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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

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

Date |
Fri, 11 Jul 2008 10:57:30 +0100 |

There are some references in Sokal, R.R. and Rohlf, F.J. 1995. Biometry. New York: W.H. Freeman. The rough argument for thinking logarithmically goes like this. It makes sense to work with the coefficient of variation whenever standard deviation is proportional to mean. That implies that variability is multiplicative, not additive, which in turn implies working on a logarithmic scale. Clearly, that in turn is possible only if values are all strictly positive. (I can also imagine that there might be problems in which cv looks attractive but in which values are all strictly negative, in which case just discard the signs for this purpose.) It might be that there are variables including zeros in which cv appears also natural, or at least convenient, in which case you do have the problem, much discussed but never fully solved, of what to do when log(zero) is implied. However, I've seen in three publications at least coefficients of variation for monthly temperatures measured in Celsius. In each case the authors were lucky that, to the resolution reported, means were never zero. But in each case negative means and so negative cvs were perceptively interpreted by the authors as a sign that the cv was not fully satisfactory as a measure of relative variability. One of these authors at least had the bright idea that changing to Fahrenheit would be a solution. However, other advice springs to mind, notably "Don't do that!". Suppressing the references I take in this instance to be the greater service to science. As Jay Verkuilen also points out in this thread, Celsius (and Fahrenheit) temperatures are interval scale measures for which ratios are not appropriate. However, another argument is worth brief airing. Contemplation of the gamma distribution shows that the coefficient of variation is a natural parameter for that family. Thus fitting gammas might be a way forward in some problems of this kind. Generalised linear models as in -glm- treat the scale parameter as ancillary and are not especially suitable for this purpose, but -gammafit- from SSC might be of use. I note also that various arguments point to the cube root as (to a good approximation) a natural transformation for the gamma. Nick n.j.cox@durham.ac.uk Austin Nichols 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 (see also http://econpapers.repec.org/paper/bocasug06/16.htm). 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: 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? http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel3/24/8488/00370217.p df?temp=x 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 * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: How do I test that two subsample have different coefficient of variation?***From:*"Austin Nichols" <austinnichols@gmail.com>

**References**:**st: How do I test that two subsample have different coefficient of variation?***From:*Antonio Vezzani <antonio.vezzani@uniroma2.it>

**Re: st: How do I test that two subsample have different coefficient of variation?***From:*Maarten buis <maartenbuis@yahoo.co.uk>

**Re: st: How do I test that two subsample have different coefficient of variation?***From:*"Austin Nichols" <austinnichols@gmail.com>

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