# Gaussian error distribution: What does it mean to have a 5 sigma detection / confirmation of the expectation?

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:

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

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 $$0$$).