# [FieldTrip] maximum statistic in cluster correction

Eric Maris e.maris at psych.ru.nl
Thu Oct 31 16:31:04 CET 2013

```Hi Ben,

> I am trying to understand how the permutation test and cluster
> correction work. the Maris 2007 and 2012 papers along with the
> tutorials on the fieldtrip site helped a lot. However, i cant seem to
> grasp the idea behind the max stat very well. let me summarize how i
> think i understand things so far so you can see where i go wrong.
>
> Per channel per trial (a sample), we calculate the t statistic between
> conditions. This is the observed statistic. Next, we collect all the
> trials (or samples?) from both conditions and put them into 1 set. We
> randomly draw trials from this set and put them into subsets of the
> same size as the original condition sets, this is called a random
> partition. A t statistic is calculated on the difference between the
> two subsets. This process is repeated a large number of times and the
> results are put in a histogram. The histogram is called the permutation
> distribution.
>
>
> Find the proportion of random partitions that show a smaller t
> statistic than the observed t statistic. This is the monte carlo
> estimate. For example, if 97% of your draws from the permutation
> distribution show a smaller t statistic then the one you originally
> observed, you have a monte carlo p value of 0.03.
>
>
> Cluster based correction means that you take all the samples that show
> a t value that exceeds a certain threshold (ie the significant
> differences) and cluster them on the basis of temporal (and spatial)
> adjacency. The idea is that samples that are close together (in space
> or in time) show a similar effect. The next step is to sum the t values
> within each cluster and find the cluster with the largest sum (the
> maximum statistic).
>
> Here is where i don't understand the next step. You take the
> permutation distribution of the cluster with the maximum statistic?
> This means basically that you redo the permutation test but this time
> only with trials that fall within that cluster?

No. The relevant distribution is the permutation distribution of the
"maximum cluster statistic". Over random permutations, the spatiotemporal
extent of the cluster with largest cluster-level statistic varies.
However, the only thing that we need is the value (one number) of the
maximum cluster statistic.

Best,

Eric Maris

Summing the t values
> from each partition would then give the permutation distribution of
> your max stat cluster. If you have other clusters, you plug their
> summed t value into that permutation distribution and compare the p
> value with your alpha value to see if they are significant as well. But
> if you do that for say 20 clusters you're still not controlling the FA
> rate? I'm at the point where the more i think about it the less things
> make sense, so i must be missing something upstream...?
>
>
> Best,
>
> Ben
>

```