# 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.
>> 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