# Chi Square and Fisher’s exact test with Monte Carlo

SPSS can’t calculate Exact test for 4x7 table of my data so I did it with Monte Carlo. The output is given below. Considering the rules of Chi-square, I should use Fisher’s $$p$$-value for the result of my data.

My question is: can I use fisher’s $$p$$-value with Monte Carlo simulations if I consider the rules?

• You can use Fisher's $p$-value. However, it seems that your sample has a small frequency in some cases (cells), so you should proceed with care. – Ertxiem - reinstate Monica Mar 28 '19 at 10:46
• Can you please clarify which assumptions are you considering? – Ertxiem - reinstate Monica Mar 28 '19 at 10:48
• Expected count must be lower than 20% but if this is not ensure,the minimum expected count can be considered that if it is lower than 5 fisher, between 5-25 continuity correction and higher than 25 pearson should be used – v.yildirim Mar 28 '19 at 11:08
• Please edit that information into your question. That's not an assumption of chi-square -- that's a version of some rules of thumb that are sometimes used to decide when the chi-squared distribution will be an adequate approximation to the distribution of the chi-squared test statistic (though it looks like some of the original conditions have been lost somewhere along the way). .If you're simulating, you're not using a chi-square approximation, so the chi-square statistic could be used even with low expected frequencies. .... ctd – Glen_b Mar 29 '19 at 14:48
• ctd... on the other hand if you're using the Fisher test (simulated or not) it's not clear why you're worried about expected frequencies at all. Power might be a consideration but the distribution of the test statistic would seem to be a nonissue. – Glen_b Mar 29 '19 at 14:49