Is This the Right Way to Determine Statistical Significance in Fourier Spectra?

[rnielsen25]

Hi everyone.

What you see here is er Fourier spectra.
If i want to conclude that there is a statistical significance difference between the peak value around 30 hz, and all the other smaller peaks.

Should i do as following.
Estimate the mean value as 2. Estimate the mean peak value to around 3. And last estimate the mean lowest peak value as 1.

Then calculate the standard deriviation to 1,225.

And after that, i could calculate 5 times sigma to 6,124.

And because the peak value is around 13, and therefore is bigger than 6,124. I can conclude with 99,97% certainty, that there is a significance difference between the peak value and the other peak values.

Is it right, what I'm doing here?

 

[DrDu]

This depends on your hypothesis: Did you look specifically for a peak at 30 Hz or do you want to estimate the significance of observing a signal of this intensity at any frequency?
Also, your signals don't seem to follow a normal distribution. Do you know how your intensities should be distributed given the null hypothesis?

 

[haruspex]

This depends on your hypothesis: Did you look specifically for a peak at 30 Hz or do you want to estimate the significance of observing a signal of this intensity at any frequency?

@Nicklas , to elaborate on DrDu's point, suppose you had millions of datapoints similar to the general background in your sample. It might not then be surprising that some value somewhere exceeds many sigma. So if this is data mining you should consider the probability that the peak in the whole data would be this high by chance.