I am not too familiar with power analysis techniques. Is my understanding correct that the power analyses typically reported in EEG research papers is the power AVERAGED across a segment of the waveform/EEG data?
You can do power analysis by averaging over some segment of the waveform using an FFT. This will give you power for whatever frequency bins you choose. However, it is generally considered better to analyze the power using something like wavelet analysis which lets you look at power and still keep the time axis. Using wavelets you end up with a plot where the Y-axis is frequency, X-axis is time, and Z-axis is power. I have used EEGLab in the past to do this type of analysis. It's available free. They have excellent documentation and a very good online community for support. Good luck.
I am studying alpha peak frequency and alpha power. I have been using wavelet to identify the alpha peak across various conditions and areas of interest. I'm however unsure about how the amplitude/ power can be measured. For instance, is it statistically correct for me to identify the alpha peak, determine the alpha range ( + 2 and - 2 frequency from the peak frequency ) and then get the average power within this frequency band to determine its power? This information may then be used for neurofeedback techniques.