I am working with very small cell counts, and am wondering if Fisher's exact test can be used in place of the chi-squared test when partitioning IxJ tables. I am interested if the same process for partitioning the tables is acceptable.
You seem to be asking two questions:
Can Fisher's exact test be used for ixj tables?
Something about partitioning tables.
The answer to 1 is easy: Yes it can. In
SAS there is an
EXACT statement in
PROC FREQ. In
R there is
fisher.test in the
The answer to 2 is unclear; you can certainly partition tables and test on the subsetted partition. If you test many partitions you run into all the multiple testing issues. If you choose your partition based on anything related to Fisher's test, then its properties will be off.