Comparing to zero

Eric Maris maris at NICI.RU.NL
Mon Jun 27 22:19:19 CEST 2005

Hi Litvak,

>> My first reaction is: if A is different from B, then (A-B) is different
>> from zero, and hence (A-B)/B is also different from zero (given that B is
>> not zero). So what is the use of testing A==B separately from testing
>> whether (A-B)==0? Do you expect your statistical sensitivity to be
>> larger?
> The point is I do the normalization for each subject separately. So I get
> % change for each subject and not absolute values that can be very
> different between individuals. I didn't think it violates any of the
> assumptions of clusterrandanalysis but if it does I'll probably have to
> look for other ways.

If I understand you correctly, then A and B denote baseline-normalized power
(i.e. percent increase/decrease relative to baseline). In that case, pass
the data structures containing (in the powspctrm-field) A and B in the
argument of clusterrandanalysis and perform a dependent samples T-test. This
does not violate any of the assumptions of randomization statistics. It is
equivalent to a test of symmetry-around-zero of the difference variable
(A-B) (see this thread some steps ago).

>> In clusterrandanalysis, the clusters are grown using a thresholded
>> parametric statistical representation of the effect of interest. The
>> summed parametric statistical measure over the whole cluster is subjected
>> to the randomization procedure (testing the hypothesis of
>> exchangeability), which results in a non-parametric test. I am not aware
>> of a parametric statistical measure for which it would be possible to
>> define a meaningfull threshold for the clustering based on the ratio
>> (A-B)/B. It could be done however using a randomization test that is not
>> based on clusters.
> I don't understand why this normalized data is different from raw data.
> You can define the distribution under the null hypothesis using
> permutations and proceed from there. If there is something basic I don't
> understand please explain it to me because it's important to know the
> limitations of the method.

No, there is nothing basic that you miss. Robert's point is that the
calculation of the cluster-level statistics is based on a thresholding that
has a parametric rationale. However, this does not make clusterrandanalysis
a parametric test. In fact, if one would threshold according to a different
rationale (e.g., by asking your girlfriend which number she likes most ;-),
then clusterrandanalysis would still control the false alarm rate.

Anyhow, I think this discussion is too long for the small problem you have
(at least, if I understand you correctly):
1. I think you want to test whether the baseline-normalized powers A and B
are different. Performing this test with clusterrandanalysis is
2. You say that you want to test whether (A-B)/B is different from zero. As
Robert points out, this is equivalent to the hypothesis that A and B are
equal. This brings us back to 1.
3. At the end of his last email, Robert mentions something about the
parametric rationale of the thresholding that is performed in
clusterrandanalysis. This remark is given under the assumption that you
really want to perform calculations on (A-B)/B, because then
clusterrandanalysis (in its current implementation) cannot help you.
However, because your question is whether A and B are different (at least,
that's how I see it), you should not worry about this.


Eric Maris

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