Exactly - elementary texts and methods books recommend the welch test
for the reason you mention. Curiously, those same texts recommend
using anova and regression without automatically correcting for the
possibility of non-constant variance. Why is the case of comparing
two means different from 3? Those same books will tell you that anova
is pretty robust to non-constant variance. well, the two sample
t-test is anova.
I don't use the welch test except as a conscious decision: ie I really
want to compare the means while suspecting that the variances differ.
Generally people are using the t test to certify that two populations
are different. If the variances are wildly different, that may be
much more important than a difference in means. in fact, to test for
a difference in means when the variances are wildly different is
almost always substantively silly. There was a great example a few
years ago from a psychiatric journal, comparing two medications, where
the investigators did a t-test for the means when one distribution was
unimodal and the other was bi-modal; there was no statistically
significant difference in the means, but there was a really important
difference in the distributions. The automatic use of the welch test
makes you feel that you are protected against Bad Things, when you
aren't.
albyn
Quoting Ian Fellows <[email protected]>:
In the case of the t.test, having the default be var.equal=TRUE is
the right way to go. There is little to no power lost by using the
welch test, and the assumption of equal variance can be difficult to
assess. For this reason, many introductory text books have now
banished the equal variance t-test from their chapters (e.g. Moore's
The Basic Practice of Statistics).
Ian
On Oct 25, 2010, at 4:05 PM, Albyn Jones wrote:
I don't know, the help file is uninformative. I'd guess the answer is
"the author wrote it that way". Other R functions like t.test include
similar unfortunate (to me) default choices, in that case
var.equal=FALSE (ie the Welch test) is the default.
albyn
On Mon, Oct 25, 2010 at 04:15:20PM -0500, Laura Chihara wrote:
Yes, thank you for this reference. But according to
this article, the score is better than continuity
correction, so why is continuity correction the default
with prop.test?
-Laura
On 10/25/2010 4:02 PM, Ralph O'Brien, PhD wrote:
I suggest:
A. Agresti and B. A. Coull. Approximate is better than ”exact” for
interval estimation of binomial proportions. The American Statistician,
52(2):119–126, 1998.
On Mon, Oct 25, 2010 at 4:38 PM, Laura Chihara <[email protected]
<mailto:[email protected]>> wrote:
Hi,
I have a question about prop.test in R:
I teach students the score confidence
interval for proportions (also called
Wilson or Wilson score interval).
prop.test(,..., correct=FALSE) gives this
interval.
The default uses a continuity correction.
When should we use one over the other?
Is it worth going over this in class? Why
is correct=TRUE the default?
Thanks for any pedagogical guidance here!
-- Laura
*******************************************
Laura Chihara
Professor of Mathematics 507-222-4065 (office)
Dept of Mathematics 507-222-4312 (fax)
Carleton College
1 North College Street
Northfield MN 55057
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Ralph O'Brien, PhD
Professor, Dept of Epidemiology and Biostatistics
Case Western Reserve University
Office: 216.368.1927
Cell: 216.312.3203
--
*******************************************
Laura Chihara
Professor of Mathematics 507-222-4065 (office)
Dept of Mathematics 507-222-4312 (fax)
Carleton College
1 North College Street
Northfield MN 55057
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--
Albyn Jones
Reed College
[email protected]
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