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

 From "Michael N. Mitchell" To statalist@hsphsun2.harvard.edu Subject Re: st: RE: standard deviation for the difference in means Date Mon, 07 Jun 2010 12:43:42 -0700

```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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* http://www.stata.com/support/statalist/faq
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*
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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/

```
```
*
* 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/

*
* 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/
```
```

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/
```
```*
*   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/
```