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# Re: st: Computing effect size for a clustered randomized control trial

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: st: Computing effect size for a clustered randomized control trial Date Tue, 4 May 2010 13:12:02 -0400

```Joe McCrary <joe.mccrary@gmail.com>:
I realize I'm coming to this discussion late, but can't you just
invert a formula like Equation 21 on page 17 of
http://www.mdrc.org/publications/437/full.pdf to get the estimated
required sample size J for an MDES of .2 with an n of 12, a fraction P
in the treatment group of 1/3, an ICC of about .1 (say) and an R1 of
. di ceil(2.8^2/(.2^2*1/3*(1-1/3))*(.1+.9*(.75)/12))
138
i.e. about 140 classrooms (with 12 students apiece)?  Also illustrates
the advantage of including classroom-level covariates (via parameter
R2, assumed to be .5 below):
. di ceil(2.8^2/(.2^2*1/3*(1-1/3))*(.1*.5+.9*(.75)/12))
94

I note in passing that .2 is a very large effect; probably you want
MDES=.1 or even .05 or smaller, even if you think the true effect is
really .2

On Mon, May 3, 2010 at 7:23 PM, Joe McCrary <joe.mccrary@gmail.com> wrote:
> I am designing a randomized control trial, where we are going to
> select about 12 students per classroom and randomize them into 3
> groups, a control and 2 treatment groups. Is there a way I can compute
> the number of classrooms needed for the study using the following
> criteria:
>
> Desired power=0.8
> Estimated effect size = 0.2
> alpha = 0.0167
> 1 pre-test measure
> 1 post-test measure
> approx correlation between the two measures = 0.25
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