> On Aug 14, 2017, at 10:49 AM, David Winsemius <dwinsem...@comcast.net> wrote: > > >> On Aug 14, 2017, at 5:17 AM, peter dalgaard <pda...@gmail.com> wrote: >> >> >>> 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. > > I don't see why that page doesn't cite: > https://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation > > ... which had several citations including to Johnson, Kotz and Balakrishnan, > v 1, ch 13 sect 8.2. I dug out my copy from the bottom of a large pile of > tomes that I had not reshelved and can confirm that the formula is almost > (but not quite) the same as appears in print. > > JK&M give a formula (p 127) with no derivation or citation: > > E[S] = sigma*( 2/n )^(1/2)*Gamma(n/2)/Gamma[ (n-1)/2 ] > > Whereas the Wikipedia page citing a 1968 TAS article gives: > > E[S] = sigma*( 2/(n-1) )^(1/2)*Gamma(n/2)/Gamma[ (n-1)/2 ] > > I looked up the Bloch note online: > > http://www.tandfonline.com/doi/abs/10.1080/00031305.1968.10480476?journalCode=utas20 > > And it does not have the formula. It was a note on an earlier article by > Cureton, who in turn cited an American Journal of Psychology article by > Holtxman(1950, v63, 615-617). > http://amstat.tandfonline.com/doi/abs/10.1080/00031305.1968.10480435?src=recsys > > Searching on that article I see the first hit is a citation to some R > documentation for hte MBESS::s.u function, which does implement it as > recommended by Holtzman. > > If I were voting on this I would put greater weight on the JK&M but that's > just because it is incredibly likely that I could do the math.
And after reading the historical note by Jarrett (cited by http://davegiles.blogspot.com/2013/12/unbiased-estimation-of-standard.html) : http://www.tandfonline.com/doi/abs/10.1080/00031305.1968.10480474 I'm wondering if these may be equivalent after corrections of varying definitions. -- David. > > Best; > David. > > > > > >> >> -pd >> >> >>> >>> Thanks, Peter. >>> Spencer Graves >>>> >>>> -pd >>>> > > David Winsemius > Alameda, CA, USA > > 'Any technology distinguishable from magic is insufficiently advanced.' > -Gehm's Corollary to Clarke's Third Law > > ______________________________________________ > 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. David Winsemius Alameda, CA, USA 'Any technology distinguishable from magic is insufficiently advanced.' -Gehm's Corollary to Clarke's Third Law ______________________________________________ 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.
