# Comparing to zero

Robert Oostenveld r.oostenveld at FCDONDERS.RU.NL
Mon Jun 27 17:07:00 CEST 2005

```On 27-jun-2005, at 9:57, Litvak Vladimir wrote:

> Dear Robert and Eric,
>
> Maybe I should explain what I really want to do and then you'll be
> able to suggest another solution for me.
>
> I want to compare power between two conditions A and B (dependent
> samples). I already tried comparing it the usual way but I want to
> also try comparing relative increase (A-B)/B.  This way I have only
> one dataset that needs to be compared to zero. If I apply the same
> transformation to B I'll get of course just an array of zeros and
> it doesn't seem right to me to compare it with the normalized A.

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?

I can think of situations where you do want to normalise the power
difference by the power itself, i.e. relative change. But in those
situations the normalisation is meant to remove variability between
subjects prior to averaging or computing variance over subjects,
which provides you with an alternative to the repeated measures test.
So, in that sense, it makes sense to do either repeated measures, or
normalise each subject towards a ratio, but not neccessary both.

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.

Robert

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