# Statistical test to establish that event B is caused by event A

I want to have a statistical test to establish that event B is caused by event A

Here event B is customers that are supposed to leaved leave for competitor stay in our company event A is an attractive offer for some customers (some may leave, and some may stay)

If we know that some of our customers is going to go for the competitor, and we come up with an attractive offer for them to stay. If in the end, we notice that there were fewer customers that are leaving for competitors (event B), is there a statistical test that helps to establish a relationship that it is the attractive offer (event A) that retains those customers that will otherwise leave (event B)?

• Do you need to show causation, or is an association enough? Causation is (much) harder to show, both mathematically and philosophically.
– Dave
Sep 5, 2020 at 1:23
• @Dave for association, how do we show? Using correlation test or? Sep 5, 2020 at 1:24
• @Dave Yea, my original question is to show causation, if it is difficult to show, then association of what you mentioned is suffice too. Sep 5, 2020 at 1:26
• Interview question: If correlation doesn't imply causation, how do you detect causation? might be of interest for you Sep 5, 2020 at 6:16

## Proving Causation

One could argue that there is no statistical test that can establish causation. This can only be done by experimental design.

Causation by definition includes time ordering. Physics demands that the cause of an event must happen before the event. Thus you must create an experiment in which you control the cause and observe the effect.

You would then use statistical tests to support an argument that the effect is strongly associated with your cause.

Even that is not sufficient because you can't know, among all possibilities in the universe, that the effect you observed was really due to the cause. This is where the question becomes more philosophical.

If you have a very plausible mechanistic model that is repeatedly validated experimentally than you are on your way to establishing causation.