Astrophysics (index)

Sigma

(σ)
(indication of the confidence level of an experiment)

Sigma (σ) is a Greek letter used in science to indicate the confidence level of a measurement, e.g., of an experiment or observation. Specifically, it indicates a count of Standard Deviations, specifically, comparing to a large number of such measurements with random errors, how many standard deviations away from the mean of the measurement results, the actual result falls. If the measurement seems to be one that would very rarely happen due to the measurement errors expected, thus has a high sigma, then it looks like it wasn't a fluke. Calculation of the sigma makes an assumption about the errors that will occur in the measurements, that they form a Normal Distribution, what would be expected if the error is made up of many small possible errors.

An experimental result is often quoted as being sigma 4 or sigma 6, or alternately σ=4 or σ=6. In some branches of science, a discovery is not claimed until a σ=6 confidence level is achieved. Even with that, σ=2 is still useful as a hint that you may be on to something. In many cases, getting more results measurements by repeating the tests would raise the sigma if the result is in fact real, assuming there is no flaw in the measurement resulting in the measurement being wrong in consistent manner, i.e., Systematic Error.

Some sigma values expressed as percentage confidence level, i.e., that the measurement wasn't a fluke:

Sigmapercent confidencesame, if clearly to a specific side of the mean
168.2689492137086%84.1344746068543%
295.4499736103642%97.7249868051821%
399.7300203936740%99.865010196837%
499.9936657516334%99.9968328758167%
599.9999426696856%99.9999713348428%
699.9999998026825%99.9999999013413%
799.9999999997440%99.999999999872%

(science,statistics,measure,measurement)
http://en.wikipedia.org/wiki/Standard_deviation
https://thecuriousastronomer.wordpress.com/2014/06/26/what-does-a-1-sigma-3-sigma-or-5-sigma-detection-mean/

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