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I work on animal behavior. I have a behavior data which is categorical/ nominal variable. It's in the form of a 4 by 4 contingency table with unfixed marginals hence unconditional. I am confused which statistical tests to use Fisher's or Barnard's. As it is unconditional which clearly violates Fisher's exact tests assumption but I have seen people still using it to analyze unconditional data. Additionally, I have come across various blogs which says Fisher's is better for higher RC contingency table and most of the biologist prefer Fisher's even for unconditional data. I am more inclined towards Barnard's statistics, and would be grateful for an opinion as I don't have a very strong statistics background. If their is some other statistical test which would be better over both please let me know.

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    $\begingroup$ Good question - see stats.stackexchange.com/q/136584/17230. When you say "unfixed marginals" do you mean no margins are fixed in the sampling scheme, or only one margin? If no margins are fixed, is the total count fixed? $\endgroup$ Jul 26, 2018 at 12:30
  • $\begingroup$ my Margins are not fixed either for rows, columns or total. As it is a behaviour data I cant decide the margins or total $\endgroup$ Jul 26, 2018 at 16:07

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