I have a question that may be fairly easy to answer but it is making my head spin. If I do a paired t test on two groups of data with sample size 3 each AND I assume that the pairs are correlated with at least an correlation coefficient of 0.5, then I should have about 90% power to detect an effect size of 2SD.
Ok, so lets say that after the experiment, I check my sample correlation and it turns out that it is only 0.2 for that sample and not 0.5. I am wondering how this would affect the power of my test since, I believe, the sample correlation value influences my p-value. Would I then have to say that I actually had less than 90% power? Or did my test still have 90% power regardless of how the sample correlation turned out? I am thinking it is the latter rather than the former but I would appreciate some help as this whole business of calculating power after a test is very confusing. Hopefully my question makes sense.