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

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

Subject |
RE: st: ttest or xtmelogit? |

Date |
Wed, 12 Mar 2008 18:14:12 -0000 |

Steven is correct. This isn't mentioned in -transint-. -transint- (on SSC) is a slightly unusual package. It is just a help file written because I wanted my (geography) students to have something better than the rather poor coverage of transformations in the books available to them. In fact, I haven't been able to find many accounts of transformations that were very concise, covered the really important ideas, but were also light on the mathematics, which is of course a contradictory desire. Anyway, it then seemed that it might be useful a little more widely. Variance-stabilisation is as Steven says the motive for the angular: it is difficult to imagine it arising except out of an algebraic argument, which I think goes back to Fisher. So, next time around, that might merit an explanation. Nick n.j.cox@durham.ac.uk Steven Samuels Not mentioned in -transint- is the variance-stabilizing property of the angular transformation: it has asymptotic variance 1/4n, which is not a function of p (Anscombe, 1948). If the observed proportion is r/ n, Anscombe showed that the arcsine of [(r + 3/8)/(n + 3/4)]^.5 is even better at stabilizing the variance, for moderate sample size. The second version has variance 1/(4n + 2). The arcsine-transformation used to be recommended because transformed proportions could be analyzed via standard ANOVA programs. I once found it useful in a variance components analysis. The 'error' variance was a mixture of a between-sample and within sample (binomial) variance. With the arcsine transformation, I could subtract out the part attributable to binomial variation. -Steve FJ Anscombe 1948. The transformation of Poisson, Binomial, and negative-binomial data. Biometrika 35:246-254 On Mar 10, 2008, at 6:02 PM, Nick Cox wrote: > By arcsin I guess you mean the angular transformation (arcsine of > square > root). > Its use seems to have faded dramatically in recent years. > > Tukey showed that this is very close to p^0.41 - (1 - p)^0.41. That > makes it weaker > than the logit. My guess is that it would be an unusual dataset in > which > the angular > was much better than leaving data as is and also much better than the > logit. It could happen, > but it seems to be rare. > > The Tukey reference is given in -transint- from SSC. > > Nick > n.j.cox@durham.ac.uk > > David Airey > > Maybe I should not have said it was pilot data! I won't disagree, but > when cluster number is too small (< 20) to invoke xtgee or xtmelogit > on the observed yes/no data, or glm on the summary statistics with > binomial family and logit link, what do you do? It seems to me there > is a sample size between 10 and 30 clusters of yes/no data that may be > better suited to some of the older approaches like arcsin transformed > proportions and then ttest or ANOVA/regress. I guess that was my > question. * * 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/

**References**:**st: ttest or xtmelogit?***From:*tiago.pereira@incor.usp.br

**Re: st: ttest or xtmelogit?***From:*David Airey <david.airey@Vanderbilt.Edu>

**RE: st: ttest or xtmelogit?***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**Re: st: ttest or xtmelogit?***From:*Steven Samuels <sjhsamuels@earthlink.net>

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