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 Best Answer
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)