Multiple proportion test with glm

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Multiple proportion test with glm

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

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

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