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!