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Re: st: RE: RE: two sample test under generalized Behrens-Fisher conditions


From   "Airey, David C" <david.airey@vanderbilt.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: RE: RE: two sample test under generalized Behrens-Fisher conditions
Date   Tue, 14 Dec 2010 15:46:37 -0600

.

> I don't think that highly of t-tests. To quote Hampel et al. (Robust Statistics: The Approach Based on Influence Functions, Wiley, NY, 1986) p. 405:
> "Many statisticians are proud of the so-called robustness of the t- test and more generally of the test in fixed-effects models in the analysis of variance. But this robustness is only a rather moderate and limited robustness of level ("robustness of validity"); the power ("robustness of efficiencey") and hence also the length of confidenceintervals and the size of standard erros is very nonrobust. Consequently, a significant result can be believed, but non- significance may just be due to the inefficiency of least squares."
> Perhaps the easiest alternative to teach would be one based on trimmed means, which are not only easy to understand (as opposed to, say, M- Estimators and robust regression), but, unlike the median, have an easy standard error formula.
> Steve
> sjsamuels@gmail.com


Thanks for pointing that out. A nice blurb about the trimmed mean t-test here: <http://mres.gmu.edu/pmwiki/uploads/Main/Ng2008.pdf>.

I guess the seminal article on this was:

Yuen, K.K. (1974). The two-sample trimmed t-test for unequal population variances. Biometrika, 61, 165-170.

But also interesting is a paper by Keselman et al.:

Keselman HJ, Kowalchuk RK, Lix LM (1998) Robust nonorthogonal analses revisited: an update base on trimmed means. Psychometrika 63:1 145-163
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