Statistics – Separation performance (statistical significance) of two Gaussian distributions


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.

  1. propagation: $ sigma_ {12} = sqrt {( sigma_1 ^ 2 + sigma_2 ^ 2)} $
  2. expected value: $ sigma_ {12} = sqrt { frac {1} {2} ( sigma_1 ^ 2 + sigma_2 ^ 2)} $
  3. 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