I was recently asked this question about Chi-square tests. This question comes up a lot, so I thought I’d share my answer.
I have to compare two sets of categorical data in a 2×4 table. I cannot run the chi-square test because most of the cells contain values less than five and a couple of them contain values of 0. Is there any other test that I could use that overcomes the limitations of chi-square?
And here is my answer:
1. The assumption of the Chi-square test is not that the observed value in each cell is greater than 5. It is that the expected value in each cell is greater than 5. (The expected value for each cell is row total*column total/overall total). Often when the observed values are low, the totals are too, so they overlap a lot, but not always.
2. If you still find that your expected values are too low, use a Fisher’s Exact test. Not all standard statistical software will do one for a 2×4 table, but it can be done. StatXAct will do it. Great software if you can get access to it.
(If you’re wondering, SPSS will only do a Fisher’s Exact for a 2×2 table).