>> -- My guess would be that if a stat-program presented just one >> "two-sample t-test", it *would* be the "Student's t-test" which pools >> the variances. (The t in "t-test" is not capitalized.)
Bob Hayden commented
> Minitab only pools the variances if you explicitly ask it to. I > think Minitab's default is the correct default. You lose very little > if the variances ARE the same and you gain a lot of they are not.
In "What is Statistics?" (Chapter 1 in the MAA's Notes Number 21, _Perspectives on Contemporary Statistics_), David Moore says:
"The pooled-sample t test ... is somewhat robust against unequal sigmas if the sample sizes are equal, but not otherwise." He uses T_p for the pooled statistic. Then, arguing for the "unpooled" statistic, labeled T, he asserts that "A substantial literature ... demonstrates the accuracy of this [i.e., the "unpooled" T] approximation for even quite small samples, and demonstrates in addition that when in fact sigma_1 = sigma_2, using T sacrifices very little power relative to T_p." (p.15)
It's this kind of "expert testimony" that is missing from so many textbooks at the elementary level--the kind of testimony that would help us make wiser decisions about the relative merits of various procedures, when working with students.
(This debate about the two t tests is not all one-sided, of course. I believe I recall Paul Velleman arguing that a good reason to teach the pooled test is that it generalizes readily to ANOVA.)
Here's another comment by David Moore whose essence is missing from most elementary textbooks: "... the F ratio for comparing variances is almost worthless. ... The reason for this ... is that no data are exactly normal. ... the F ratio is so sensitive to even small departures from normality as to be almost useless." (same source, p. 14)
============================================== Bruce King Department of Mathematics and Computer Science Western Connecticut State University 181 White Street Danbury, CT 06810 (email@example.com)