# sourcestatistics: what to compare?

Robert Oostenveld r.oostenveld at FCDONDERS.RU.NL
Fri Jul 28 16:17:24 CEST 2006

```Hi Floris

On 28 Jul 2006, at 13:01, Floris de Lange wrote:
> I have a question about what conditions/comparisons make most sense
> to statistically compare with sourcestatistics.
> I have 2 conditions, A and B, and each condtion has its own pre-
> stimulus baseline: basA and basB.
>
> Now, first I'd like to see which regions are showing stronger beta-
> band power during A than the baseline. So I want to compare A to
> basA. There's 2 ways of going about it:
> 1) compare (the grand average of) A.avg.pow with basA.avg.pow
> 2) compare (the grand average of) the neural activity index (NAI)
> of A with the baseline
>
> Any ideas which would be best? Or is this just an empirical issue?
> (i.e., take the best)

Both are valid, you could take the best. There are some exceptions/
predictions though that I can share with you: the NAI is power
divided by estimated (projected) noise. It is inherently difficult to
estimate the noise level (the default is the smallest singular value
of the CSD matrix, but you can manipulate it with cfg.lambda in
sourceanalysis). If you have different numbers of trials in active
v.s. baseline, the noise estimate probably will be different. So then
you would have NAIa = Pa/Na and NAIb = Pb/Nb, if Pa==Pb and Na~=Nb,
these will be trivially different, which is not what you want
(remember Pa==Pb was assumed).

You can compare the projected noise in both conditions, the source-
noise-estimate is uniformely scaled (i.e. on all voxels the same)
with the estimated noise from the CSD. There is no reason to assume
that the noise is different, so if the noise is different, you would
have to explain that.

> To compare A and B, one has even more options:
> 1) compare A.avg.pow with B.avg.pow
> 2) compare (A.avg.pow/basA.avg.pow) with (B.avg.pow/basB.avg.pow)
> 3) compare NAI(A) with NAI(B)
> 4) compare NAI(A)/NAI(basA) with NAI(B)/NAI(basB)
>
> Is there's any principled reason for a priori picking any of the
> above choices?

I presume that by "compare" you mean "look at the the difference".

In general you should only use the NAI for plotting data if you only
have one condition (and no baseline). The noise estimate that goes
into the NAI is too poor to be of real value. Although sometines it
looks nice in figures, the NAI tends not to be very robust (it
contains global flucuations that mess up the statistic, although the
figure still looks nice).

The baseline is only interesting if you expect something differently
to happen in the two baselines. If that is the case, you better try
to get another baseline in your experimental design. If you would
combine actA, basA, actB, basB into a single number, and that number
would be significant, you still would not be able to tell whether the
difference is betwen the active conditions, theis baselines, or some
weird combination of the 4 "conditions" that you combine.

Typically there is no reason to assume taht the baselines are
different. So
(A.avg.pow/basA.avg.pow) with (B.avg.pow/basB.avg.pow)
= (A.avg.pow/basC.avg.pow) with (B.avg.pow/basC.avg.pow), where C
means common
= (A.avg.pow-B.avg.pow)/basC.avg.pow.
I.e. you are comparing A and B directly, with a spatially normalizing
for the different baseline-estimated noise at different source
locations.

Whether you want to spatially normalize (divide by some baseline
estimated-source-power) depends on the leadfields (it is neccessary
if cfg.normalize=no, if you want to do multiple comparison
correction, and if you want to look at an additive effect). If you
want to look at a multiplicative effect, you would look at the ratio
between two conditions instead of the difference. The ratio of the
conditions is best implemented with a log transform, after which you
again can look at the difference between the log-transformed power
estimates in both conditions (log(A/B) = log(A) - log(B)). In the
ratio or log-ratio between the powers in both conditions you have
also corrected for the spatial (depth) noise-bias.

good luck with the stats,
Robert

PS as I am on holiday the next 2 weeks, you could ask Ingrid about
more details on this. She is more or less at the same stage in her
analysis (about to do group sourcestatistics), but I suspect that she