So I have two groups of products with different sizes and each group has a different group of products in it. I created these groups by ensuring that the difference between these two groups’ cumulative revenues over the last year is as small as possible. I created these groups to use them in A/B test. So I have data of
- Cumulative revenues of each group over the last one year (but I can also calculate cumulative weekly/monthly/daily revenues of each group over the last one year).
- Yearly individual revenue of each product in each group (again I can calculate weekly/monthly/daily individual revenue of each product in each group).
Now I am looking for such a statistical test that proves or disproves that whichever time period I compare the ratio of these two groups’ total revenues, it falls into some neighbourhood of the current ratio of total revenue of two groups. So that whenever I use these groups in my A/B test I can make it (almost) sure that an increase in ratio beyond my accepted neighbourhood is due to the change of the variable that I want to test its effect.
What might be some feasible ways to do that?