What is the best alternative for Fisher's Exact test for contigency tables that are NOT 2x2?

I am a newbie to data mining. I am trying to find associations between two categorical variables. Since more than 20% of my expected frequencies are less than 5, I wanted to use Fisher exact test but it turns out it is generally used for contingency tables 2x2 but my variables have more than two values. Would really appreciate recommendations on the best course of action for me now. Here are some options I found after some search:

  1. Use Freeman-Halton extension to Fisher's Exact test for more than 2x2 table.
  2. Merge multiple attributes values so that I end up with 2x2 contingency table and then use Fisher's Exact test.
  3. Merge multiple attributes values so that I end up with expected counts 5 and then use chi square test for independence.
  4. Use the Crammer V test.

I would like to know what is the standard practice in this case when your categorical variables with 2 possible values end up with less than 5 expected counts?

Thanks,

Topic chi-square-test correlation categorical-data

Category Data Science


Fisher's exact test has a ready generalization to tables of an arbitary dimension and it is applicable here (Metha and Pathel, 2012).

You can for example use the fisher.test built-in function to compute this in R.

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