> On 14 Aug 2017, at 13:43 , Spencer Graves > <spencer.gra...@effectivedefense.org> wrote: > > > > On 2017-08-14 5:53 AM, peter dalgaard wrote: >>> On 14 Aug 2017, at 10:13 , Troels Ring <tr...@gvdnet.dk> wrote: >>> >>> Dear friends - I hope you will accept a naive question on lm: R version >>> 3.4.1, Windows 10 >>> >>> I have 204 "baskets" of three types corresponding to factor F, each of size >>> from 2 to 33 containing measurements, and need to know if the standard >>> deviation on the measurements in each basket,sdd, is different across >>> types, F. Plotting the observed sdd versus the sizes from 2 to 33, called >>> "k" , does show a decreasing spread as k increases towards 33. >>> >>> I tried lm(sdd ~ F,weight=k) and got different results if omitting the >>> weight argument but would it be the correct way to use sqrt(k) as weight >>> instead? >>> >> I doubt that there is a "correct" way, but theory says that if the baskets >> have the same SD and data are normally distributed, then the variance of the >> sample VARIANCE is proportional to 1/f = 1/(k-1). Weights in lm are >> inverse-variance, so the "natural" thing to do would seem to be to regress >> the square of sdd with weights (k-1). >> >> (If the distribution is not normal, the variance of the sample variance is >> complicated by a term that involves both n and the excess kurtosis, whereas >> the variance of the sample SD is complicated in any case. All according to >> the gospel of St.Google.) > > > The Wikipedia article on "standard deviation" gives the more general > formula. (That article does NOT give a citation for that formula. I you > know one, please add it -- or post it here, to make it easier for someone > else to add it.) >
Er, I don't see that (i.e. var(S) etc.) in there? My sources were https://math.stackexchange.com/questions/72975/variance-of-sample-variance https://stats.stackexchange.com/questions/631/standard-deviation-of-standard-deviation which contains further links, but no references to publications. I suspect that this stuff is easy enough to do ab initio that people don't bother to fire up a literature search. -pd > > Thanks, Peter. > Spencer Graves >> >> -pd >> >> >>> Best wishes >>> >>> Troels Ring >>> Aalborg, Denmark >>> >>> ______________________________________________ >>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >>> https://stat.ethz.ch/mailman/listinfo/r-help >>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >>> and provide commented, minimal, self-contained, reproducible code. > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
