Most of the young researchers get confused with these two statistical tests while analyzing. In order to better understand this issue, I am putting forward a discussion for expert opinions. When is the chi-squared test not the exact fishing test to be carried out? and when to perform fisher's exact test instead of the chi-squared test?
Chi Square is less accurate when an expected value in a cell is less than 5. That usually happens when the sample size is small. You can merge groups in a variable together and perhaps get larger observed and expected values.
The Fisher exact does not have such accuracy limitations, however it is only applicable when the groups are (n x n). Some softwares like spss only calculate the Fisher's for (2 x 2) groups only. You can either merge or delete some groups in the variables to make Fisher exact applicable. Example for (2x2) crosstabs are Male/Female x Smoker/nonsmoker.
There is an alternative test which is similar to the Pearson's chi square, which is the G-test which can give similar or better estimations than chi square. Here is a link for more info: http://www.biostathandbook.com/gtestind.html
Dear Dr. Jochen Wilhelm ,
What do you mean by "Marginals are fixed by design"?
Thanks
Maybe this helps:
https://www.uvm.edu/~dhowell/StatPages/Chi-Square-Folder/chi-square-alternatives.html
https://stats.stackexchange.com/questions/136584/on-fishers-exact-test-what-test-would-have-been-appropriate-if-the-lady-hadnt
When at least one of the expected value is below 5 --> Fisher exact test, otherwise --> Chi-square test.
Fisher's test is more accurate than chi-square when the number of events expected is small. It is recommended to use it whenever it is possible. The higher the number of events, more similar will be the result of both tests
Chi Square is less accurate when an expected value in a cell is less than 5. That usually happens when the sample size is small. You can merge groups in a variable together and perhaps get larger observed and expected values.
The Fisher exact does not have such accuracy limitations, however it is only applicable when the groups are (n x n). Some softwares like spss only calculate the Fisher's for (2 x 2) groups only. You can either merge or delete some groups in the variables to make Fisher exact applicable. Example for (2x2) crosstabs are Male/Female x Smoker/nonsmoker.
There is an alternative test which is similar to the Pearson's chi square, which is the G-test which can give similar or better estimations than chi square. Here is a link for more info: http://www.biostathandbook.com/gtestind.html
@Yazan Haddad
Wow. I didn't know about G-test. Thanks for your suggestion.
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