When we need to apply Fisher exact test and how to do it in SPSS and how to interpret it there! What are the differences in procedure and interpretation with it with Chi square test? Can anybody make it SIMPLE please?
The Fisher's exact test only works on 2 by 2 designs whereas the Chi square test works on any size design. Fisher's exact test is preferred for small sample sizes in 2 by 2 designs (e.g. less than 40). If the sample size is large then it will take a long time to calculate.
If your design is larger than 2 by 2 then take care to make sure enough cells in your table have expected count larger than 5 - you need at least 80% of them like this. This information is reported in the SPSS output. If your percentage is less than 80% you will need to combine some cells together.
Some software (i.e. SAS) allow for Fischer's exact test even for larger (more than 2x2 contingency tables) there is no mathematical reason for limiting exact test to 2x2 tables (after all is a Montecarlo test with no distribution assumption but only based on the enumeration of all possible combinations). the only limiting factor is the running time that can be very long.....
If the marginal totals (i.e., row and column totals) for your 2x2 table are not fixed in advance, and if all expected frequencies are equal to 1 or more, then you would be better off using the N-1 Chi-square test, as it has better power than Fisher's exact test while maintaining good control over the Type I error rate. See Ian Campbell's website and Statistics in Medicine article for more info. And by the way, when you analyze a 2x2 table via SPSS CROSSTABS, the result reported for the test of "Linear-by-linear association" is equivalent to the N-1 Chi-square (see second link below).
By the way, as Campbell notes in his article, the test best known as Fisher's exact test was also developed independently by J.O. Irwin--see the 3rd link below, and search for 1935. For that reason, Campbell refers to the test as the Fisher-Irwin test, which I think is a nice tribute.
HTH.
http://www.iancampbell.co.uk/twobytwo/twobytwo.htm
https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/notes/chisqr_assumptions
http://statprob.com/encyclopedia/JosephOscarIRWIN.html
Chi Square test is used for larger sample whereas fisher exact test is used for smaller sample
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