# Fisher exact test (9x2) vs pearson chi-square (SPSS)

I am doing one analysis where I have 9 different conditions and only two options as outcome. I have done a pearson chi-square test, and in some of the cases I violated the assumption that expected counts should be greater then 5. What should I do? In the same test I had asked for the Fisher exact test p-value, can I use this p-value to all the cases or should I run another analysis only with those that violated the assumption of the expected counts?

• I get that you are doing one analysis on the contingency table. What do you mean by saying that "in some cases" the condition is violated? You can always use Fisher if it's computationally feasible. Jan 3, 2015 at 21:01
• "expected values > 5" is not an assumption. It's a rule of thumb - for many purposes, substantially too strong - that's used to try to make sure that the asymptotic chi-square approximation to the distribution of the test statistic under the null is reasonable. There are much more nuanced rules of thumb that have been developed over the last 50 years or so, but in general I like to use simulation to try to get a handle on how bad it might be. R can also do simulation of the null distribution of the chi-square under the assumption of fixed margins (as with Fisher), giving a simulated p-value. Jan 4, 2015 at 3:07
• @Glen_b Glad you pointed out that expected >5 is not an assumption and that fixed marginals are assumed for the exact test. The exact test has the best name (what can be better than an "exact test"?) but, as you suggest, is way too conservative in practice. The number of results deemed not significant because a test with very low power was conducted must be astronomical. Feb 22, 2017 at 3:24

## 1 Answer

I would simply use the Fisher exact p-value for in call cases. You already have the values. This is a well accepted test that will be reliable in all cases. Unless the counts are small, Fisher's exact test and Pearson chi-square will give similar results anyway.

I work in the biomedical genomic research and one hardly never sees a Pearson chi-square test in that literature. Fisher's exact test is standard.