I have data of drug response (0,1) and genotypes (1,2,3). in genotypes, some catagories have count less than 5.
Fisher exact test cannot be applied as the data is 2X3. Which other test will be suitable for this data?
Hello Mismah,
The key isn't whether a cell has an observed frequency fewer than 5, but an expected frequency below 5. For a given cell, expected frequency is row n x column n divided by N (sum of all cases).
However, if cell counts are low (as your question implies), do understand that the statistical power of pretty much any test will be low, unless the departure from no relationship (between variables) is strong.
In any event, here's a more populated thread from RGate on the same issue: https://www.researchgate.net/post/What_is_the_alternative_test_of_Chi-square_if_there_exist_many_cells_have_expected_frequency_less_than_5
As well, here's a thread on extending exact tests beyond a 2 x 2 framework: https://www.researchgate.net/post/Alternatives_of_Fishers_exact_test_for_more_than_2_groups2
The Cytel package, Exact (Test), which can be had as an add-on in SPSS and SYSTAT, will handle 2 x 3 designs as well.
Finally, if you use the R package, both the fisher.test function (in stats module) and the exact.text function (in Exact v1.0 library) will handle your design.
Good luck with your work!
There is a modification of the Fisher test (called Fisher Halton) that works for the 2x3 case. A calculator is also available. Both are at this link:
https://www.google.com/search?client=firefox-b-1&ei=ffB1W4mHJsj0tAWv45jQCA&q=fisher+exact+test+for+2x3+table&oq=exact+test+for+2x3&gs_l=psy-ab.1.1.0i22i30k1l3.253952.274283.0.286227.61.33.1.0.0.0.283.3490.9j19j2.30.0....0...1.1.64.psy-ab..40.21.2456...0j0i67k1j0i131k1j0i131i67k1j0i10k1j0i3k1.0.lkYJhpqMxn4
since the expected frequency < 5 criterion is about how well a binomial approximates a normal distribution, I would prefer the exact test in this instance. Best wishes, David Booth
Having cell counts of less than 5 should not obviate the practicality or the validity of the chi-square test. As mentioned, apply the Fischer's exact test. I applied this test even when every cell/condition exceeds five. By default, SPSS will render you the p-value from the Fischer's exact test. Usually this will not deviate too much from the conventional p-value related to the chi-square statistic.
Thank you so much David Morse David Eugene Booth and Jimmy Y. Zhong for you valuable suggestion. These helped me a lot to decide an accurate analysis method for my data.
However, I have one more question. what kind of model (GLM, GLIM, regression etc.) I can apply to same data? The total number of samples are 45, from which 30 are responsive (coded as 1) and 15 are non responsive (coded as 0).
I believe that what you want is logistic regression. The attached notes may be helpful. Best wishes, David Booth
Adding on to David's response, you may want to perform logistic (or "multinomial" if it's more than two categories) regression if you insist on the current 2 x 3 design, which will give you 6 categories. If so, your predictors need to be continuous in nature. Otherwise, adhere to chi-square exact tests if all you have were frequencies.
As far as I know fisher exact test can be applied even if the table is larger than 2x2.
I have one last response. a) if you think a Fisher exact test can be applied to more than a 2X2 table I invite you to try it and report back to us. b) JImmy she says the outcomes are 0,1. I take her at her word. Best wishes to all, David Booth
This is an old post, but I throw in an answer in case somebody reads this thread again. Thank you all from previous answers. I tried Fisher's exact test with SPSS v.23 with 4x4 table. No problem. It took less than a minute to calculate 14 different 4x4 tables. I had frequencies below 20 in every cell, some where zeros. Total number of samples was 120.
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