[R] Power calculation with measurement error

[Mike Lawrence]

On 26-Jun-07, at 8:12 AM, Mike Lawrence wrote:
> Hi all,
> Hopefully this will be quick, I'm looking for pointers to packages/
> functions that would allow me to calculate the power of a t.test when
> the DV has measurement error. That is, I understand that, ceteris
> paribus, experiments using measure with more error (lower
> reliability) will have lower power.

I came across a reference (http://memetic.ca/reliability.pdf) that  
provides a formula for calculating the noncentrality parameter for  
tests using imperfect measures (see Eq. 4), as well as a table of  
some resulting power estimates. However, while I have created a (very  
slow) monte carlo function that so far as I can tell matches their  
results, when I attempt to implement their analytic solution it's way  
off. Can anyone see what I'm doing incorrectly?

n=100
r=.5 #reliability
e=.5 #effect size
delta=(sqrt(r*n)/2)*e
power.t.test(n,delta,sig.level=.05,alternative='one.sided')

      Two-sample t test power calculation

               n = 100
           delta = 1.767767
              sd = 1
       sig.level = 0.05
           power = 1
     alternative = one.sided

NOTE: n is number in *each* group


Meanwhile, their tables and my monte carlo method say that the power  
in that circumstance should be .7

Help?

Mike