I've got a question related to this thread and I've been looking everywhere on the web but I can't find an answer.

I know that if the assumptions (n<20, one of the cells < 5 [or a little bit less stringent maximal 20%]) one can stick to Fisher's Exact Test.

When should I use the exact version of the CHISQ (in SPSS)? Can it be used as an substitute for the FET (if so, i which cases)? In other words, is it equivalent?

In 2x2 tables one will get both for the FET and CHISQ the 1-sided exact test in SPSS. Does the 1-sided CHISQ have the sample principle as the FET which uses upward diagonals and downward diagonals? Besides that for bigger tables one can use the 2-sided exact test for each only I found out. And does the exact test for CHISQ also assumes fixed margins (conditional) like the FET?

Further I am thinking about if my data meets the assumptions of the FET, because I did an oberservational study and registered looking (left, right, not) in case of turning (left, right) as a driver and I registered looking (left, right,not) in combination with a bicyclist from (left, right, none) as a driver.

See the first document at the bottom. In the case of the lady example with coffee and milk poured a new data collection would be the same since the lady must guess 48 of each (first or second milk) again and there are 48 cups of each (these are both know by forehand). Also, the document states that if one would do a recount or collecting new data and when those row or column marginals change then it's voilated. if only one marginal is fixed one can do a FET says the document.

Does a constant row marginal in my study mean that I do for example 20 turning left and 40 turning right (row totals like in my first data collection) in a new data collection (i know/choose it by forehand) and observe looking behaviour (which probably is not the same). On the other hand, if I would have recorded those drivers on tape and score them again it ould result in the same 2x2 table with the same total column and row margins (this might be not a logical or allowed idea).

This might be an interesting link:

http://www.uvm.edu/~dhowell/StatPages/More_Stuff/Chi-square/Contingency%20Tables.pdf
And (cast doubt on the relevance of marginals, did not read the article myself):

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V0M-45GVWV2-4&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=ef731c40b4e88804bab7ad6e0fe61024
Are there any other alternatives to CHISQ (for my problem, with 2x2 and 2x3 tables)?

Is the Yates' correction a good alternative (I've read somewhere that it is very convervative)? I think it's called in SPSS 'Likelihood Ratio'. And maybe Barnard’s Test? It is only for 2x2 and not in SPSS.