Our team does A/B testing rigorously. I am from reporting side and for the initial reporting for every A/B test, we have a adobe dashboard explaining the results with KPIs like impressions, clicks, CTR, lift and few down stream metrics for each version. Typically, we have 2-4 versions for very test - one control and 3 variants. I want to add statistical significance in each dashboard. I have calculated it using the below logic.
Imagine a test with only 2 recipes - 1 control and 1 variant
CTR 1 = clicks1/impressions1
CTR2 = clicks 2/impressions 2
Pooled CTR = (clicks 1+clicks 2)/(impressions 1+impressions 2)
Standard Error (SE) = Square root(Pooled CTR*(1-Pooled CTR)*((1/Imp1)+(1/Imp2)))
Z Score = abs(CTR1-CTR2)/SE
Standard significance = cdf-z function (Z score)
I create every calculated metric separately and finally calculate the standard significance. But this is not scalable. Because I have to create 7 calculated metrics for each test. So if a A/B test has 4 variants, I would be needing statistical significance to be calculated 3 times against the control (Which makes it 7*3=21 calculated metrics).
Is there any easy way to do this? Any efficient way of achieving this would be of great help. Thanks!