# Activation vs. baseline

Pascal Fries pascal.fries at FCDONDERS.RU.NL
Mon Feb 27 17:57:10 CET 2006

```Hi Tom,

> Pascal Fries wrote:
> > OK. I had been asking, because coherence (and also power)
> have a bias
> > that is sample size dependent. For those measures, particularly for
> > coherence, I would suggest to use equal sample sizes.
>
> Correct me if I am wrong, but this bias is due to the slow
> convergence of the covariance; with more samples, the
> covariance converges more (assuming it converges at all).
> Furthermore it probably converges 'up', so if you have more
> samples, you'll see (apparently) more power.

I still haven't fully understood the sample size bias of power.
For coherence, the issue is simple to understand. As you write, it has to do
with the slow convergence towards the true value as the sample increases.
But in the coherence case, values will converge "down" towards the true
value, not 'up'. For one trial, coherence is numerically always one and will
then decrease as you add more trials. In the case of a true coherence of
one, it will not decrease and in the case of a true coherence zero, it will
rapidly decrease.

This is one of the most important things on the agenda for the basic
spectral analysis in FieldTrip: To get a good estimate of the coherence bias
and subtract it. Until this is finalized, the safest approach is to trim
datasets before comparison to equal size.

> I have sometimes dealt with this problem in the past by
> simply z-scoring the volumes afterwards, thus shifting the
> means back to zero.  But perhaps there are skewness issues as
> well?  I've mostly done that when playing around with things
> like overlapping windows; for example, using an active window
> of 0 to 300 ms and a control window of 0 to 250 ms, you
> expect a slightly higher power in the active state because of
> the increase convergence, but then normalizing that spatially
> can give you an estimate of active areas for that 250-300 ms
> window.  There may also be problematic beamformer overlap in
> this case, though, but that can be dealt with too.  Just a thought.

I agree: If sample sizes are not orders of magnitude different, then a
z-transformation can take care of most of the bias.

Best, Pascal

```

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