Fisher's exact test is applied when sample size is small. In this link it is said that
If any expected counts are less than 5, then some other test should be used (e.g., Fisher exact test for 2×2 contingency tables)
This link http://www.theanalysisfactor.com/observed-values-less-than-5-in-a-chi-square-test-no-biggie/ also gave similar statement.
But here http://www.biostathandbook.com/fishers.html author recommended to use Fisher's exact test when the total sample size is less than 1000.
Can I use a Fisher's exact test whatever the sample size is?
Edit:
I know Fisher's exact test is conservative and many authors recommend not to use this conditional test rather an unconditional test should be used (Reference: Recommended tests for association in 2×2 tables) .
Then my question is more precisely that when should I do an exact test instead of chi-square test?
Best Answer
When the chi-squared test is inappropriate due to small sample sizes or highly unequal cell distribution, one can instead use Fisher’s exact test.The chi-squared test is basically an approximation of the results from the exact test, so erroneous results could potentially be obtained from the few observations.