[Eeglablist] Understanding mean power calculations

[John Johnson]

Perhaps someone can help me understand. I occasionally run across 
[code](https://sccn.ucsd.edu/wiki/Makoto%27s_useful_EEGLAB_code) that 
takes the mean of decibel values, or the mean of power values, and 
treats them as being equivalent. It seems that using the mean of decibel 
values is not correct, since decibels are logarithmic values (i.e. the 
exponents of a base number, 10 in this case). For example:

Mean power
(10+100)/2 = 55

Mean of log values (i.e. dB)
n.b. 10 is 10^1, 100 is 10^2

(1+2)/2 = 1.5, 10^1.5 = 31.6

Using code modeled from the website linked above:

% meanPowerDb(channelIdx) = mean(psdOutDb(channelIdx, 
lowerFreqIdx:higherFreqIdx));
% meanPowerMicroV(channelIdx) = mean(10.^((psdOutDb(channelIdx, 
lowerFreqIdx:higherFreqIdx))/10), 2);

dBs = [1, 3, 2, 4, 5, 1];

meandB = mean(dBs) 				<< 2.6667

meanPower = mean(10.^(dBs/10))	<< 1.962

10.^(meandB/10) 				<< 1.848

So we can see that the mean of the dB values is artificially inflated. 
(10+100)/2 ≠ 10^((1+2)/2).

Given the above, what is the correct way to find the mean power of a 
montage of electrodes?

Thanks,
John

John T. Johnson
PhD Candidate - Cognitive Motor Control Laboratory
Lab TA NEURO 4001 Neuroscience Capstone
School of Biological Sciences
Georgia Institute of Technology
john.johnson at gatech.edu
he/him/his