R help - Sep 2008 - test for a single variance

Dear R Gurus:

Is there a test for a single variance available in R, please?

Thanks,
Edna Bell

Edna Bell <edna.bell01 <at> gmail.com> writes:
> 
> Dear R Gurus:
> 
> Is there a test for a single variance available in R, please?
> 
> Thanks,
> Edna Bell
> 
  Do you mean a test for homogeneity of variance?
If so, try RSiteSearch("variance homogeneity")
and see what you get ...

   Ben Bolker

If you are trying to test the hypotheses:

H0: sigma^2 == sigma[0]^2
Ha: sigma^2 != sigma[0]^2

i.e. is the variance of the distribution from which the data came different from
the hypothesized value?

Then the normal theory test can be done fairly simply (I don't know of any
prepackaged equivalents) by something like:
> pchisq( var(y)*(length(y)-1)/sigma0, length(y)-1, lower.tail= var(y) <
sigma0 ) * 2
Assuming "sigma0" is the hypothesized variance and I remember the
formula correctly.

However, this is only valid if the data comes from a distribution that is very
close to a normal distribution.  Inference on the mean is robust to normality
assumptions, but not the variance, hence this is not used much in practice.

If you are really interested in the test on the variance (a good thing, many
problems really should look at the variance as the 1st outcome of interest,
rather than as a nuisance variable), then a possibly better approach would be to
calculate a confidence interval on the variance using something that does not
depend on distributional assumptions (bootstrap could be one option) and compare
that to the hypothesized value.

Hope this helps,

--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
(801) 408-8111


> -----Original Message-----
> From: r-help-bounces at r-project.org
> [mailto:r-help-bounces at r-project.org] On Behalf Of Edna Bell
> Sent: Tuesday, September 09, 2008 4:31 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] test for a single variance
>
> Dear R Gurus:
>
> Is there a test for a single variance available in R, please?
>
> Thanks,
> Edna Bell
>
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