044	0.173	0.232	0.718	0.930	0.995	1.000
	𝐧3	0.071	0.053	0.152	0.150	0.549	0.717	0.958	0.995
	𝐧4	0.059	0.051	0.475	0.776	0.999	1.000	1.000	1.000
𝝀3	𝐧1	0.056	0.045	0.093	0.114	0.301	0.507	0.722	0.943
	𝐧2	0.058	0.046	0.151	0.204	0.614	0.878	0.977	0.999
	𝐧3	0.070	0.048	0.131	0.145	0.458	0.654	0.903	0.990
	𝐧4	0.061	0.055	0.397	0.755	0.994	1.000	1.000	1.000
	ARE	24.03	6.83

𝝀₁=(1,1), 𝝀₂=(1,5), and 𝝀₃=(1,10). 𝐧₁=(7,7)₂₀, 𝐧₂=(10,10)₂₀, 𝐧₃=(7,10)₂₀, and 𝐧₄=(30,15)₂₀.