12.6 One-Factor MANOVA

Suppose that we have k multivariate normal populations with possibly different mean vectors, but the same covariance matrix. Let {Yij: j = 1, …, ni} be iid Np(μiΣ), i = 1, …, k. We may write the one-factor MANOVA model as

Yij=μi+εij,j=1,,ni,i=1,,k,

si191_e

where {εij} are iid Np(0Σ). We can also rewrite the above as a factor-effect model

Yij=μ+αi+εij,

si192_e

where μ=(ni/n)μisi193_e, αi =μiμ and n = n1 + ⋯ + nk is the total number ...

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