How to choose a sample size for two group repeated measures anova design given power, alpha, and effect size? How would I go about computing the sample size for repeated measures ANOVA design, given power, significance and the required effect size (2 groups, I know the mean difference that I want to be able to catch and approximate standard deviation)?
 A: There's a nice tutorial on this which uses the R language/environment: 
http://gjkerns.github.io/R/2012/01/20/power-sample-size.html
How to attack it
The avenue of attack is simple: for a given sample size, use prior research and practitioner experience to decide what difference would be "meaningful" to detect,
    simulate data consistent with the above difference and run the desired statistical test to see whether or not it rejected, and
    repeat step 2 hundreds of times. An estimate of the power (for that sample size) is the proportion of times that the test rejected.
If the power isn't high enough, then increase the given sample size and start over. The value we get is just an estimate of the power, but we can increase the precision of our estimate by increasing the number of repetitions in step 3.
What you find when you start down this path is that there is a lot of information required to be able to answer the question. Of course, this information had been hiding behind the scenes all along, even with those old research papers and online calculators, but the other methods make it easy to gloss over the details, or they're so complicated that researchers will give up and fall back to something like Cohen's T-shirt effect sizes.
