[R] t-test for standard deviations

Berton Gunter gunter.berton at gene.com
Thu Jan 12 20:57:58 CET 2006

Sorry, Ted:

Google on "Brown-Forsythe" and "Levene's test" and you will, indeed, find
that rather robust and powerful t-tests can be used for testing homogeneity
of spreads. In fact, on a variety of accounts, these tests are preferable to
F-tests, which are notoriously non-robust (sensitive to non-normality) and
which should long ago have been banned from statistics tects (IMHO).

OTOH, whether one **should** test for homogeneity of spread instead of using
statistical procedures robust to moderate heteroscedascity is another
question. IMO, and I think on theoretical grounds, that is a better way to
do things.

Best yet is to use balanced designs in which most anything you do is less
affected by any of these deviations from standard statistical assumptions.
But that requires malice aforethought, rather than data dredging ...


-- Bert Gunter
Genentech Non-Clinical Statistics
South San Francisco, CA
"The business of the statistician is to catalyze the scientific learning
process."  - George E. P. Box

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Ted Harding
> Sent: Thursday, January 12, 2006 10:53 AM
> To: mirko sanpietrucci
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] t-test for standard deviations
> On 12-Jan-06 mirko sanpietrucci wrote:
> > Dear R-users,
> > I am new to the list and I would like to submit (probably!!!!)
> > a stupid question:
> > 
> > I found in a paper a reference to a t-test for the evaluationg the
> > difference between the standard deviations of 2 samples.
> > This test is performed in the paper but the methodology is not
> > explained and any reference is reported.
> > 
> > Does anyone know where I can find references to this test 
> and if it is
> > implemented in R?
> > 
> > Thenks in advance for your help,
> > 
> > Mirko
> If the paper says that a
> 1) "t-test"
> was used for evaluating the difference between the
> 2) "standard deviations"
> of 2 samples
> then I suspect that one or the other of these is a misprint.
> To compare standard deviations (more precisely, variances)
> you could use a (1)F-test.
> Or you would use a t-test to evaluate the difference between
> the (2)means of 2 samples.
> If it is really obscure what was done, perhaps an appropriate
> quotation from the paper would help to ascertain the problem.
> Best wishes,
> Ted.
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
> Fax-to-email: +44 (0)870 094 0861
> Date: 12-Jan-06                                       Time: 18:52:31
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