# cluster statistic on one sample

Floris de Lange florisdelange at GMAIL.COM
Tue Oct 21 00:33:45 CEST 2008

```Dear Eric and other fieldtrippers,

I am a bit puzzled about your comment that:
"Your null hypothesis is a typical parametric null hypothesis; the
expected value of some
(matrix-valued) variable being equal to zero.The null hypothesis that is
tested by a nonparametric permutation test is equality across experimental
conditions of the probability distribution from which the
(condition-specific) data are drawn."

If I understand what SnPM (for fMRI) does well, it uses a permutation
test on one sample, creating a probability distribution by randomly
changing the sign of the observations. I quote (taken from
http://www.sph.umich.edu/ni-stat/SnPM/)

"Under the null hypothesis we can permute the labels of the effects of
interest. One way of implementing this with contrast images is to
randomly change the sign of each subject's contrast. This
sign-flipping approach can be justified by a symmetric distribution
for each voxel's data under the null hypothesis. While symmetry may
sound like a strong assumption, it is weaker than Normality, and can
be justified by a subtraction of two sample means with the same
(arbitrary) distribution.

Hence the null hypothesis here is:
H0: The symmetric distribution of (the voxel values of the)
subjects' contrast images have zero mean.

And some more detail on the assumptions:

(..) to analyze a group of subjects for population inference, we need
to only assume exchangeability of subjects. The conventional
assumption of independent subjects implies exchangeability, and hence
a single exchangeability block (EB) consisting of all subjects.

(On a technical note, the assumption of exchangeability can actually
be relaxed for the one-sample case considered here. A sufficient
assumption for the contrast data to have a symmetric distribution, is
for each subject's contrast data to have a symmetric but possibly
different distribution. Such differences between subjects violates
exchangeability of all the data; however, since the null distribution
of the statistic of interest is invariant with respect to
sign-flipping, the test is valid.)

I don't see why this approach wouldn't be applicable for MEG data?
As a side note, comparing my regression weights with a condition of
all zeros with a dependent sample T-test works well, and is
mathematically equivalent to a one-sample T-test as far as I can see,
at least in the parametric domain?

Best wishes,
Floris

--
--
Floris de Lange
http://www.florisdelange.com

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