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

Paul Johnson pauljohn32 at
Sun Mar 5 07:22:45 CET 2006

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


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

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