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Math Help - ANOVA and random effects model

  1. #1
    Newbie
    Joined
    Feb 2009
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    4

    ANOVA and random effects model

    Consider a one-way layout in which  I groups being compared are regarded as a sample from some larger population.  J is the number of subsamples taken from each  I . The random effects model is:
     Y_{ij} = \mu + A_i + \epsilon_{ij}

     A_i are random and independent of each other with  E(A_i) = 0 and  Var(A_i) = \sigma_A^2

     \epsilon_{ij} are independent of  A_i , independent of each other and have  E(\epsilon_{ij}) = 0 and  Var(\epsilon_{ij}) = \sigma_{\epsilon}^2

     Var(Y_{ij}) =\sigma_A^2 + \sigma_{\epsilon}^2

    Show that for this model:
     E(MS_W) = \sigma_{\epsilon}^2
    and
     E(MS_B) = \sigma_{\epsilon}^2 + J\sigma_A^2

    MS is the sum of squares divided by degrees of freedom. W means within subsamples and B means between groups.
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  2. #2
    Junior Member
    Joined
    Feb 2007
    Posts
    39
    Bump. I am stuck on this problem as well. To do this, I know I have to figure out Cov(Yij, Yi.) where Yi. is the mean of group i.

    I am not quite sure how to find this covariance. Any suggestions?
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