[R] population variance and sample variance

[Kingsford Jones]

On Thu, Feb 4, 2010 at 11:07 AM, Peng Yu <pengyu.ut at gmail.com> wrote:

> I'm so surprised that even this basic definition does not have unique
> name in the nomenclature, which might cause confusion in certain
> context. Just some of my thought---if both definitions are OK, then
> the wiki page might be revised
> http://en.wikipedia.org/wiki/Variance#Population_variance_and_sample_variance.
> After all, many none pure statisticians relies on wiki for easy access
> of some simple terms.

I believe the nomenclature in your link is pretty well accepted.  The
point made earlier is that when sampling one uses (n-1) to get an
unbiased estimate of the *population* value, so one needs to be
careful w/ semantics and it's really better to be mathematically
explicit.  Also when we discuss the variance of a random variable we
are referring to its 2nd central moment (Var X = E(X - E X)^2), so
again the definition is context dependent.

Kingsford




>
>
>>> -----Original Message-----
>>> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
>>> project.org] On Behalf Of Ista Zahn
>>> Sent: Tuesday, February 02, 2010 12:03 PM
>>> To: Peng Yu
>>> Cc: r-help at 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.ut at gmail.com> wrote:
>>> > On Mon, Oct 19, 2009 at 12:53 PM, Kingsford Jones
>>> > <kingsfordjones at 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.ut at 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
>>> >>>>
>>> >>>
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>>> >>
>>> >
>>> > ______________________________________________
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>>>
>>>
>>>
>>> --
>>> Ista Zahn
>>> Graduate student
>>> University of Rochester
>>> Department of Clinical and Social Psychology
>>> http://yourpsyche.org
>>>
>>> ______________________________________________
>>> R-help at 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 at 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.
>