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Ask Dr. SETI ®

Chapter 1: Astrophysics

Levels of Significance

Dear Dr. SETI:
I am a Project Argus participant who recently detected an interesting candidate signal. I sent the spectrogram to an astrophysicist. He asked, "Is there a 'sigma' level of significance on that spike?"

Unfortunately, I don't know what he means. Can you help me?
Peter, Canada

The Doctor Responds:
I certainly can, Peter.

As you know, what your radio telescope receives, most of the time, is noise (Karl Jansky, arguably the world's first radio astronomer, called it 'Cosmic Static'). The noise level coming out of your receiver is not constant. Rather, it varies up and down around an average level (the mean), by an amount determined by the variability of the noise (its standard deviation). Sigma is statistical terminology for the number of standard deviations away from the mean a given observation is.

When we do statistical analysis of signals, we typically measure the variability of the background noise, calculate how much signal strength one standard deviation (one sigma) would be, and then determine by exactly how many times that amount the signal exceeds the noise. This is the signal's significance: the more sigmas, the more credible the signal.

For example, if the receiver had a fixed noise level that varied plus or minus 3 dB 98% of the time, we would calculate that one standard deviation (one sigma) of change would be about one dB. Now, if a signal were 10 dB out of the noise, with one sigma being 1 dB, we could say that the signal was ten sigma above the noise.

For your information, the famous Ohio State University "Wow!" signal of 15 August 1977 was about 30 sigma -- a really strong signal! The probability that a 30-sigma event could occur at random is pretty close to zero. For our purposes, a signal that is six standard deviations above the background noise (that is, a six-sigma event) is generally considered to be credible, non-random, and worthy of further analysis.

Why six sigma? It's admittedly arbitrary, but if we set our decision rule too low (say, three sigma), we run the risk of having too many false positives. That is, every noise spike that comes along gets tagged as a real signal, and we spend all our time and resources chasing ghosts. On the other hand, if we set the decision rule too high (say, twenty sigma), we run the risk of throwing out the baby with the bath water, have an unacceptably high incidence of false negatives, and may thus miss ETI's call altogether.

Unfortunately, since most of us doing amateur SETI have not done statistical analysis on the receiver noise, we are generally not equipped to quantify the statistical significance of a detection, in terms of how many sigma a given event may have reached. It's much easier for us to calculate how many dB out or the noise a signal is than by how many sigma it exceeds the noise. That is why we test significance of our signals in other ways, such as by striving for multiple, independent confirmations by distant stations.

Of course, those of our members who have the ability to do statistical analysis of receiver noise are encouraged to do so. That would give us just one more analytical tool for testing the significance of a detection.

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