# Re: st: How do I test that two subsample have different coefficient of variation?

 From "Austin Nichols" To statalist@hsphsun2.harvard.edu Subject Re: st: How do I test that two subsample have different coefficient of variation? Date Thu, 10 Jul 2008 14:51:23 -0400

```Antonio Vezzani <antonio.vezzani@uniroma2.it> et al.--
Maarten provides a link to testing equality of variances (of errors)
using -robvar- (help sdtest) and Nick proposes working on a log scale
(for strictly positive variables only), but neither of these are
actually a test of equality of CV.  I suspect Yulia Marchenko could
outline a general procedure using -xtmixed-
(http://www.stata-journal.com/article.html?article=st0095).  I will
propose yet another answer that does not do exactly what you want:
-geivars- on SSC will calculate SEs for the squared coef of variation
a simple command to follow

sysuse auto, clear
tabstat price, stat(cv) by(for)

allowing a test of equality of CV, I don't think there is one.

I believe the sampling distribution of the CV is tricky...  esp. if
one is unwilling to stipulate that the variable of interest is
normally distributed in the population:
http://www.ripublication.com/ijss/ijssv1n1_5.pdf
Gupta RC, Ma S. Testing the equality of the coefficient of variation
in k normal populations. Communications in Statistics.
1996;25:115–132.
Wilson CA, Payton ME. Modelling the coefficient of variation in
factorial experiments. Communications in Statistics-Theory and
Methods. 2002;31:463–476.

Perhaps working with the reciprocal (mean/sd) offers greater stability?
but I can't see that paper, just this abstract:
Sharma, K.K. and H. Krishna. 1994. "Asymptotic sampling distribution
of inversecoefficient-of-variation and its applications" IEEE
Transactions on Reliability, 43(4):630 - 633. This paper develops the
asymptotic sampling distribution of the inverse of the coefficient of
variation (InvCV). This distribution is used for making statistical
inference about the population CV (coefficient of variation) or InvCV
without making an assumption about the population distribution.

On Thu, Jul 10, 2008 at 1:13 PM, Maarten buis <maartenbuis@yahoo.co.uk> wrote:
> --- Antonio Vezzani <antonio.vezzani@uniroma2.it> wrote:
>> If, for example,  in auto.dta I want to test that price have
>> different coefficient of variation for foreign and domestic auto,
>> which is the right procedure?
>
> Christopher F. Baum (206) Stata tip 38: Testing for groupwise
> heteroskedasticity, The Stata Journal, 6(4): 590--592.
> http://www.stata-journal.com/article.html?article=st0117

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