Different p-values for Chi squared and Fisher's Exact R I'm trying to find whether there's a correlation between two variables using Chi Square test and Fisher's Exact test. I get two different p values when I run Chi Square test and Fisher's Exact test. Which value should I take? Take Chi squared p value and do not reject H0 or take Fisher's Exact p value ad reject H0?
I ran Fisher's Exact test as well because I get the following error msg when I run Chi Squared test.
Contingency table

> chisq.test(ebtable6)

    Pearson's Chi-squared test

data:  ebtable6
X-squared = 7.3866, df = 2, p-value = 0.02489

Warning message:
In chisq.test(ebtable6) : Chi-squared approximation may be incorrect

> fisher.test(ebtable6)

    Fisher's Exact Test for Count Data

data:  ebtable6
p-value = 0.05018
alternative hypothesis: two.sided

 A: You should not run two different tests. Choose your test first, before you run any tests and preferably before you examine your data values (though it would be permissible to consider the marginal totals).
By looking at both p-values before you decide which to use, you are (quite rightly) open to charges of p-hacking. 
Since you're prepared to condition on the margins (you did an exact test after all), you could consider using simulated p-values to deal with the low expected in the (1,1) cell... I just did a million such simulations in R, it only takes a couple of seconds (the chisq.test default of 2000 is a bit small)
(However, you'll still have looked at the p-values... so that issue won't go away)
A: This is not surprising since the tests have different statistical bases. The Fisher Exact test is a randomization test computed assuming both the row and column marginals are fixed (which they very rarely are) and is very conservative when they are not. The Chi Squared test is an approximation but works well in practice, even with sample sizes much smaller than yours. The warning message doesn't make sense since it is a given that an approximation is not exact so it's unclear what is meant by "incorrect." You have expected frequencies less than 5 that some might say is a problem, but simulation studies indicate it is not in most cases. In short, your marginals are not fixed so I recommend you go with the Chi Squared Test.
