= Wilks lambda statistic
{c}
{title2=$\Lambda=|E|/|E+H|$}
For nonsingular within-group scatter $E$ and between-group scatter $H$, the statistic is $\prod_j(1+\theta_j)^{-1}$, where $\theta_j$ solve the <generalized eigenvalue problem> $Hv=\theta Ev$. It is small when the group means differ strongly relative to within-group variation. Maximizing a common-covariance normal likelihood under equal and unrestricted means gives the likelihood ratio $\Lambda^{N/2}$. Its determinant factors cancel under any nonsingular change of response coordinates. For one response it is equivalent to the <analysis of variance> F-test.
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