I am using Chi-square in my study, but there are some variables which have their expected value less than 5. I was thinking of using Fisher’s exact test but I know it is used for 2X2 table only. So, is there any other option?
Fisher exact test is for r x c contingency table. You must make the comparison on chi-square statistic not to an asymptotic chi-square distribution but the exact permutation distribution of the chi-square statistic for the accurate results.
If you have small samples, then, optimal data analysis is ideal for it. It provides alternatives for chi-square. You can refer to APA book with software: Yarnold and Solystik (2005). Optimal data analysis. American Psychological Association.
Also, look into the journal whose link is attached below: http://odajournal.com/.