deletions | additions       diff --git a/The_assumption_of_independence_between__.tex b/The_assumption_of_independence_between__.tex  index 1eb5566..401b804 100644  --- a/The_assumption_of_independence_between__.tex  +++ b/The_assumption_of_independence_between__.tex 
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The assumption of independence between the unobserved difference between groups and the scaling factor of a site is certainly invalid if people that who  have more disease have tissue with different properties that affect regional contrast. It would mean that the scaling factor is correlated with the unobserved effect because different patient groups have different scaling factors. In dropping the covariance terms here, power would be overestimated because the denominator of the non-centrality parameter would be larger. We scanned MS patients to see how different the scaling factors were to address this concern. The scaling factors were very similar and in one case, identical, with the caveat that the images were QC'd more carefully to check and correct for gross segmentation missclassifications. The full equation for the calculation of variance has been added to the appendix, which includes the covariance terms before they are dropped: \begin{equation}  \begin{split}