# st: Calculating a confidence interval for population variance based upon sample.

 From "Carl Mastropaolo" To Subject st: Calculating a confidence interval for population variance based upon sample. Date Mon, 1 Feb 2010 12:09:03 -0500

```Thank you all for your input.  I am currently modifying an ado file from
Paul V which I believe will work well.  And I will also work with the ado
file sent by Tirthankar.  I will also review the doc sent by Peter
Lachenbruch.

Thank you all for the help.

Carl

----- Original Message -----
From: "Tirthankar Chakravarty" <tirthankar.chakravarty@gmail.com>
To: <statalist@hsphsun2.harvard.edu>
Sent: Monday, February 01, 2010 12:00 PM
Subject: Re: st: RE: RE: RE: Fw: Calculating a confidence interval for
population variance based upon sample.

There is some literature on the sampling distribution of the sample
variance, where the parent distribution is highly non-normal,
particularly, this:
http://www.jstor.org/pss/3314982

The basic, chi2-based confidence interval can be calculated as below.

/***** Compute the sampling distribution of the sample variance *****/
clear*
sysuse auto

// assuming that the variable is normally distributed
scalar alpha = .05
sum price
di "The " 1-alpha " percent confidence interval for the sampling
variance: "  r(Var) " is " ///
"[" ((`r(N)'-1)/invchi2(`r(N)'-1,1-alpha/2))*`r(Var)' ", "
((`r(N)'-1)/invchi2(`r(N)'-1,alpha/2))*`r(Var)' "]. "
/***** Compute the sampling distribution of the sample variance *****/

T

2010/2/1 Visintainer PhD, Paul <Paul.Visintainer@baystatehealth.org>:
> Rosner's approach is based on the chi-square, but he does note that it is
> applicable only for normally-distributed samples.
>
> -p
>
> ___________________________________
> Paul F. Visintainer, PhD
> Director of Epidemiology and Biostatistics
> Baystate Medical Center
> Division of Academic Affairs - 3rd Floor
> 280 Chestnut Street
> Springfield, MA 01199
> (T) 413.794.7686
> (F) 413.794.7689
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Lachenbruch,
> Peter
> Sent: Monday, February 01, 2010 11:36 AM
> To: 'statalist@hsphsun2.harvard.edu'
> Subject: st: RE: RE: Fw: Calculating a confidence interval for population
> variance based upon sample.
>
> This is usually based on the chi-squared distribution - but it is rarely
> used because the variance is affected by a) outliers, b) distribution. I
> don't have my Rosner handy so I'm uncertain if it's the procedure he
> recommends.
> I would propose a couple of alternatives:
> 1. find a bootstrap confidence interval for the variance using percentiles
> or accelerated bootstrap.
> 2. Abandon the chi-square and get estimates of the percentiles of interest
> (e.g., 0.025, 0.05, 0.1 and their complements) with centile. This may have
> a problem if sample size is small.
> After finding the confidence interval for the variance, you can find the
> standard deviation easily enough
>
> Tony
>
> Peter A. Lachenbruch
> Department of Public Health
> Oregon State University
> Corvallis, OR 97330
> Phone: 541-737-3832
> FAX: 541-737-4001
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Visintainer
> PhD, Paul
> Sent: Monday, February 01, 2010 7:15 AM
> To: 'statalist@hsphsun2.harvard.edu'
> Subject: st: RE: Fw: Calculating a confidence interval for population
> variance based upon sample.
>
> Carl,
>
> There is a procedure in Rosner [Rosner, B. "Fundamentals of Biostatistics,
> (6th ed.), Duxbury, Press (The Thompson Company): Belmont, CA, 2006, pgs.
> 199-201.]
>
> If you send me your email, I can pass along a "not-ready-for-prime-time"
> .ado that I use for the calculation.
>
> -p
>
>
>
> ___________________________________
> Paul F. Visintainer, PhD
> Baystate Medical Center
> Springfield, MA 01199
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Carl
> Mastropaolo
> Sent: Monday, February 01, 2010 9:47 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Fw: Calculating a confidence interval for population variance
> based upon sample.
>
> Hi
>
> I have STATA10.
>
> I can not figure out how to calculate a simple confidence interval for a
> population variance
> based upon sample data. STATA will calculate the sample standard
> deviation,
> but I can not figure out how to compute a confidence interval for the
> population standard deviation. Is there a command which will do this?
>
> Any help?
>
> Thanx,
> Carl
>
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