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From |
"Isabel Canette, StataCorp LP" <icanette@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Problem with centile and normal confidence limits |

Date |
Thu, 06 Sep 2007 17:06:57 -0500 |

James Shaw <james_shaw2004[at]yahoo[dot]com> reported an inconsistency between the formula used to compute the normal standard errors for the centiles and the formula in the entry Manual for the command -centile-. >> I am having trouble replicating the normal confidence >> limits produced by -centile-. The manual states that >> the standard error (Sq) of a given quantile, Cq, may >> be computed under the assumption of normality using >> the equation on p. 202 in the Stata Reference Manual >> (Release 9, A-G). However, I have to multiply Sq by >> sqrt(n) to get the same endpoints as Stata. My sample >> code and output are provided below. James guesses that there may be a typo in the manual entry, and he is right. The actual formula for the standard errors in the normal case is: s_q = sqrt( q(100-q)/n ) * 1/(100*Z) We will fix this typo in the manual. The formula also can be found in: Kendall's Advanced Theory of Statistics, by A. Stuart and K. Ord, 6th Edition, Edward Arnold. (see formula 10.29 on page 358). Isabel icanette[at]stata[dot]com James Shaw wrote: > Dear Statalist: > > I am having trouble replicating the normal confidence > limits produced by -centile-. The manual states that > the standard error (Sq) of a given quantile, Cq, may > be computed under the assumption of normality using > the equation on p. 202 in the Stata Reference Manual > (Release 9, A-G). However, I have to multiply Sq by > sqrt(n) to get the same endpoints as Stata. My sample > code and output are provided below. > > I am not sure why I cannot replicate Stata's results > using the equation presented in the manual. Given > that I can approximate the limits produced by > -centile, normal- using the bootstrap, I suspect that > the notation in the manual may be incorrect. I do not > have access to the original source (Kendall & Stuart) > and am therefore unable to verify whether or not this > is the case. > > Regards, > > Jim > > > . drawnorm y > . qui: summ y > . scalar sm1= r(mean) > . scalar sd1 = r(sd) > . scalar sn = r(N) > > . qui: centile y, normal > . scalar smd2 = r(c_1) > . scalar stul = r(ub_1) > . scalar stll = r(lb_1) > > . /* from Stata */ > . scalar li smd2 stul stll > smd2 = .02788301 > stul = .10364515 > stll = -.04787914 > > . scalar sq = > sqrt(50*(100-50))/(100*sn*normalden(smd2,sm1,sd1)) > > . /* using formula given in manual */ > . scalar ul11 = smd2 + sq*invnormal(.975) > . scalar ll11 = smd2 - sq*invnormal(.975) > . scalar li smd2 ul11 ll11 > smd2 = .02788301 > ul11 = .03027881 > ll11 = .0254872 > > . /* multiplied by sqrt(n) */ > . scalar ul12 = smd2 + sq*invnormal(.975)*sqrt(sn) > . scalar ll12 = smd2 - sq*invnormal(.975)*sqrt(sn) > . scalar li smd2 ul12 ll12 > smd2 = .02788301 > ul12 = .10364515 > ll12 = -.04787914 > > > > > ____________________________________________________________________________________ > Yahoo! oneSearch: Finally, mobile search > that gives answers, not web links. > http://mobile.yahoo.com/mobileweb/onesearch?refer=1ONXIC > * > * 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/ > * * 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/

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