There are two Gaussian distributions in which I can extract the mean and σ.

I want to know its severity (~ statistical significance), which is usually defined as

S = | m1 – m2 | / σ12

here I found several definitions of σ that refer to textbooks and papers.

- propagation: $ sigma_ {12} = sqrt {( sigma_1 ^ 2 + sigma_2 ^ 2)} $
- expected value: $ sigma_ {12} = sqrt { frac {1} {2} ( sigma_1 ^ 2 + sigma_2 ^ 2)} $
- simple average: $ sigma_ {12} = frac {1} {2} ( sigma_1 + sigma_2) $

what is statistically correct ??

3. is statistically probably not correct. If anyone knows what's right, please tell me …

Kind regards