Dear ALLSTAT,

as a summary was asked for I send it, just copying relevant (parts of)
replies below. Thanks to everybody who answered.

D. Alte

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Original Query (16 Aug 2002)
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I want to compare CVs of a lab-parameter in two groups in a
population.
Can anybody recommend a test for (un-)equality for this problem?
Any hints and references are welcome.


- Answers: -


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N T Longford
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Permutation test.

1.  Assign the collected values into two groups at random (with the
same sample sizes as in  the collected data).

2.  Calculate the difference (or ratio) of the within-group variances.

Repeat 1. and 2.  10746 times, obtaining a simulated value for each
replication.
Calculate the same comparison (difference/ratio) for the collected
data.
If the `data-based' comparison is in the tail of the distribution of
the simulated values
-- reject the null hypothesis.  Do not reject otherwise.


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"Bandyopadhyay,S" <[log in to unmask]>
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I may be wrong, but this is a guess - since the CV is the ratio of the
variance to its own mean, the ratio of the two Cvs should follow the
same (F distribution) test as that of the ratio of two variances. I am
not quite sure whther the degrees of freedom should change (whether at
all), but my initial guess would be that it still can be tested using
the standard F test. Because of this, I would not expect any
text/papers to document a separate test for CVs.

follow-up:
It struck me now that the cv is the ratio of the sd and mean. So an F
test would not apply.

I am unaware of any test for a statistic of this sort. If you do not
hear from
anybody, you may wish to confirm that using the variance/mean instead,
and
doing an F test on that, is the right/acceptable way to test for it.


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Dr. Parmil, University of Jammu
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The cv is nothing but standardized variance or standard deviation.
so, u can apply the same tests as are applied to test the equality
of varinces but with little modification.


-------------------------------------
Nick Cox ([log in to unmask])
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Compare standard deviations of logs.


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"Quentin L. Burrell" <[log in to unmask]>
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This must have been done in detail somewhere, but for starters the
sample CV
is (of course!) asymptotically Normally distributed. Hence if you have
large
samples a test akin to that for the difference in sample means based
on the
Normal approximation is fairly straightforward.

The tricky bit is the se of the estimator, ie of the sample CV. It is
not
usually covered in standard texts, but you can find it in eg Kendall's
Advanced theory of statistics Vol 1, and Dudewicz & Mishra Modern
mathematical statistics.


-------------------------------------
Yin Bun Cheung ([log in to unmask])
-------------------------------------
I'm also doing something similar. I examine whether the 95% C.I. of
the
ratio of CVs include 1 by using bootstrap method.


-------------------------------------
"Michael McStephen" <[log in to unmask]>
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We've been puzzling over the usefulness of the CoV here for some
time.  I haven't been able to find a derivation or history of it in
any literature and I can't see what exactly it is testing.  If the
means of the groups are the same, then use a test of equality of
variance; if the variances are the same, then compare means; if both
are diffferent, you may well end up with the CoV being the same
(depending on the differences).  If you get a difference in the CoV,
then I'd still ask, why?  Is it due to the mean or SD difference? So
you're back to square one.

As for a statistical distribution, you use the sample to generate a
point estimate so I can't see an obvious way of getting a sampling
distribution of the statistic.  You could try bootstrapping the two
samples to see if you can generate a statistical test or not.
But I'm still not sure what value your interpretation will have.

I'd be interested in any information you've got on the CoV and any
criticism you have of my thinking on this.  Also, I'd like to hear any
responses anyone else has to your question.

-------------------------------------

Regards

--
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 Dietrich Alte (Statistician, Dipl.-Stat.)
 - SHIP // Project Management -
 University of Greifswald - Medical Faculty
 Institute of Epidemiology and Social Medicine
 Walther-Rathenau-Str. 48, D-17487 Greifswald, Germany
 Phone      +49(0)3834-867713, fax ++49(0)3834-866684
 Email      [log in to unmask]
 Institute  http://www.medizin.uni-greifswald.de/epidem/
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