Is Fisher test appropriate for a small binomial distribution? The Chicago Bulls, a basketball team, have won 20 straight games when their game is televised nationally on TNT. Over the same period of time they have 206 wins and 184 losses when it is not. 
Is it appropriate to test the significance of these ratios using Fisher's Exact Test? 
Where: 
a = 20 (TNT Wins)
b = 206 (Non TNT Wins)
c = 0 (TNT Losses)
d = 184 (Non TNT Losses)

H0: The proportions of wins and losses are independent of them being televised on TNT.
H1: The proportions of wins and losses are not independent of the game being televised on TNT.

It seems pretty obvious that we'll reject H0 even before calculating P, which is why I want to confirm that my setup is correct.
 A: *

*Yes, the Fisher test doesn't have a particular problem caused by small expected counts (though your smallest expected count is over 9 anyway so it's not clear why that would be an issue anyway). Personally I'd have used a chi-squared test or perhaps a likelihood ratio test (if my objections listed below didn't apply)


*Yes, it's obviously not random (and so not really any need to formally test). That doesn't mean you did anything wrong. However, unless you have a fair bit of experience with such 2x2 tables you should be cautious judging by eye -- people tend to misjudge things if they haven't done many such tests before.


*If you're testing because when there was 20 straight wins someone said "hey, that's weird! what's the chances of that?" or "Wow, is that significant?" (i.e. you're testing a data-generated hypothesis) then your p-values are not meaningful. For tests to have their nominal level (and p-values to mean what they're supposed to mean) you need to choose the hypothesis before you know what the data are.
Very low p-values from data-generated hypotheses are a dime a dozen.
