Comparing to zero

Robert Oostenveld r.oostenveld at FCDONDERS.RU.NL
Fri Jun 24 09:54:22 CEST 2005

Hi Eric and others,

The test that Vladimir refers to does not test the hypothesis of the
expected value of the mean being zero, but it tests the null
hypothesis of exchangeability of the sign of the data. If it is very
improbable (say p<0.05)  that the sign can be exchanged, you would
accept the alternative hypothesis which states that the random
distribution of your data is not symmetric with respect to zero. That
is already very close to what Vladimir is interested in.

However, not only a shift in the mean of the random distribution
would violate the null hypothesis, but also any other asymmetry with
respect to zero. Therefore it is not possible to immediately
translate the alternative hypothesis (as I phrased it above) into a
statement about the mean (which is what Vladimir wants).

What you could do, after finding with the randomization test that the
distribution is not symemtric around zero, is
1) assume that that assymetry is caused by a shift in the mean and
not test it (which seems fair enough to me in quite some cases, e.g.
when you know that the random distribution is close to a normal
distribution), or
2) perform a second test in which you test whether the distribution
of the random variable is symmetric around its estimated mean (i.e.
repeat the same test as done before, after subtracting the mean of
the random variable).

I think that that would be relatively simple to implement in FieldTrip.


>> What would be the best way to find clusters that are significally
>> different from zero (or any other constant value for this matter)?
>> I once
>> saw in SnPM of Nichols an option to have a single input with the
>> permutations done my toggling the sign, but there is no such
>> option in the
>> current version of clusterrandanalysis
> As far as I know, there is no randomization/permutation test by
> means of which
> one can test the null hypothesis that some random variable has
> expectation zero.

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