glm gives t test sometimes, z test others. Why?

[Paul Johnson]

I just ran example(glm) and happened to notice that models based on
the Gamma distribution gives a t test, while the Poisson models give a
z test. Why?

Both are b/s.e., aren't they?

I can't find documentation supporting the claim that the distribution
is more like t in one case than another, except in the Gaussian case
(where it really is t).

Aren't all of the others approximations based on the Wald idea that

    bhat^2
   ------------
    Var(bhat)

is asymptotically Chi-square?  And that sqrt(Chi-square) is Normal.


While I'm asking, I wonder if glm should report them at all. I've
followed up on Prof Ripley's advice to read the Hauck & Donner article
and the successors, and I'm persuaded that we ought to just use the
likelihood ratio test to decide about individual parameters.

--
Paul E. Johnson
Professor, Political Science
1541 Lilac Lane, Room 504
University of Kansas