deletions | additions       diff --git a/The_number_of_phantom_subjects__.tex b/The_number_of_phantom_subjects__.tex  index d3ac4b8..503967f 100644  --- a/The_number_of_phantom_subjects__.tex  +++ b/The_number_of_phantom_subjects__.tex 
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The number of phantom subjects do not contribute to the power equation in Figure 1. The power equation that was 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. Our consortium was not asked to change protocols, so the true bias variability might be higher than that of a harmonized study, and sample sizes we would calculate would be smaller than  what is actually needed if harmonized data was used to calculate bias. For other researchers planning multisite studies, our measurements of $CV_a$ could be used to get a better power estimate for protocols that are close to the 3D-MPRAGE protocols that were described here. This is especially useful for the inclusion of retrospective data. To power an estimate of $CV_a$, two sample sizes are required - the subject level, and the site level. The sample 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 (around 0.9). Ideally, we would have more than 12 subjects to get better a better estimate of the intercept, and this was listed as a study limitation in the discussion. 20 sites were sampled because these same sites will be used in a future study on MS genetics and MRI phenotypes, although the inclusion of more sites would also improve the $CV_a$ estimate.