Dear Leon,
> To expand on this, is it possible to instead employ fraction of grey matter volume (GM volume divided by TIV) as a covariate for VBM analysis (as done by Muhlau et al 2007)?
>
I am not familiar with Muhlau 2007, so I can't give you an answer to that.
Small brains tend in general to have a greater proportion of grey matter than large brains. That means that if you compare two groups (let's call them SB and LB) you will find a greater grey matter density along most of the cortex for the SB group. If you have a large enough group size you will find a significant effect in most of the cortex. If you have a smaller group size you may not have enough statistical power to detect it everywhere and instead you may find isolated blobs where it reaches significance and you will interpret these as "local changes".
So it is not that those blobs are actually wrong, there may well be an effect there. The problem is that maybe that effect is in reality global and not restricted to the areas that you end up reporting.
So, what is then a "local effect" in the context of a "global effect"? On the one hand one might argue that a global effect is nothing but a lot of local effects and is equally interesting to report. I personally don't think that is true. If an effect is global it should be reported as such.
My take on it is that a "truly local" effect in the context of a "global effect" is an effect over and above that which would be expected from the global effect. The strictest test for that would entail including a "global brain size" or "global grey matter volume" regressor. I attach two little figures that would illustrate what I consider a "true local effect" and what I would not consider a local effect, even though in both cases there is a clear difference between the groups. SB in red and LB in blue.
Here I would consider the effect on the left "local" while I would not consider the effect on the right as "local". The reason for this is that in the plot to the right both groups fall on the same line which implies that if I could find a "blue" group with equally small brains as the "red" group but otherwise with the same properties it seems likely that the difference would disappear.
However, the question of what is truly a "local" effect is almost a philosophical one and this was just my 5p.
Jesper
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