I wrote:
Having checked with DeGroot, I stand by this value...
As for the case where we're _not_ assuming a constant variance and
both samples are large, I really don't know. In setting up
gretl's hypothesis test calculator I took a formula for the
standard error of the difference of means in this case from some
statistics text (but evidently not DeGroot).
Having read DeGroot and googled on the "Behrens-Fisher problem"
(hypothesis testing on the difference between two means, with the
repespective population means unknown and not assumed equal), the
case seems more or less hopeless. DeGroot says the problem is
"very difficult", and that while "various test procedures have
been proposed", "most of them have been the subject of controversy
in regard to their appropriateness or usefulness".
Allin Cottrell