Ah, that makes sense. Thanks for the clarification Greg. -Ista
On Thu, Feb 4, 2010 at 5:58 PM, Greg Snow <greg.s...@imail.org> wrote: > Probably not a typo, but a different textbook used originally. Statistics is > still a relatively young science, so we have not settled on a single set of > notation/symbols/jargon yet (look at intro textbooks, is p the population > proportion (with p-hat the sample) or is p the sample proportion (with pi as > the population)? > > I originally learned that dividing by n gives the 'population' variance since > if you have the entire population then mu is known exactly and you do not > need to correct for unknown mu. You should only divide by n when you have > the entire population. When you have a sample you need to divide by n-1 to > adjust for using the sample mean. > > So from that I learned: population-divide by n; sample-divide by n-1. > > But I have seen others use the approach of dividing a sample sum of squares > by n gives the variance of the sample data, but dividing by n-1 gives the > estimate of the population variance. > > So from that thinking: population-divide by n-1; sample-divide by n. > > Both make sense, so to be clear it is best to just state the divisor rather > than using terms like population and sample and expecting to be unambiguous. > > I have also seen them referred to as unbiased (n-1) and maximum likelihood > (n), but these are not perfect descriptors once you start talking about > standard deviations rather than variances. > > -- > Gregory (Greg) L. Snow Ph.D. > Statistical Data Center > Intermountain Healthcare > greg.s...@imail.org > 801.408.8111 > > >> -----Original Message----- >> From: r-help-boun...@r-project.org [mailto:r-help-boun...@r- >> project.org] On Behalf Of Ista Zahn >> Sent: Tuesday, February 02, 2010 12:03 PM >> To: Peng Yu >> Cc: r-h...@stat.math.ethz.ch >> Subject: Re: [R] population variance and sample variance >> >> Probably a simple typo, but just to keep things straight: you want to >> divide by n when describing the standard deviation of a sample, and >> divide by n-1 when estimating a population standard deviation (your >> initial description had it backwards I think). >> >> On Tue, Feb 2, 2010 at 5:25 PM, Peng Yu <pengyu...@gmail.com> wrote: >> > On Mon, Oct 19, 2009 at 12:53 PM, Kingsford Jones >> > <kingsfordjo...@gmail.com> wrote: >> >>> sum((x-mean(x))^2)/(n) >> >> [1] 0.4894708 >> >>> ((n-1)/n) * var(x) >> >> [1] 0.4894708 >> > >> > But this is not a built-in function in R to do so, right? >> > >> >> hth, >> >> Kingsford >> >> >> >> On Mon, Oct 19, 2009 at 9:30 AM, Peng Yu <pengyu...@gmail.com> >> wrote: >> >>> It seems that var() computes sample variance. It is straight >> forward >> >>> to compute population variance from sample variance. However, I >> feel >> >>> that it is still convenient to have a function that can compute >> >>> population variance. Is there a population variance function >> available >> >>> in R? >> >>> >> >>> $ Rscript var.R >> >>>> set.seed(0) >> >>>> n = 4 >> >>>> x = rnorm(n) >> >>>> var(x) >> >>> [1] 0.6526278 >> >>>> sum((x-mean(x))^2)/(n-1) >> >>> [1] 0.6526278 >> >>>> >> >>> >> >>> ______________________________________________ >> >>> R-help@r-project.org mailing list >> >>> 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 >> > 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. >> > >> >> >> >> -- >> Ista Zahn >> Graduate student >> University of Rochester >> Department of Clinical and Social Psychology >> http://yourpsyche.org >> >> ______________________________________________ >> R-help@r-project.org mailing list >> 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. > -- Ista Zahn Graduate student University of Rochester Department of Clinical and Social Psychology http://yourpsyche.org ______________________________________________ R-help@r-project.org mailing list 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.
