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

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

Subject |
RE: st: Computing medcouple |

Date |
Thu, 13 Aug 2009 18:16:50 +0100 |

This raises various questions, including 1. What is the Platonic skewness that you know you've measured successfully? We often write things like skewness = <formula> but the = sign is here profoundly ambiguous. Those who think that the <formula> is the thing and the name (here "skewness") is just an arbitrary label are not in agreement with those who think that there is an essential underlying thing and the formula our best guess at how we measure it. The = sign should be := or =: to indicate direction of assignment (a notation that I think started in Algol). In Britain circa 1960 bananas used to bear sticky labels explaining that they were indeed bananas. (This in turn was presumably a hangover from post WWII when bananas were not widely available and as such unfamiliar to shoppers.) It was a recurrent amusement of my childhood to peel off these labels, stick them on friends and siblings and declare "So-and-so is a banana". (We lacked other toys and were easily amused.) This silly pursuit has a useful personal legacy in underlining that labels may be sticky but that has no bearing on whether they are appropriate. 2. What is so special about particular quantiles anyway? I think the median has a special role as the middle of any symmetric distribution but I find it hard to see that even quartiles have any special role. They may be simple to understand, familiar from introductory courses and/or convenient in practice, but that doesn't make them statistically natural. Of course, this is precisely why other quantiles further out in the tail are also used, with an insurance problem of avoiding the extremes to get some robustness against outliers. I think it's a major criticism of box plots that they sanctify quartiles. Nick n.j.cox@durham.ac.uk Lachenbruch, Peter A few years ago I tried to develop a measure of skewness based on percentiles: "Skewness" = [(P75-P50)-(P50-P25)]/[P75-p25] And also similar ones based on P90 and P10. I did fairly extensive simulations and found that the P90, P10 based ones did a bit better in expressing skewness. In addition, the distribution of this was not nicely behaved, but by log-transforming you would get a statistic that looked very nicely normal. In doing this I learned of the l-moments articles and was delighted that Nick had already written a routine for this. Nick Cox This sounds a little similar in spirit to using L-moments to calculate a skewness measure. The latter approach arguably has two features: it is systematic and it is already implemented in Stata through -lmoments- from SSC. As far as medcouple is concerned, you could compute it exactly or by sampling. I've no code to offer. My prejudice here is that for most problems you would be better off either transforming the data or using a graph form that discarded less of the information than a box plot does. Otherwise put, if the data are very skew you usually need to see more detail about the tails than a boxplot provides. Ronnie Babigumira <rb.glists@gmail.com> Vandervieren and Hubert (2004) present what they call a robust measure of skewness using the medcouple Given a distribution F, medcouple (MC(F)) is defined as MC(F) = med h(xi,xj) given xi<med<xj where - h = (xj-m_F)-(m_F-xi) ----------------- xj-xi - m_F is the median of F I would like to compute MC but dont know how to even start. Any pointers will be much appreciated. Reference Vanderviere, E. & Huber, M. (2004). An adjusted boxplot for skewed distributions. In J. Antoch (Ed.), COMPSTAT2004 Symposium: proceedings in computational statistics (pp. 1933-1940). Heidelberg, Germany: Physica-Verlag. The paper can be downloaded here http://wis.kuleuven.be/stat/robust/Papers/boxplotCOMPSTAT04.pdf * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: Computing medcouple***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**RE: st: Computing medcouple***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

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