# [FieldTrip] maximum statistic in cluster correction

Eric Maris e.maris at psych.ru.nl
Sun Nov 3 11:41:22 CET 2013

```Hi Ben,

This is useful for others that want to follow the discussion.)

> Thanks for the answer. I really just dont see it... Where does the
> permutation distribution of the max cluster stat come from if you don't
> do a permutation test?

Without a permutation test, there is no permutation distribution. You
construct the permutation distribution as a part of the test.

>
> But you don't actually need that distribution just the statistic??

You need both the distribution and the statistic, just like in parametric
(Neyman-Pearson) statistics. However, unlike parametric statistics, in
permutation statistics you construct your own reference distribution
(i.c., the permutation distribution).

how
> do you know then where your max stat (and the other clusterstats) is
> compared to the critical value at alpha?
>
> lets say your max clusterstat = 10
>
> P(max(clusterstat) _> cv) = 0.05
> so the probability that we see 10 or higher is 5% if h0 is in fact
> true. we actually are seeing 10 and thus (falsely) reject h0. so that
> always happens when h0 is true - you always reject the max cluster when
> h0 is true? doesn't make sense :(

Your conceptual problem probably is due to the fact that you do not see
how the maximum cluster statistic is generated under the permutation
distribution. Under this distribution, this statistic really is a random
variable.

Maybe there is someone in your university to discuss this point. These
conceptual issues are much faster clarified in a one-to-one discussion.
Alternatively, attend one of our Fieldtrip courses.

Best,

Eric Maris

>
> Thanks,
> Ben
>

```