Chi-squared vs Fisher's Exact Test w/ 5x6 contingency table & some cells <5?

Question

I don't have the minimum required data of 5 in each cell for a chi-squared test, but my contingency table is greater than 2x2, so I can't use a Fisher's exact. Would it help to use a chi-squared test set to either exact or Monte Carlo to prevent it from making the assumption of normal distribution?

I'm looking at trauma patterns created by five different tools; six categories of trauma have been defined. I would like to see whether the patterns of trauma (by occurrence of each type) differ significantly from one another. N=67, but not all tools have all types of trauma.

SAS can perform Fisher's Exact test for table bigger than 2x2. See here, option FISHER for details. Just remember it may take for very big table, it may take a long time. — Penguin_Knight, Aug 20 '12 at 14:34
See Given the power of computers these days, is there ever a reason to do a Chi-squared test rather than Fisher's exact test? — Andy W, Aug 20 '12 at 14:56
One thing to note is that the 'requirement' is expected frequencies <5, not raw counts. Also, what software are you using? — gung - Reinstate Monica, Aug 20 '12 at 15:12
@AndyW Even with fast computers Fisher's test can take an inordinately long time to compute a p-value for large contingency tables where the number of possible permutations get extremely large. SAS puts out a warning about the computing time required when this happens. — Michael R. Chernick, Aug 20 '12 at 15:30
if you have less than 5 expected frecuencies, you can try exact tests, an excellent software (of course r will do it too) is StatXact — AnastD, Aug 20 '12 at 15:31
@gung Although the rule of thumb deals with expected frequencies, the problem of sparse cells is also identified by the actual sparseness of the cells and so having raw numbers below 5 is a concern. — Michael R. Chernick, Aug 20 '12 at 15:32
@MichaelChernick, I was simply referring to the discussion on the linked question. I was not myself asking that question. It is certainly related to the OP's original question, which is only a 2X2 contingency table (which would seem to make the comment about computation time a bit moot, at least in this circumstance). — Andy W, Aug 20 '12 at 15:48
whoops I see the OP is saying contingency tables greater than 2X2. Regardless, the question I linked to has relevant discussion. — Andy W, Aug 20 '12 at 15:57
Closely related threads where answers are relevant and useful here: http://stats.stackexchange.com/questions/1805, http://stats.stackexchange.com/questions/14226 — whuber, Aug 20 '12 at 15:59
@whuber The second link is the same as Andy Ws. Both are very relevant to this discussion. — Michael R. Chernick, Aug 20 '12 at 16:28

score 3 · Accepted Answer · answered Aug 20 '12 at 14:16

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There is a form of Fisher's test that is applicable to general rxc contingency tables. Use it or other alternatives to chi square in situations like yours where the chi square approximation is likely to be poor.

answered Aug 20 '12 at 14:16

Michael R. Chernick

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Thanks for the responses! Most of my expected counts are under five, so I've used FET as suggested, using SPSS. – Kendra Aug 21 '12 at 19:39

Chi-squared vs Fisher's Exact Test w/ 5x6 contingency table & some cells <5?

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