# 3dClustsim - smaller cluster size threshold at more stringent p threshold

Hi AFNI gurus,

I recently ran 3dClustSim with -acf and am confused by the output - it seems like the necessary cluster size should increase as the per voxel p value gets smaller, but the opposite occurs. That is, shouldn’t clusters need to be bigger for them to reach significance as the significance thresholds are made more stringent?
For example, I got the following results for the NN3 1sided output:

# ------ | ------ ------ ------ ------

0.050000 2197.0 2758.5 4073.0 5640.0
0.010000 297.7 373.5 581.0 967.0
0.005000 168.6 208.1 321.0 587.0
0.001000 56.6 72.2 114.0 213.0

Why would a more stringent per voxel threshold yield a smaller cluster size at which clusters may be significant? For example at alpha = .05, pthr = .005 the cluster size is 208.1 vs. at the more stringent pthr = .001 the cluster size is 72.2. Shouldn’t it be the other way around? Is my thinking backwards on this? Thanks for your help.

Best,
Lauren

The thresholding process envisioned and implemented in 3dClustSim has 2 steps:

(1) Per-voxel thresholding at some p-value. Smaller p-values are more strict: fewer voxels will “survive”.

(2) From the “surviving” voxels, form spatially contiguous clusters. Delete those that are smaller than the cluster-size threshold.

Consider the case where you lower step 1’s per-voxel p a lot (raise the t-statistic threshold high). Say you have Nvox=10[sup]5[/sup] voxels, and set per-voxel p=5x10[sup]-7[/sup]=0.05/Nvox. Then the Bonferroni correction tells you that the probability of ANY false positive voxel is less than 0.05 – that is, a cluster-size threshold of 1 voxel is good.

Now imagine increasing p (lowering t) – then there is a bigger chance of false positive voxels. At some point as p increases, when more false positive voxels occur, they will clump together, and the chance of getting a cluster of size 2 voxels FROM NOISE ALONE will get large.

And so on. Larger per-voxel p means more false positive voxels, means that to keep the overall (or global) false positive probability at 5%, we have to eliminate more clusters.

Got it! Thanks, Bob!