[R] t-test for standard deviations

[(Ted Harding)]

On 12-Jan-06 Berton Gunter wrote:
> 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).

Not sure that I would consider either of these as a "t-test"
as usually undestood.
.
Both are based on deriving a "dispersion variable" transform
of the observations in each group (dquared or absolute deviation
from the mean for Levene, absolute deivation from the mean for
Brown-Forsythe), and performing an analysis of variance with
the derived variable.

Granted, in the case of two groups the ANOVA is equivalent to
a "squared t-test" and one could indeed use a t-test instead
of a 2-group ANOVA to get the directional information as well.

But I would be surprised to find such a procedure referred to
as a "t-test" as cited by Mirko. I think it would help if he
told us a bit more about what the paper actually says.

> 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 ...

Your comments on the merits and advisability of these things
are good -- but not forgetting that it is also a good idea to
have enough understanding of what one is dealing with to be
able to judge what might be best for the case in hand. However,
I'm entirely with you when it comes to uncircumspect habitual
use of standard procedures.

Best wishes,
Ted.

> 
> Cheers,
> Bert
> 
> -- 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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E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 12-Jan-06                                       Time: 21:09:19
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