large cell counts - Fisher's Exact vs. chi2

#1
Hi everyone,
I read a while back that chi2 was most accurate for observed cell counts of only between 5-70, but now I can't find that reference. I'm wondering if anyone can point me in the right direction. I have samples of 450-650 and have used Fisher's Exact as a result of having observed cell counts over 70. I'm looking to justify this approach with a source. Any help would be appreciated.
Thanks!
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
You should always use Fisher's test, given that it will run in a timely fashion. It has factorials and big numbers in it, so it can take awhile some times when you have large counts.
 
#3
There is a lot of received wisdom around non-parametric tests, particularly those relating to 2x2 contingency tables with the unquestioned assumption being that unless the expected cell count is <5, one must use chi2. Unfortunately, I'm stuck in such a position of needing to prove chi2 is not the best test. Do you have a source regarding Exact tests always being better than estimated p? Thanks!