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I have a table of contingency which is 6X2 and in my case, it is not an option to "convert" it in a 2X2 table. Also, I need to be able to use the hypothesis of "less than" and "greater than" (I mean, I cannot be restricted to the "two sided"). The Fisher test in R (fisher.test) allows for all three hypothesis only when the table of contingency is 2X2. Do you know of any other test that I can apply here?

Marlom
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    What would less than or greater than mean here in a multidimensional sense? Combined, are they equivalent to different? – Henry Feb 11 '24 at 13:44
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    A reason why Fisher's exact rarely goes beyond 2x2 is that the calculations become very cumbersome (already in the standard case there's a lot of factorials in there). The $\chi^2$ test with appropriate correction is just outright better as long as your expected cell frequencies exceed 1 - see here for more discussion. – PBulls Feb 11 '24 at 14:07
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    And since Fisher’s “exact” test is not very accurate, why ever use it? This has been discussed at length on this site. Another issue: what makes up the 6 categories? Can they be ordered? – Frank Harrell Feb 11 '24 at 14:22
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    @Pbulls It's easy to obtain p-values to any desired level of accuracy for a specific set of margins by simulation; it's not really necessary to worry about lots of factorials. Very large tables become unwieldy but 6x2 is not problematic. – Glen_b Feb 11 '24 at 16:59

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