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

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

Subject |
st: RE: RE: -omninorm- updated on SSC |

Date |
Wed, 15 Apr 2009 17:16:16 +0100 |

Thanks for Tony's comments. (And thanks to Marcello for forwarding the original, which the server refused twice.) Tony's measure W is itself asymmetric as it is bounded below by 0, 1 if the data are symmetric in its sense, and unbounded above, so logging should usually help. The quotation from George Box he alludes to is in G. E. P. Box. 1953. Non-Normality and Tests on Variances. Biometrika 40: 318-335 This was the paper that introduced robustness as a technical term. Nick n.j.cox@durham.ac.uk Lachenbruch, Peter This is a welcome update (I hadn't known about it before). I've found that bad asymmetry (skewness) is the biggest hazard with many tests relying on normality. Another measure of asymmetry is based on lmoments which is available in a program from Nick Cox (we have to control that guy :-) ). I've found a simple descriptive measure is W=(P90-P50)/(P50-P10) which should be 1 if the data are symmetric. In some simulations (unpublished) I found that ln(W) is more closely normal than W. I forget the variance, but bootstrapping would work nicely. I use asymmetry as an indicator - I'd be reluctant to use it to determine what test to use. At once time I compared a couple of strategies for determining whether to use a normal test, a ranksum test, or a test for normality followed by a ranksum if p<0.05 or a z test otherwise. Basically the ranksum won when data weren't normal. Lachenbruch, P.A. (1991) "The Performance of tests when observations have different variances," Journal of Statistical Computation and Simulation, 40:83-92. More generally, preliminary tests of normality are usually unnecessary as (I think) Box said regarding testing for unequal variance in ANOVA doing such a test "is like going to sea in a rowboat to see if it's OK for the Queen Mary to sail" Marcello Pagano The package -omninorm- on SSC by Kit Baum and myself has been updated. -omninorm- requires Stata 9 (except for the older version, -omninorm7-, frozen as was, which requires only Stata 7). To install, use -ssc-. The update is in one sense minor, but still notable for people interested in what -omninorm- does, provide an omnibus test for univariate or multivariate normality. -omninorm- implements a test proposed by Doornik and Hansen in a 1994 working paper (highly accessible and much cited). That working paper has now been written up as a standard journal paper, which should satisfy anybody queasy about using ideas that have not received the sanctification of peer review for a journal. The 2008 reference has now been included in the help file. Doornik, Jurgen A. and Hansen, Henrik. 1994. An omnibus test for univariate and multivariate normality. Working Paper, Nuffield College, University of Oxford. See http://ideas.repec.org/p/nuf/econwp/9604.html or http://www.doornik.com/research/normal2.pdf Doornik, Jurgen A. and Hansen, Henrik. 2008. An omnibus test for univariate and multivariate normality. Oxford Bulletin of Economics and Statistics 70: 927-939. This test is widely used in other statistical software. At least one of us most of the time, and both of us some of the time, regard normality tests as over-rated. If you care about normality, draw a plot. If you care about normality, wonder why, as normality is less often an assumption, and less often an important assumption, than is frequently asserted or believed. That said, if you are going to test for normality, the arguments in the Doornik and Hansen paper should lead you to treat their test as a good competitor, and at least in some senses as superior to those previously implemented in Stata. What's more, most of the alternatives only provide univariate tests. Nick n.j.cox@durham.ac.uk * * 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**:**st: -omninorm- updated on SSC***From:*Marcello Pagano <pagano@hsph.harvard.edu>

**st: RE: -omninorm- updated on SSC***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

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