Re: st: RE: standard deviation for the difference in means

[Michael McCulloch <mm@pinestreetfoundation.org>]

Thanks Peter and Michael,
What I'm wanting to do here is perform a sample size estimate with  
summary data obtained from a published study.
Unfortunately I do not have the raw data. I only have:

Group A:,
	mean of a continuous variable,
	standard deviation of that continuous variable,
	sample size,
Group B:,
	mean of the same continuous variable,
	standard deviation of that continuous variable,
	sample size,

And,  the P value based on a two-sample t test comparing differences  
in between-group means.
My question is,  with those values (and none other) available,  is it,  
possible to estimate the standard deviation for the difference in  
means between groups A and B?
Thank you for your thoughts on my question.
Michael McCulloch



On Jun 7, 2010, at 8:44 AM, Lachenbruch, Peter wrote:

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu 
> ] On Behalf Of Michael Mitchell
> Sent: Sunday, June 06, 2010 7:18 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: standard deviation for the difference in means
>
> It is true, that the formula that Peter gave is based on the
> assumption of equal variances for each group.
>
> If you were using Stata, the equivalent command for comparing the
> means of two independent groups with equal population variances would
> be, for example...
>
> . sysuse auto
> . ttest weight, by(foreign)
>
> If you do not believe the population variances are not equal in the
> two groups, you could add the -unequal- option, as shown below.
>
> . ttest weight, by(foreign) unequal
>
> or you can use the -welch- option, as shown below
>
> . ttest weight, by(foreign) welch
>
>  The methods and formulas are provided at the end of the manual entry
> for the ttest command, see -help ttest- and then see the manual entry.
>
> I hope that helps,
>
> Michael N. Mitchell
> Data Management Using Stata      - http://www.stata.com/bookstore/dmus.html
> A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html
> Stata tidbit of the week         - http:// 
> www.MichaelNormanMitchell.com
>
>
> On Sun, Jun 6, 2010 at 6:07 PM, Michael McCulloch
> <mm@pinestreetfoundation.org> wrote:
> > Thanks Peter, I'm not sure. I'm comparing two groups randomly  
> > assigned to
> > treatment, so they are independent, but my understanding was the  
> > pooled
> > variance assumes equal variances in each group.
> >
> > On Jun 6, 2010, at 1:17 PM, Lachenbruch, Peter wrote:
> >
> > > Are you asking for
> > > pooled variance:  sp^2=[(n1-1)s1^2+(n2-1)s2^2]/[n1+n2-2]  ?
> > >
> > > Then the sd for the difference in the means will be sp*sqrt(1/n1+1/ 
> > > n2)
> > >  aka standard error.
> > >
> > > ________________________________________
> > > From: owner-statalist@hsphsun2.harvard.edu
> > > [owner-statalist@hsphsun2.harvard.edu] On Behalf Of Michael  
> > > McCulloch
> > > [mm@pinestreetfoundation.org]
> > > Sent: Sunday, June 06, 2010 12:57 PM
> > > To: Statalist Statalist
> > > Subject: st: standard deviation for the difference in means
> > >
> > > Apologies for a basic statistics question:
> > >
> > > I wish to estimate sample size for an experiment in which, from
> > > previously published data, I have available the following summary
> > > measures (but not the raw data):
> > >
> > > Group A:
> > >       mean of a continuous variable
> > >       standard deviation of that continuous variable
> > >       sample size
> > > Group B:
> > >       mean of the same continuous variable
> > >       standard deviation of that continuous variable
> > >       sample size
> > > And, the P value based on two-sample t tests comparing differences  
> > > in
> > > between-group means.
> > >
> > >
> > > My question is, with those values (and none other) available, is it
> > > possible to estimate the standard deviation for the difference in
> > > between-group means.
> > >
> > >
> > > Best wishes,
> > >
> > > Michael McCulloch, LAc MPH PhD
> > > Pine Street Foundation
> > > 124 Pine Street
> > > San Anselmo, CA 94960-2674
> > > tel:    415-407-1357
> > > fax:    206-338-2391
> > >
> > > *
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> >
> > Best wishes,
> >
> > Michael McCulloch, LAc MPH PhD
> > Pine Street Foundation
> > 124 Pine Street
> > San Anselmo, CA 94960-2674
> > tel:    415-407-1357
> > fax:    206-338-2391
> >
> > *
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> > *   http://www.ats.ucla.edu/stat/stata/
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Best wishes,

Michael McCulloch, LAc MPH PhD
Pine Street Foundation
124 Pine Street
San Anselmo, CA 94960-2674
tel:	415-407-1357
fax: 	206-338-2391

*
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*   http://www.ats.ucla.edu/stat/stata/