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Lecture17_RMANOVA

# Lecture17_RMANOVA - AMS588 One-way Repeated Measures ANOVA...

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AMS588. One-way Repeated Measures ANOVA: The Univariate and the Multivariate Analysis Approaches Suppose there are k regions of interest (ROI’s) and n subjects. Each subject was scanned on baseline (soda) as well as after drinking alcohol. Our main hypothesis is whether the change between baseline and alcohol is homogeneous among the ROI’s. That is 0 1 2 : k H μ μ μ = = = L , where j μ is the effect of alcohol on the j th ROI, 1, , . j k = L The Univariate Analysis Approach For subject i , let Y ij denote the paired difference between baseline and alcohol for the jth ROI, then the (univariate) repeated measures ANOVA model is: ij j i ij Y S μ ε = + + , where j μ is the (fixed) effect of ROI j , i S is the (random) effect of subject i , ij ε is the random error independent of i S . With normality assumptions, we have ( 29 2 ~ 0, iid i s S N σ and ( 29 2 ~ 0, iid ij N ε ε σ . Let ( 29 ' 1 2 , , , i i i ik Y Y Y Y = L , we have ( 29 ~ , iid i k Y N μ Σ , 1, , i n = L , where ( 29 ' 1 2 , , , k μ μ μ μ = L and 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 s s s s s s s s s ε ε ε ρ ρ σ σ σ σ ρ ρ σ σ σ σ σ ρ ρ σ σ σ σ + + Σ = = + L L L L M M O M M M O M L L with 2 2 2 s s ε σ ρ σ σ = + and 2 2 2 s ε σ σ

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Lecture17_RMANOVA - AMS588 One-way Repeated Measures ANOVA...

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