# Fisher's exact test and chi-squared test when cell counts are big

Let's say I have a $2\times2$ table where all of the expected values are at least one, and no more than 20 percent of the counts are less than 5 (hence, Cochran's rules are not violated). In such a situation is there a difference between using the Fisher's exact test or the chi-squared test to determine independence or homogeneity?

 chisq.test(data.frame(x=c(20,26), y=c(14,40)))
fisher.test(data.frame(x=c(20,26), y=c(14,40)))


I get a p-value of 0.09 and 0.10 for the chi-squared test and Fisher's exact test respectively.

• With Fisher's test the multinomial distribution depends on the marginal totals. Summing (obs-exp)$^2$/exp does not lead to an asymptotic distribution that depends on the marginal totals. – Michael R. Chernick Nov 20 '17 at 20:04