# [FieldTrip] Question about cluster-based statistical testing (sum of t-stats or suprathreshold t-stats?)

Artemy Kolchinsky akolchin at indiana.edu
Mon Dec 17 21:16:54 CET 2012

Thank you greatly for the response!

Keep in mind that in the “Bullmore-style” cluster-mass statistic****
>
> ** **
>
> \sum_i (t_i - c_i) where t_i > c_i****
>
> ** **
>
> the thresholds c_i are constants (i.e., independent of the data).
>

I think I see what you mean.  In my case, t_i are t-statistics, and I use a
p < 0.05 cutoff on both tails for the t distribution.  So yes, here all the
c_i would be the same for all voxels and independent of the data.

> Importantly, these constants also enter in the permutation distribution
> that is used to evaluated the significance of the maximum cluster-mass
> statistic, to the effect that the Bullmore-style and the Fieldtrip-style
> permutation distributions are shifted versions of each other. As a result,
> the p-values that roll out of the two approaches are identical.
>

If I understand correctly, having the same resulting p-values could only be
if the two methods assign the same rank-ordering to a given a set of
clusters.  But I don't think that is the case. Let's imagine that the
t-statistic cutoff 'c' is equal to 1, and the data contains two
suprathreshold clusters (let's say this is a spatial test and the clusters
are composed of electrodes):

- The first cluster has 10 electrodes, each one with a t-statistic equal to
1.1
- The second cluster has 2 electrodes, both with a t-statistic equal to 3

As I understand, Bullmore's method would assign cluster 1 a mass of
10*(1.1-1) = 1 and cluster 2 a mass of 2*(3-1)=4 , while your method would
assign cluster 1 a mass of 10*1.1 = 11 and cluster 2 a mass of 2*3 = 6.
Hence, given a null distribution, it should be possible to choose a
cluster-based threshold that indicates as significant only cluster 1 under
Bullmore's method, and only cluster 2 under yours.

Thanks again,
-Artemy
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