deletions | additions       diff --git a/Assumption_about_independence_of_MRI__.md b/Assumption_about_independence_of_MRI__.md  index 0b343f1..c0919a5 100644  --- a/Assumption_about_independence_of_MRI__.md  +++ b/Assumption_about_independence_of_MRI__.md 
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* Assumption about independence of MRI-related biases and biological effect being studied (a_j ($a_j$  is independent from D_u,j). $D_{u,j}$).  It was shown that there is significant differences in detecting anatomical changes due to ageing and acquisition parameters ( see Streitburger 2014 "Impact of imageacquisition on voxel-based-morphometry investigations of age-related structural brain changes" for differences between 12-channel and 32-channel RF coil in MPRAGE and for differences caused by varying resolution). In \cite{streitburger2014impact}, the researchers found that different pulse sequences and hardware (12 ch vs 32ch RF coil) altered the estimate of the coefficient on gray matter density in an age regression. This is what we are hypothesizing for regional volumes as well. $D_{u,j}$ is the **unobserved** effect - in the case of \cite{streitburger2014impact}, the true GM density dependence on age that cannot be measured directly. We propose that the reason for the differences seen in regional volume analyses (and possibly VBM) is due to different scaling baises, $a_j$, for different pulse sequences. So it is definitely true that $a_j$ and $D_{Y,j}$(the **observed** effect) are correlated, but we do not think there is a correlation between the **unobserved** effect with the $a_j$, which is only dependent on scanner hardware/acquisition.