Blob‐wise Statistical Approach

Instead of using a single maximum voxel, this approach identifies the maximum median statistical value within a spatially constrained blob for each permutation. This reduces the influence of isolated statistical extremes potentially arising from noise, residual artifacts, or boundary effects, while emphasizing spatially sustained effects. The blob radius is defined as half of the FWHM of the smoothing kernel. Considering:

where ($\sigma$) is the Gaussian kernel standard deviation. And also considering (After some algebra...):

where (d) is the distance between voxels, for Gaussian smoothing, the spatial dependence induced between smoothed values can be approximated by:

So, the induced correlation is approximately ($\rho$ = 0.707), indicating approximately 70.7% spatial correlation.

Thus, defining the blob radius as half the smoothing-kernel FWHM provides a local neighborhood within which substantial smoothing-induced spatial dependence is expected.