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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)?

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  • $\begingroup$ When you say you know the standard deviation, is this of the variables, or of the difference? (If the former, if you know the correlation, you can calculate the latter.) $\endgroup$ – Jeremy Miles Feb 28 '14 at 21:00
  • $\begingroup$ You say this is between two groups. In that case, is there a reason to use ANOVA rather than a paired t-test? $\endgroup$ – David Robinson Feb 28 '14 at 21:01
  • $\begingroup$ Maybe it's a RM ANOVA with a between-subjects factor? It's as if there weren't enough uncertainty in statistics already... $\endgroup$ – Nick Stauner Feb 28 '14 at 22:36
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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.

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