So I have N=147 control time-series signals and N=134 treatment (THC) signals. I want to compare if there are any significant differences in frequency power in the two groups.
The top part of the figure below shows the median frequency power for each frequency of the two groups.
Thus for each frequency, I run a 2-sample t-test to get the mean difference and confidence bounds for each frequency. The mean difference (black line) and confidence bounds (grey shading) are shown in the bottom of the figure. Obviously, whenever the CB's dont cross 0, it is a significant difference.
Here is my issue:
The two groups have different overall power (where power=E(x(t)^2]). Thus if I ran the t-test on the naive data, it would show that the group with more power has higher power across all frequencies. To avoid this, I normalized each signal by its power, so that they all had a total power of 1. This revealed a significant difference from 5-10Hz, which is exactly what the theory predicts, but also showed a negative difference from 12-20 Hz. I suspect this is an artifact of the normalization method, since all the power must now be equal, and the control group had more power in the 5-10Hz range, it meant that the normalization lowered the power in the 12-20 Hz range to compensate, resulting in the observed significant difference.
So in conclusion, my questions are
- how can I avoid this artifact of normalization?
- Is there any theory/literature on the method I am using?
Thanks so much guys!
