# cluster statistic on one sample

Floris de Lange florisdelange at GMAIL.COM
Tue Oct 21 17:47:30 CEST 2008

```Dear Eric,

>This quote is about a study involving TWO experimental conditions that are
>manipulated within every subject. This is also called a paired-samples
>design. So, it is NOT a one-sample study.

I agree. Note that in my original question I didn't ask about a one-sample
*study*, but a one-sample *T-test* (on regression weights, which reflect a
weighted difference between several conditions, so not a one-sample study).
Ali's suggestion of simply comparing the regression weights against a matrix
of zeros, using paired samples T-test is excellent I think, and amounts to
the same as sign-flipping in a one-sample T-test.

Thanks at any rate for your clarification, and best wishes from Paris
Floris

>In your quote, also the concepts "symmetry of the distribution" and
>"exchangeability" are mentioned. To keep things clear in our minds, it is
>good to know that
>
>1. Some statisticians (e.g., Tom Nichols, the author of your quote) motivate
>permutation tests from considerations involving the shape of the probability
>distribution (such as symmetry). Other statisticians (like Fortunato
>Pesarin, and I) motivate permutation tests from considerations about
>exchangeability between experimental conditions.
>
>2. "Exchangeability" is a very general concept that can be used in very
>different contexts. Some statisticians (e.g., Tom Nichols) use the term
>"exchangeability" to denote a property of the probability distribution from
>which the subjects are drawn, not mentioning the fact that these subjects
>were observed in two experimental conditions. Other statisticians (like I)
>use "exchangeability" with explicit reference to the data observed in the
>two experimental conditions. For me, exchangeability involves that the
>probability distribution of paired observations is invariant under random
>permutations of the members of these pairs. This assumption of
>exchangeability implies that the data in the two experimental conditions
>have the same marginal probability distribution.
>
>
>(If you like this explanation, Floris, you could join Jan-Mathijs in his
>effort to make a Wiki-tutorial about the statistical rationale of
>permutation tests.)
>
>
>
>
>Don't start cursing the statisticians now!
>
>
>Eric Maris
>
>>
>> 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
>>
>> ----------------------------------
>> The aim of this list is to facilitate the discussion between users of the
>FieldTrip
>> toolbox, to share experiences and to discuss new ideas for MEG and EEG
>analysis.
>> See also http://listserv.surfnet.nl/archives/fieldtrip.html and
>> http://www.ru.nl/fcdonders/fieldtrip.
>
>----------------------------------
>The aim of this list is to facilitate the discussion between users of the
FieldTrip  toolbox, to share experiences and to discuss new ideas for MEG
and EEG analysis. See also
http://listserv.surfnet.nl/archives/fieldtrip.html and
http://www.ru.nl/fcdonders/fieldtrip.

----------------------------------
The aim of this list is to facilitate the discussion between users of the FieldTrip  toolbox, to share experiences and to discuss new ideas for MEG and EEG analysis. See also http://listserv.surfnet.nl/archives/fieldtrip.html and http://www.ru.nl/fcdonders/fieldtrip.

```

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