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From |
"Stas Kolenikov" <skolenik@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Skewness estimates with svyset data |

Date |
Mon, 3 Nov 2008 16:01:57 -0500 |

On 11/3/08, Richard Palmer-Jones <richard.palmerjones@gmail.com> wrote: > Could you please clarify the nlcom formula, please? > > nlcom (_b[ht3] - 3*_b[ht2] * _b[ht] + 2*_b[ht])/(_b[ht2] - _b[ht] * _b[ht])^3/2 > > (ht being height, ht = ht^2 and ht3 = ht^3) > > I suspect my translation is not correct as the coefficients I get are > not close to skewness (and is it the formula for skewness?). Uhm... I was doing this all in my head, so let me think aloud here for another couple minutes. So, skewness = E[(x-m)/sigma]^3 = E(x-m)^3/( E(x-m)^2 )^(3/2) = E[ x^3 - 3m x^2 + 3 x m^2 - m^3]/(E[ x^2 - 2m x + m^2])^1.5 = E[ x^3 - 3m x^2 + 2 m^3 ] / (E[ x^2 -m^2])^1.5. The last expression in the first set of parentheses should be _b[ht]^3. See if that is producing sensible skewness numbers. Note that those are asymptotic expressions. An unbiased estimator for variance, for instance, would be 1/(n-1) (sum x^2 - mean(x)^2), rather than 1/n times the same thing. The latter however will have smaller MSE. If you are checking the skewness for some 20 groups, you would need to have some multiple testing corrections in mind. Bonferroni says, divide your usual alpha by the number of tests -- so you would be rejecting for alpha = 0.05/20 = 0.0025. To Nick: yes, I've used skewness and kurtosis to test for normality a bunch of times (and there's a famous Mardia's multivariate generalization that I programmed up :)). But frankly I personally don't remember seeing confidence intervals on skewness anywhere at all. Estimation and testing are two related ways of looking at data with statistics, but with skewness and kurtosis you really estimate something to see that it is close enough to zero... and sometimes you don't even estimate a thing and go straight to the test statistic. -- Stas Kolenikov, also found at http://stas.kolenikov.name Small print: I use this email account for mailing lists only. * * 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/

**Follow-Ups**:**RE: st: Skewness estimates with svyset data***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**References**:**st: Skewness estimates with svyset data***From:*"Richard Palmer-Jones" <richard.palmerjones@gmail.com>

**Re: st: Skewness estimates with svyset data***From:*"Stas Kolenikov" <skolenik@gmail.com>

**RE: st: Skewness estimates with svyset data***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**Re: st: Skewness estimates with svyset data***From:*"Richard Palmer-Jones" <richard.palmerjones@gmail.com>

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