deletions | additions       diff --git a/We_needed_to_emphasize_that__.tex b/We_needed_to_emphasize_that__.tex  index 8a1458c..6e56a25 100644  --- a/We_needed_to_emphasize_that__.tex  +++ b/We_needed_to_emphasize_that__.tex 
...
We needed to emphasize that the number of phantom subjects do not contribute to the power equation in Figure 1. The power equation we derived does not account for any sort of calibration or scaling. Instead, it requires an estimate for $CV_a$, which is the variability of scaling biases between sites. Because we are not asking our consortium to change protocols, we knew thought  thatif we calculated this value from ADNI data (which has standardized acquisitions),  our true variability would certainly be higher than that of ADNI, a harmonized study,  and sample sizes we would calculate would be smaller than we actually need. need if we used harmonized data to calculate it.  For other researchers planning multisite studies, they could use our measurements of $CV_a$ to get a better power estimate. estimates, especially if they want to include retrospective data in their analyses.  So to power an estimate of $CV_a$, we'd need enough subjects to get accurate estimates, estimates of scaling factors within sites,  and enough sites to get a better variance estimate. This was estimates. The sample sizes here were  restricted by funds. Ideally, we would have more than 12 subjects to get better estimates of scaling factor, and even get a better estimate of the intercept (This is listed as a study limitation in the discussion). We sampled from 20 sites because these same sites will be used in a future study on MS genetics and MRI phenotypes. In the text, we've emphasized that the derived power equation does not require phantom subjects or calibration to be used: