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

[Michael McCulloch <mm@pinestreetfoundation.org>]

Thanks Michael for the simple and practical suggestion!
Great books you write, by the way!
Michael

On Jun 7, 2010, at 12:43 PM, Michael N. Mitchell wrote:

> Dear Michael
>
>  I would use the -sampsi- command and you can just plug in the  
> values you have based on your published study (see -help sampsi-).  
> Here is an example...
>
> . sampsi 10 12, sd1(5) sd2(6) n1(150) n2(150)
>
> Estimated power for two-sample comparison of means
>
> Test Ho: m1 = m2, where m1 is the mean in population 1
>                    and m2 is the mean in population 2
> Assumptions:
>
>         alpha =   0.0500  (two-sided)
>            m1 =       10
>            m2 =       12
>           sd1 =        5
>           sd2 =        6
> sample size n1 =      150
>            n2 =      150
>         n2/n1 =     1.00
>
> Estimated power:
>
>         power =   0.8803
>
>  If the mean for group1 was 10, the mean for group2 was 12, the sd  
> for group1 was 5, the sd for group2 was 6, the the proposed n1=150  
> and n2=150, the power is .8803.
>
> Best luck,
>
> 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 2010-06-07 12.00 PM, Michael McCulloch wrote:
> > 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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> >
> >
> > 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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