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Unformatted text preview: AMS588. One-way Repeated Measures ANOVA: The Univariate and the Multivariate Analysis Approaches Suppose there are k regions of interest (ROIs) 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 ROIs. That is 1 2 : k H = = = L , where j 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 = + + , where j is the (fixed) effect of ROI j , i S is the (random) effect of subject i , ij is the random error independent of i S . With normality assumptions, we have ( 29 2 ~ 0, iid i s S N and ( 29 2 ~ 0, iid ij N . Let ( 29 ' 1 2 , , , i i i ik Y Y Y Y = L , we have ( 29 ~ , iid i k Y N , 1, , i n = L , where ( 29 ' 1 2 , , , k = 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 + + = = + L L L L M M O M M M O M L L with 2 2 2 s s...
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This note was uploaded on 01/31/2011 for the course AMS 572 taught by Professor Weizhu during the Fall '10 term at SUNY Stony Brook.
- Fall '10