This question is rather mathematic, and I am quite sure some theory should already exist but I can not find it...
Say I have some data records, and for a certain record X two independent statistical tests give two different probabilities of X being something (for example an outlier).
Lets say these probabilities are
0.87. Since each test is independent and also calculated using a different part of X, I would like to see a combination method that would make the final outcome actually higher than
Since each test gives a very high probability, the overall probability should be even higher in my opinion (they strengthen each other). Is there some standard way to combine these probabilities?
Perhaps (something that comes to mind to me now) is this the same as Fishers Method (for p-values)?
Please let me know if I am not clear.