I am very aware that the Fisher's exact test can be used ahead of Chi-square for a smaller sample size, and if the expected cell count is less than five. Then i was wondering if the test can be used outside a dichotomous contingency table.
What do you mean by this phrase?
"outside a dichotomous"
Where exactly do you want to use it?
Yes, good software can run an extended Fisher test for tables larger than 2 x 2. Or a Monte Carlo or permutation approach can be used for large tables for which there might not be enough computing power to reach a solution with direct calculations.
In the SPSS documentation, the extension of Fisher's exact test* is called the Fisher-Freeman-Halton test.
- https://www.ibm.com/support/pages/fisher-exact-test-rxc-table-fisher-freeman-halton-test
Freeman, G.H. and Halton, J.H., "Note on exact treatment of contingency, goodness of fit and other problems of significance," Biometrika, 38:141-149, 1951.
* Ian Campbell refers to Fisher's exact test as the Fisher-Irwin test in his nice simulation study on the N-1 Chi-square. He does so because Joseph Oscar Irwin developed the same test independently of Fisher, but rarely gets any credit for doing so. I thought it was very good of Campbell to acknowledge Irwin, and now try to do so as well.
- https://www.iancampbell.co.uk/twobytwo/twobytwo.htm
Article Comments on 'Chi-squared and Fisher-Irwin tests of two-by-tw...
- https://en.wikipedia.org/wiki/Joseph_Oscar_Irwin
J. O. Irwin (1935) Tests of Significance for Differences between Percentages Based on Small Numbers, Metron, Vol. 12, pp. 83–94.
The following can be run in R, or at https://rdrr.io/snippets/ for Fisher's test on a table larger than 2 x 2. The second call for fisher.test() uses Monte Carlo simulation.
Data = read.table(header=TRUE, row.names=1, text="
Group Pass Fail
A 100 20
B 20 11
C 50 8
D 30 10
")
Table = as.matrix(Data)
Table
fisher.test(Table)
fisher.test(Table, simulate.p.value=TRUE, B=10000)
OFF TOPIC
This use of the word outside in this thread has reminded me of a well-known quote about dogs, books and best friends.
https://quoteinvestigator.com/2010/09/08/dog/
Language is a wonderful thing, innit! ;-)
Not infinite (maybe). You don't mention any computational constraints, but I am guessing the future won't help us speed up computation indefinitely, and you don't mention any time constraints, so I assume this is a theoretical question. Assuming the universe doesn't collapse, one prediction is a "big chill" and things moving away from each other. Perhaps this would end the computation of your problem, maybe not for quantum computers???? But, I don't know and I don't of the expertise even to speculate.
If you want an answer to a different question, you should delete this question and ask what you want. For example, in software X what are the size limitations for function Y for whatever computer specs you have. And worth noting, a lot of software would have work arounds to do the same procedure as Y but without the constraints. And of course, say why you would want to do a Fisher's exact with loads of degrees of freedom. It is likely a better question would start "What can I do instead ...", but really you should be able to find that information in books.
- Badges
- Science topic
- Similar topics
- Correction