Re: st: Effect size / sample size / power calculation

[Miranda Kim <mk@mrc.soton.ac.uk>]

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



sjsamuels@gmail.com 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 <mk@mrc.soton.ac.uk> 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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>
>   

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