How exactly does Wilks' Lambda distribution generalize the Hotelling distribution? According to Wikipedia, Wilks' Lambda distribution generalizes Hotelling's distribution. I am having some problems seeing how this works. I can see how Hotelling's distribution generalizes Student's t-distribution (a RV distributed as Hotelling's law with $p=1$ is just the square of a RV distribution as Student's t), but cannot see how to get to Wilks' Lambda. Is there some setting of the parameters $p,m,n$ such that a RV distributed as Wilks' lambda is some transform of a Hotelling RV?
 A: These NCSU course notes say 

Multivariate tests in contrast to the overall F test, answer the
  question, "Is each effect
  significant?" or more specifically,
  "Is each effect significant for at
  least one of the dependent variables?"
  That is, where the F test focuses on
  the dependents, the multivariate tests
  focus on the independents and their
  interactions. These tests appear in
  the "Multivariate Tests" table of SPSS
  output. The multivariate formula for F
  is based not only on the sum of
  squares between and within groups, as
  in ANOVA, but also on the sum of
  crossproducts - that is, it takes
  covariance into account as well as
  group means....
Hotelling's T-Square is the most common, traditional test where there
  are two groups formed by the
  independent variables.... 
Wilks' lambda, U. This is the most common, traditional test where there
  are more than two groups formed by the
  independent variables.... The t-test,
  Hotelling's T, and the F test are
  special cases of Wilks's lambda....

So I presume that if you take Wilks' lambda, and reduce the number of groups formed by the independent variables to two, then you get something like Hotelling's T-Square.
A: My question was about the distributions, not the test, and I think I've figured out the answer: a t-distribution squared has an F(1,n) distribution, which is a Hotelling distribution (up to rescaling by a constant determined by the parameters). I believe one can say that an F(m,n) distribution is the same as a Wilks' $\Lambda(1,m,n)$ distribution, which is the kind of 'generalization' I was looking for. (I guess I'm now enough of an 'expert' to edit the wikipedia page ;)
