I have always learned that if you have a contingency table that violates the chi square assumption of more than 20% of cells having expected count less than 5, the chisq. test is invalid. If that happens use the fisher exact test. SAS is the only program that I have found to support the test greater than a 2x2 table. Does everyone agree with me to this point? Secondly, if there is a singificant result in the chi sq test, different procedures including simple nonparametric tests, marascuilo procedure or checking the residuals can serve as the post hoc test to see which subgroup is signficantly different in terms of its distribution of the y responses. Is there a "post hoc" test for the fisher's exact test. What is the next step if there is reported signficance for the fishers test. Let's assume this is nominal data since there is a whole slew of tests and models that can be run for nominal data.
I know SAS will run Fischer with more than 2X2 table. I would imagine SPSS and others do as well. The point about using Fischer when chisquare is violated is true.
I have never heard of a "post hoc" test for fischer. I am not sure what you mean by this, however. Post hoc test in ANOVA say look at whether means at specific levels of an IV vary from each other signficantly on the dependent variable. Fischer does analyze means at all; it commonly is used for nominal data which has no mean. All it tells you is if the variables are associated, not how.
If you have ordinal data, which chi square is sometimes use for there are test like Cramer's V which provide more information. But your data has to be at least ordinal to do this.
If your data is ordinal or interval you probably should not be using Fischer. If it is nominal than I don't think there is anything other than descriptive statistics that compares across the artificial levels of the nominal variable. Certainly you can not use any analysis tied to a mean.
I was using the term post hoc to mean a follow up test. To simplify what I said in the last post, fishers is substituted for chi square when violations occur. Checking residuals or procedures such as marascuilo are used to follow up the chi square test to see exactly where the difference in distribution occurs. Is there a follow up procedure for the fishers test.
Lastly, you are saying that fishers is only for ordinal data? If it is nominal, the only thing to do is run a chi square test? ...but then what if you violate the chi square assumptions?
No fisher is used only for nominal data. Well you can use it for ordinal or even interval data, but you should chose a better method.
If the nominal data violates the chi square assumptions (normally due to sample size or sometimes the structure of your data) than fisher is the way to go. My point is that there is no follow up test as far as I know (I have never seen one mentioned). Fisher (like chi square) only tells you if two variables are related. It does not tell you how, if certain levels of one of the variable differ statistically from another, or the strength of the difference. That is a limiting factor of nominal data.
The only follow up I can think of would be contingency tables - essentially descriptive statistics. I am someone confused about your comments on residual analysis. Fischer does not predict the value of anything - so what are the residuals about? You can't (obviiously) find a discrepancy if you don't predict in the first place.