David,

Thanks for your reply--I appreciate your thoughts. I will look at prop.test.

The reason I chose fisher.test over chisq.test is that fisher.test is more
appropriate when observed counts are not numerous--empty cells and cells
with counts < 5 are less a problem. 

Expected values are needed to test a null hypothesis against observed
counts, but if total observed counts are 20 for 3 categories, then a null
hypothesis of a random effect would use expected values = 6.67 in each of
the 3 categories (20/3). 

Yes, fisher.test is for count data and so is chisq.test, but chisq.test
allows 6.67 to be input as expected values in each of 3 categories, while
fisher.test does not seem to allow this? 

I don't think it is inherent in Fisher's exact test itself that expected
values must be integers, but not sure.





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