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

From   "Lachenbruch, Peter" <>
To   <>
Subject   RE: st: How do I test that two subsample have different coefficient of variation?
Date   Thu, 10 Jul 2008 13:50:12 -0700

Perhaps a na´ve approach would be to bootstrap the cv with a few thousand reps.  An obvious problem arises if the mean is near 0.  I suspect one should restrict this to positive random variables, but I have no theory to go on.


Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001

-----Original Message-----
From: [] On Behalf Of Austin Nichols
Sent: Thursday, July 10, 2008 11:51 AM
Subject: Re: st: How do I test that two subsample have different coefficient of variation?

Antonio Vezzani <> 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-
(  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
(see also  As for
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:
Gupta RC, Ma S. Testing the equality of the coefficient of variation
in k normal populations. Communications in Statistics.
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 <> wrote:
> --- Antonio Vezzani <> 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.

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