# calculating frequency interaction (now with the complete message)

Thomas Thesen tnt at PHYSIOL.OX.AC.UK
Mon Aug 15 23:41:55 CEST 2005

```Hi Rob,

Thanks for the simulation. That really helped to make the issue clear!

If others are interested to see how the phase relationship between two
signals relates to the linearity or non-linearity of the summed power or
amplitudes can have a look at these figures that were derived from Robs code
below:
http://www.physiol.ox.ac.uk/~tnt/fieldtrip/

FT_phase1.jpg
FT_phase2.jpg

One example shows perfect phase and one anti-phase.

The bottom graph shows the phase relationship of the signals for condition A
and V, and their sum A+V. In the code that's s1 to s3.
The top graphs show the values for amplitude (ampl1 to ampl3) and power
(pow1 to pow3). Diff is the subtraction of pow3-pow2-pow1 (or the same foe
amp). If diff is zero the summation is linear.

interaction are very insightful. Thank you. Considering that MEG/EEG data
contain a lot from both of these options it seems unwise to do this type of
testing. One couldn't tell wether a different phase relationship or a true
effect might be responsible for non-linear summation. Or am I wrong there?

I just saw at a conference a poster where they tried the same thing using
bootstrapping. The web link above contains a copy of that poster
using FieldTrip?

Thanks a lot,

Thomas

On Mon, 15 Aug 2005 09:55:20 +0200, Robert Oostenveld
<r.oostenveld at FCDONDERS.RU.NL> wrote:

>Hi Thomas,
>
>On 14-aug-2005, at 17:05, Thomas Thesen wrote:
>
>
>> Calculating the interaction as above could then result in erroneous
>> estimates of the integration effect:
>>
>> A = 3 units; squared = 9
>> V = 3 units; squared = 9
>> AV = 6 units; squared = 36
>>
>> integration effect = 6^2-(3^2+3^2) = 18
>>
>> even though it is quite evident that the neuronal response to AV is
>> a direct
>> summation of A and V.
>>
>
>The effect of summation of the two signals on the estimated power (or
>amplitude) of their sum depends on the phase relation between the two
>signals.
>1) If the two signals are in perfect phase alignment in each trial
>(i.e. zero deg phase difference), they will add up as you described.
>2) If they are in perfect antiphase (180 deg), they will cancel out.
>3) If they have a random phase with respect to each other, i.e. the
>phase difference is different in each trial, they will add up "a
>little".
>In case 1, the amplitude (i.e. sqrt of the power) depends linearly on
>the amplitude of the two signals. In case 3, the power depends
>linearly on the power of the two signals.
>
>Please try playing with the following lines of code
>
>real_pow1 = 3;
>real_pow2 = 3;
>t = linspace(0, 2*pi, 1000);
>
>for trl=1:100
>   s1(trl,:) = sqrt(real_pow1)*sqrt(2)*sin(t);
>   phasediff = 2*pi*rand(size(t));     % CHANGE THIS TO SEE THE EFFECT
>   s2(trl,:) = sqrt(real_pow2)*sqrt(2)*sin(t + phasediff);
>end
>
>% add the two signals for each trial
>s3 = s1+s2;
>
>% estimate the single trial power
>pow_s1 = sum(s1.^2,2)/length(t);
>pow_s2 = sum(s2.^2,2)/length(t);
>pow_s3 = sum(s3.^2,2)/length(t);
>
>% estimate the power and amplitude
>pow1  = sum(pow_s1)./100
>pow2  = sum(pow_s2)./100
>pow3  = sum(pow_s3)./100
>
>ampl1 = sqrt(pow1)
>ampl2 = sqrt(pow2)
>ampl3 = sqrt(pow3)
>
>I hope that this clarifies it. Of course, it does not yet help you
>deciding how to test for the interaction, since the additive effect
>(which you expect under the null hypothesis) can be either on
>amplitude or on power. To choose the right test, you will have to
>consider the sources of the two signals that are being mixed on the
>channel level, i.e. are they coming from one source, or from two
>sources, and in the latter case, are the two sources strongly
>coherent or not?
>
>best regards,
>Robert
>
>
>=======================================================
>Robert Oostenveld, PhD
>F.C. Donders Centre for Cognitive Neuroimaging