I have a question regarding the use of SPSS (i.e. its capability) to execute a Fisher's Exact test for large, sparse RxC contingency tables. I would like to test whether or not a certain correlation exist between my rows (diagnostic groups) and columns (laboratory tests) (see below).
Currently, I have a contingency table of 7 rows and 9 columns, that includes the data of 164 patients. Rows consist of certain diagnostic groups (e.g. different neurological diseases grouped together in a 'neurological disease' diagnostic group) while columns are the number of patients that have undertaken a certain laboratory test. However, multiple diagnostic groups have zero patients that underwent a certain test, and only 11.11% of the results are larger than 5 patients. As such, I can not use the Chi square test. Many suggest combining different rows and columns to evade this problem. However, in this case, I would like to avoid this since I am researching whether or not certain tests are associated with certain diagnostic groups, and by combining rows/columns, my research question would be in vain.
Therefore, I am looking for other possibilities to determine the presence of a correlation. One of my options would be to use a Fisher's exact test for R x C tables, since this test does not use the assumptions of the Chi squared test. I already know how to execute a Fisher's Exact test in SPSS for R x C tables. However, is it feasible to execute a Fisher's exact test for a table as large as 7x9, or should I use other statistical tests (and if yes, which tests do you recommend)?
Thanks in advance.