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

 From Michael Mitchell To statalist@hsphsun2.harvard.edu Subject Re: st: RE: standard deviation for the difference in means Date Sun, 6 Jun 2010 19:17:42 -0700

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:
>
>> 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
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

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