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pooled t test vs "unpooled" t test
Posted:
Nov 4, 1996 8:39 PM


To this observation
>>  My guess would be that if a statprogram presented just one >> "twosample ttest", it *would* be the "Student's ttest" which pools >> the variances. (The t in "ttest" 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 pooledsample 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 levelthe 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 onesided, 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 (kingb@wcsub.ctstateu.edu)



