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In experimental sciences you often hear of "5 sigma" detections/confirmations, where 5 is of course just an example. What does that mean?

Suppose a theory predicts a certain quantity to have exact value 1, and my measurement results in this value to be 1.1 ± 0.2, where the ± 0.2 are 1 sigma Gaussian error estimates. Obviously my measurement is compatible within 1 sigma with the theory. But is it even better than 1 sigma, and if so, how do I determine at how much sigma I have a confirmation precisely?

What I understand is this:

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But I don't understand how to get from there to the answer of my question. Thanks for help!

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1 Answer 1

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This question has likely already been asked and answered on this site, but briefly, the five-sigma rule is used as part of null hypothesis significance testing. This is a complicated, well-documented topic, but the basic idea is that rather than testing if the data is consistent with your theory, you test whether the data is sufficiently inconsistent with a different theory, called the null hypothesis (for example, that the value of interest should be $0$).

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  • $\begingroup$ thanks for the answer! However the description here on Wikipedia is both, extremely general and descriptive, and I cannot follow it. There should be a simple way to work this out for a normal distribution example as I have above. $\endgroup$
    – Britzel
    Dec 1, 2020 at 10:49
  • $\begingroup$ There are hundreds of very good explanations of null hypothesis significance testing online, including about a dozen on this site, so it doesn't make sense to repeat that information here. $\endgroup$
    – Eoin
    Dec 1, 2020 at 11:27
  • $\begingroup$ Would it make sense to forward me to a link? I am also primarily interested in a demonstration on this simple example, not in "the null hypothesis" as such. The Wiki article you linked doesn't help me with my problem. I did read it. $\endgroup$
    – Britzel
    Dec 1, 2020 at 12:32
  • $\begingroup$ @Britzel the description on Wikipedia is very general, but so is your question. You state that you cannot follow it, but it is unclear what you cannot follow. There are dozens of links on this website alone about five sigma or about six sigma, read some of them to be better able to state what you cannot follow and improve your question. $\endgroup$ Oct 24, 2022 at 10:16

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