# Check if a difference between paired means within two populations is constant

I have a data from two experiments E1 and E2. Samples in both of them were divided into paired groups so the first group G1 in E1 has a mirror group G1' in E2, both the same size and sharing same conditions, etc.

Question: Does anyone know of a statistical test which would tell me if the difference between means in paired groups is constant through the whole experiment?

I.e. if mean(G1)-mean(G1') = mean(G2)-mean(G2') = ... = mean(GN)-mean(GN')?

Please notice that experiments outcomes in groups are binary (0 or 1) and both experiments are independent.

# | E1 | E2
------------
1 | G1 | G1'
2 | G2 | G2'
3 | G3 | G3'
...
N | GN | GN'