Fisher’s Exact Test – Applying Fisher’s Exact Test to Contingency Tables Larger Than 2×2

contingency tablesfishers-exact-testspssstata

I was taught to only apply Fisher's Exact Test in contingency tables that were 2×2.

Questions:

  1. Did Fisher himself ever envision this test to be used in tables larger than 2×2 (I am aware of the tale of him devising the test while trying to guess whether an old woman could tell if milk was added to tea or tea was added to milk)

  2. Stata allows me to use Fisher's exact test to any contingency table. Is this valid?

  3. Is it preferable to use FET when expected cell counts in a contingency table are < 5?

Best Answer

The only problem with applying Fisher's exact test to tables larger than 2x2 is that the calculations become much more difficult to do. The 2x2 version is the only one which is even feasible by hand, and so I doubt that Fisher ever imagined the test in larger tables because the computations would have been beyond anything he would have envisaged.

Nevertheless, the test can be applied to any mxn table and some software including Stata and SPSS provide the facility. Even so, the calculation is often approximated using a Monte Carlo approach.

Yes, if the expected cell counts are small, it is better to use an exact test as the chi-squared test is no longer a good approximation in such cases.

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