I am conscious that there is some debate about the use of Fisher's Exact test for dimensions other than 2 x 2 (e.g. where the number of table rows is greater than 2). Nevertheless, I am also aware that SPSS generates p-values for such cases. I would be grateful for advice on the use of these p-values and whether they are trustworthy. The context is teaching statistics to non-specialists who lack time to dabble in alternative tests unless strictly necessary.
P.S. In saying "alternative tests", I meant tests other than Fisher's Exact test when the 80% rule for expected counts is violated for use of the chi-square test of association.
To address my own query and hopefully save others some time, I have come across a relevant discussion at https://stats.stackexchange.com/questions/1805/fishers-exact-test-in-contingency-tables-larger-than-2x2 .
for dimensions other than 2 x 2 when the well-known rule for expected counts in not satisfied for use of the chi-square test of association.
Margaret, I believe that you found a good answer for your question.
The usual chi-square test is justified asymptotically, as sample size grows large.
The rules of thumb that are commonly taught are not very good.
or use the exact test form of tests of independence in the general rxc table.
Thanks, Tony. The nagging concern at the back of my mind is the quality of the algorithm that is used by SPSS for Fisher's Exact test for dimensions other than 2 x 2. I expect that if I had time, I could do lots of comparative simulations across packages but I don't and it is unrealistic to expect my students to learn R on top of their other non-specialist learning given their time-scales and lack of prior learning.
a "network" algorithm and could be based on the original work referenced above.
there are several ways of ordering what-is-extreme.
a criterion. Chi-squared with Yates's correction gives a very good estimator of that test, for 2x2.
when it is small. Thus, a non-significant chi-squared result is robust.
The Exact Tests both Monte Carlo and exact calculations code beyond 2x2 comes from well known experts in this area.
Thanks, Tony. I wasn't aware of any such connection. On searching the StatXact website for documentation for Fisher's Exact test, I am pointed to the networked algorithm at https://www.jstor.org/stable/2288652?seq=1#page_scan_tab_contents, which allows extension beyond the 2 x 2 case. This suggests that the above algorithm is the one used by StatXact and, it seems from your reply, also by SPSS.
anyone has ever investigated that possibility.
Based on Small Numbers, Metron, Vol. 12, pp. 83–94.
> there are several ways of ordering what-is-extreme.
> estimator of that test, for 2x2.
> for the more general case.
> when it is small. Thus, a non-significant chi-squared result is robust.
> counts in not satisfied for use of the chi-square test of association.
> Comments are still welcome!
> the chi-square test of association.