On Thu, 30 Nov 2000, Stefan Kiebel wrote:
> I try to explain my point a litte bit more formal.
> Given two volumes V_1 and V_2 sampled at discrete points, in both V_1
> and V_2 homologous locations (A_1 and A_2) show the same mean and the
> same activation effect, where A_1 and A_2 are the only locations showing
> an activation effect. Let the voxel intensities in V_1 and V_2 around
> A_1 and A_2 be different. Now apply a spatial convolution L to both V_1
> and V_2.
> Note that the estimated mean intensities in the convolved V_1 and V_2 at
> voxel A_1 and A_2 will be different, whereas the measured activation
> effect will not be a function of the intensities around A_1 and A_2.
But the assuption that "A_1 and A_2 are the only locations showing an
activation effect" seems a bit dodgy... we never have exactly zero
What we get after convolution is a mix of everything from the
local neighborhood... the estimated baseline at A_1 after convolution is
a mixture of baseline around A_1... the estimated activation a mix
activation around A_1.
> This example can be generalized to a range of other spatial
> configurations. In other words, relating the signal change to the voxel
> mean intensity can be misleading, if some low-pass filter L has been
> applied to the image prior to the statistical analysis.
Smoothing the data means you're smoothing both the signal and the
baseline. Maybe there is a more compelling example where one would
get misleading answers?