Here is a table selected and grouped from table where i store information about client - if he churned(TRUE - he churned, FALSE he stayed) and how many refund he got. CNT counts number of rows per class.
I want calculate the probabilites, so let's prepare the numbers step by step. (I am inspired by this example)
I will convert the refund into discrete (refund is zero or greater than zero) variable and create a pivot table:
Then I calculate probabilities per class (certain cell divided by sum):
And then relative probabilities per class (I don't know the exact term - for example 0.36% is calculated as 6.03% * 6.02% from previous table):
So now I can calculate the probabilities:
X = Refund is 0; C = Client churned; not X = Refund > 0; not C = Client stayed;
What is the chance that client will leave if he has 0 refund?
Pr(C|X) = Pr(X|C)*Pr(C) / Pr(x) = 0.36%/(0.36%+88.27%)=0.41%
What is the chance that client will stay if he has 0 refund?
Pr(not C|X) = Pr(X|not C)*Pr(not C) / Pr(x) = 88.27%/(0.36%+88.27%)=99.59%
What is the chance that client will leave if he has >0 refund?
Pr(C|not X) = Pr(not X|C)*Pr(C) / Pr(not x) = 0.00%/(0.00%+0.03%)=2.36%
What is the chance that client will stay if he has >0 refund?
Pr(not C|not X) = Pr(not X|not C)*Pr(not C) / Pr(not x) =0.03%/(0.00%+0.03%)=97.64%
My question is - Can i assume anything if my data have one dominant class like this? Seems like the refund has no influence over churn. But I believe that it does have some effect.
If anyone verify the steps, it would be nice too.