deletions | additions       diff --git a/We_needed_to_emphasize_that__.tex b/We_needed_to_emphasize_that__.tex  index 6e56a25..9ef8874 100644  --- a/We_needed_to_emphasize_that__.tex  +++ b/We_needed_to_emphasize_that__.tex 
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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 thought that our true variability would certainly be higher than that of a harmonized study, and sample sizes we would calculate would be smaller than we actually 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 estimates, estimates if the protocols in their consortiums are close to the 3D-MPRAGE protocols described here. This is  especially useful  if they want to include retrospective data in their analyses. So to To  power an estimate of $CV_a$, we'd need enough subjects to get accurate estimates of scaling factors within sites, and enough sites to get a better variance estimates. The sample sizes here were restricted by funds. size of 12 is enough to estimate the slope of the calibration line (which is around 1), because the scan-rescan reliability of the ROIs is very high.  Ideally, we would have more than 12 subjects to get betterestimates 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. phenotypes, although the inclusion of more sites would also improve the $CV_a$ estimate.  In the text, we've emphasized that the derived power equation does not require phantom subjects or calibration to be used: