Hi Dario,
I’m just starting our myself but, here is my noob answer to your question.
Proceed as if this was a simple t-test or better yet its bayesian alternative.
Except that when you are coding you model for estimating differences in means each one of your random variables will have shape parameter with len(days_of_month) in it. This change will change each variable into a vector of variables so that you end up testing for differences on each day individually.
But you might also want to compare this approach to most basic difference in means test using bayes factors, the great thing about bayesian statistics it that MC will determine if the extra parameters(days of the month) are actually adding any value.
There are few way to improve my proposition if results seem odd one way would be use hierarchical model which are really easy to make in bayesian framework/pymc3.
I’m curious to hear propositions from more experienced users.