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I am applying Fisher's exact tests to my data as my data sample is small, my data is very similar to this one(which I found through Reddit).

N1 = Man N2 = Woman
Menu 1 1 6
Menu 2 2 9
Menu 3 2 4
Menu 4 4 3
Menu 5 4 3
Menu 6 3 3
Total 16 28

However, apart from using Fisher's exact test to test if gender has a relationship with how the menus are chosen, I also want to test several hypotheses, for example, the number of Women who chose Menu 1 is significantly different compared to Men, the number of Women who chose Menu 2 significantly differs to Man, etc, what kind of tests I shall do?

To my understanding, I need to create six separate contingency tables like the one below to conduct Fisher's exact test for each hypothesis.

N2 = Man N2 = Woman
Menu 1 selected 1 6
Menu 1 not selected 15 22

I'd like to ask is this approach correct? Also I want to know if I do so, do I need to apply the Bonferroni correction?

Thank you for your answers!

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  • $\begingroup$ Does each person choose only one menu? Or can they choose multiple menus? $\endgroup$
    – Peter Flom
    Commented Dec 3 at 14:17
  • $\begingroup$ Hi, They can choose multiple menus $\endgroup$
    – moteez
    Commented Dec 3 at 16:14
  • $\begingroup$ If you reformat it by person with seven variables: their sex (0/1) and for each menu a 0/1 variable for whether they chose it you can then do a logistic regression to see if menu predicts sex (well strictly speaking retrodicts it). Would that answer your question? $\endgroup$
    – mdewey
    Commented Dec 3 at 16:37
  • $\begingroup$ You say that a given person can choose multiple menus. Then, in your grand totals, there is some double counting (the same person is counted more than once), and Fisher (or $\chi^2$ for that matter), are not appropriate tests (the multiple categories need to be mutually exclusive!). 2x6, or 2x2 contingency tables are not the right tool... $\endgroup$
    – jginestet
    Commented Dec 3 at 22:30
  • $\begingroup$ @mdewey Hi, thank you for your answers! I tried the logistic regression, but it seems my sample size is still not very efficient to converge Do you know what approach I shall use if I want to demonstrate for individual rows, for example, Men Choose Menu 2 significantly greater than Women? $\endgroup$
    – moteez
    Commented Dec 4 at 10:55

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