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Re: st: Effect size / sample size / power calculation
The formula to get standardized effect size for a one sample test is:
. di sqrt((invnorm(.975)+invnorm(.9))^2)/sqrt(150)
.26466864
But actually, I cheated and used PASS software.
P
Miranda Kim wrote:
Thank you for your responses Steve and Paul. I will illustrate my
problem with an example…
For example, previous research on a given association yields a
correlation coefficient 0.41 with p-value 0.131 and n=15.
Initially I was looking at what sample size n would be required to
have 90% power to detect a correlation coefficient 0.41 using a test
at the 5% level of significance.
I used the fact that the correlation coefficient of two variables with
unit standard deviation is the same as the regression coefficient
between those two variables.
So in effect, I wish to perform a sample size calculation for a
regression coefficient of two variables with unit standard deviation.
In this case the standard error of the regression coefficient is
sqrt((1-(b*b))/(n-2)), so standard deviation of the regression
coefficient is approximately sqrt(1-(b*b)).
For this example, this gives a standard deviation of 0.91.
I then used the command
sampsi 0.41 0, p(0.9) sd(0.91) onesam
which yielded n=52.
I now know that I will have approximately n=150 in the study, and want
to know how this affects this correlation coefficient at 90% power and
80% power (5% significance)?
I have a dataset with approximately 20 correlation coefficients, so I
was hoping to automate the calculation.
Paul, what formula did you use to obtain 0.265 in your response?
Best wishes and many thanks for your help,
Miranda
[email protected] wrote:
Miranda,
-sampsi- is not the right command to do the initial calculation, for
the effect size for multiple linear regression is not beta, but
delta = r/sqrt( 1 - r^2)
where r = partial correlation of Y and X, adjusted for the other
predictors Z.
and beta = r SD(X|Z) /SD(Y|Z))
To solve for the detectable beta, use Russ Lenth's online Java
calculator (Linear regression) at:
http://www.stat.uiowa.edu/%7Erlenth/Power/ . You have to enter the
Variance Inflation Factor VIF.
ding, since the
-Steve
On Wed, Jan 6, 2010 at 9:27 AM, Miranda Kim <[email protected]> wrote:
Could anyone help me with this...
To detect a regression coefficient of 0.41 with standard deviation
0.91 I
can compute a sample size (using a 5% level of significance with 90%
power)
with the following command:
sampsi 0.41 0, p(0.9) sd(0.91) onesam
How could I work out what regression coefficient (effect size) is
detectable
with a sample size of 150, based on this information?
I need to do this with about 20 regression coefficients.
I am using stata 11.
Many thanks,
Miranda
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--
E. Paul Wileyto, Ph.D.
Assistant Professor of Biostatistics
Tobacco Use Research Center
School of Medicine, U. of Pennsylvania
3535 Market Street, Suite 4100
Philadelphia, PA 19104-3309
215-746-7147
Fax: 215-746-7140
[email protected]
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