I used across combined files/epochs option for selected files when computing ImCoh, however, the result is quite different with the Average all files option. Is my understanding of the average method wrong?
Average all files:
The result is different as these approaches are not the same:
https://neuroimage.usc.edu/brainstorm/Tutorials/Connectivity#Coherence
These are the equations to compute imaginary coherence, between two signals (x and y):
where with C_{xy} being coherency or complex coherence, IC_{xy} imaginary coherence, S_{xy}(f) the estimated cross-spectrum, and S_{xx}(f) and S_{yy}(f) the estimated power spectral densities of x and y.
When you use the across combined files/epochs option, all the windows from all the trials are used to estimate S_{xy}(f), S_{xy}(f) and S_{xy}(f) , then non-linear operations are carried out to obtain IC_{xy}, because of these non-linear operations, average IC across files is not the same IC compute using all files.
