[FieldTrip] maximum statistic in cluster correction

van Lier Ben ben.vanlier at bsse.ethz.ch
Wed Oct 30 16:01:17 CET 2013

```Hi all,

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? 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

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