I'm new here. I am planning a neuroscience experiment. I will be measuring brain signals from about twenty subjects. I will present the subjects four different kinds of stimuli. After all the data processing, I will have four power spectrums for each participant (one per stimulus type). That is, I will see the magnitude (power) of each frequency (something like <a href="http://en.wikipedia.org/wiki/File:NormSPD.png">this</a> but calculated from the brain data). There is also a fifth stimulus type, which is rest (no stimulus; used as as control measure or "baseline" in neuroscience jargon).
 
From each of the power spectrums, I will pick two frequency bands and calculate the average power in each band. The first band is 8-12 Hz ("alpha" in neuroscience jargon) and the other 16-22 Hz ("beta" in neuroscience jargon). 

I am expecting to observe four phenomena:

- For stimulus type 1, alpha is larger than beta. Both are larger than baseline.
- For stimulus type 2, beta is larger than alpha. Both are larger than baseline.
- For stimulus type 3, alpha is larger than baseline activity. Beta is equal to baseline.
- For stimulus type 4, beta is larger than baseline activity. Alpha is equal to baseline.

How should I do my statistical tests? Is my experimental design sufficient?

I am asking this because our field appears to have some problems regarding the rigour of statistical analyses (see e.g. http://www.nature.com/neuro/journal/v14/n9/full/nn.2886.html).