# Is Fisher's exact test appropriate if one cell is much larger than the rest?

Say I have 2 * 2 contingency table where one of the cells is substantially larger than all the other cells, like this:

   P1  P2
C1 6   11
C2 81  12201


Is it appropriate to use Fisher's exact test here and can you point me to a reference defending that choice? If not, what would be a better test for significance?

## 1 Answer

Yes, you could use Fisher's exact test here (why not?). You could also use a z test of proportions in each of "P1" and "P2".

It would be difficult to provide a specific reference. The better question may be "can you point me to a reference that says it is wrong to use Fisher's exact test here"?

• Thanks for your response. So yes, if anyone could identify a reference indicating it is not appropriate here that would also be really useful. I'm being challenged that the test isn't appropriate because that value in c2/p2 is so large in comparison to the other values. I can't see why this should be a problem, but I also don't know how to back up my position..
– Ben
Sep 12, 2011 at 18:44
• Can the other person back up their position? Sep 12, 2011 at 19:04
• Not really, its from a peer review and they didn't cite a source. In the paper we are trying to prove an effect where, in one case we get contingency table 0, 3, 87, 12209 but if we add a new quality to our system it goes to the 6, 11, 81, 12201 example I posted. In the first case, you get p = 1 while in the latter you get p = 1.22E-09 so the new quality appears to have a significant impact on the result. The reviewer mentioned an odds ratio test as an alternative - would that make any more sense?
– Ben
Sep 12, 2011 at 19:30
• @Ben Be careful: you are trying to infer something from changes in the p-value in a way that appears to be completely inappropriate. Try to post your real goal! Sep 12, 2011 at 20:48
• @Ben I suggest you post this as a separate question to get it the attention it deserves. In short you will have to look at the samples that are classified differently by the two methods. Perhaps McNemar's test, but it depends on the specifics. Sep 13, 2011 at 15:31