# Alternatives for chi-squared test for independence for tables more than 2 x 2

What are some alternatives to the chi-squared test for categorical variables with tables larger than 2 x 2 and cells with a count less than 5, if I don't want to merge classes?

• The Chi-Square-test can also be used with larger tables than 2x2. Could you explain why the Chi-Square-test should not be appropriate for your problem? Additionally, could you state the problem you're hoping to solve? Jun 28 '15 at 16:33
• I have a 2 x 3 contingency table, and cells with a count less than 5 Jun 28 '15 at 16:37
• Thanks, please edit your question and add this information as not everyone reads the comments. A usual rule of thumb regarding the Chi-Square-test is that its results can be inaccurate if the expected cell counts are lower than 5. Usually, a Fisher-Test is recommended in these cases. Barnard's test may also be an option. Jun 28 '15 at 16:52

There are some common misunderstandings here. The chi-squared test is perfectly fine to use with tables that are larger than $2\!\times\! 2$. In order for the actual distribution of the chi-squared test statistic to approximate the chi-squared distribution, the traditional recommendation is that all cells have expected values $\ge 5$. Two things must be noted here:
1. It does not matter what the observed cell counts are—they could well be $0$ with no problem—only the expected counts matter.
2. This traditional rule of thumb is now known to be too conservative. It can be fine to have $\le 20\%$ of the cells with expected counts $< 5$ as long as no expected counts are $<1$. See:
1. Your best bet is probably to simulate the sampling distribution of the test statistic, or to use a permutation test. In R, for example, you can simply set chisq.test(..., simulate.p.value=TRUE). Other software should also make this possible.