# Test if P(A) and P(A|b) are statistically different

I am using Apriori to find association rules, where each instance is a vector of True/False value, indicating whether an item is bought or not. Suppose that we obtain a rule b=>a with confidence c, which means that P(a|b)=c. Then, we can compute the lift of the rule by P(a|b)/P(a).

Let P(A) denote the distribution where P(A=True)=P(a), and P(A=False)=1-P(a). I think if P(A|b) and P(A) are not statistically different, we might not say there is a real lift. It happens because my data set is small. So I want to run a significance test between P(A) and P(A|b). As we can see, the data for P(A) is from the entire data set, and P(A|b) is from the subset of data for P(A).

I am wondering which test I should use. I used Welch's t-test, but I am not sure if it is ok for me, and whether I should use other tests instead. Thank you for your advice!

• Your notation is not very clear and this may lead to confusion. Could you explain what exactly do the symbols mean? – Tim May 13 at 9:11