I'm currently facing the following situation. We have run a marketing campaign providing to some members one of two type of coupones. In addition to this, some of these members were already contacted in the previous one by another campaign.

So I have the following dataset, where:

-mixpre3M= is a flag variable telling us if the customer had already purchased somethign in the past

• bono recibido: is the kind of coupon recived by the customer. The type "3euros" is the coupon identifying the customers already touched in the past by a campaign. the type "benchmark" identify the customer who haven't received any coupon (control group)

• tran_during: is the N of redeemers or purchasers

• enviados: is the number of people included in each group

mixpre3M bono_recibido TRAN_DURING_CAMP_FLG enviados

  0     benchmark                 5948                 33336
  1     benchmark                  557                 2102
  0    BONO3EUROS                   96                 1233
  1    BONO3EUROS                   17                 83
  0    BONO6EUROS                 4823                 25434
  1    BONO6EUROS                  626                 1793

What I want achive is if there is a redemption or purchasing rate significatively different between each group, and see between which group there is difference

Now, I have the following doubts:

a. I understand I should run a multiple comparison test, like maybe a GLM with binominal distribution, but I'm not sure it is a correct procedure, considering that some of the groups (for instance the fourth one, with n=83) are quite smaller than the main other groups. Is the model I choose the correct one for this kind of analysis, and I should exclude the smaller groups?

b. I understand this is a kinda similar to a multiple A/B test. Does anyone know any tutorial or material which could help with the topic? Never managed this kind of test before

Many thanks for the help Bests