I have three unordered categorical variables. I have made a 3x2x2 table, but I'm uncertain of how to test for independence. The usual manner is a chi-squared statistic, but I think this is inappropriate when the expected values of the cells are small. I have one cell that is 0, so this is an issue for me. In a 2x2 table, I think that the Fisher-Irwin exact test would work, but I can't find anything covering a table with three dimensions. Any ideas?