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I have some data with three independent categorical variables (one has a sense of order, the others do not) and one dependent categorical variable. Is there an analogue to Fisher's exact test where I can simultaneously evaluate whether the independent variables affect the dependent one?

Specific details for anyone who is curious: Subjects (37) do a series of 3 different activities. After completing all activities, we ask them to rank the activities in order of their preference (6 possible ranking orders: ABC, ACB, BAC, BCA, CAB, CBA) (dependent variable). We also collect their age range (4 levels, ordered), impairment (4 categories: cognitive, motor, motor and cognitive, none), and order they performed the activities (2 possible). So, in multiple dimensions, this creates a table of 6x4x4x2.

I can certainly run fisher's exact test for each factor with the dependent variable. But that doesn't seem complete or satisfying.

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  • $\begingroup$ Are you sure the ranking orders are the independent variable? Please state precisely which are the independent and with is the dependent variables. $\endgroup$
    – frank
    Commented Feb 17, 2022 at 6:58
  • $\begingroup$ wow, I need more sleep. Thanks @frank for calling that out. Edited to fix. $\endgroup$ Commented Feb 17, 2022 at 7:28
  • $\begingroup$ You might want to consider a multinomial probit model. Here you model the preference of the categories A, B, C as random draws from conditional Gaussian distributions, and these Gaussian distributions relate to the categorical probability of the different orders ABC, ACB, BAC, BCA, CAB, CBA as function of the independent variables. $\endgroup$ Commented Feb 17, 2022 at 9:44
  • $\begingroup$ Hmm, that is actually really interesting. I am going to explore using linear models for this a bit more. Thanks $\endgroup$ Commented Feb 18, 2022 at 20:50

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If you want to know, whether your dependent variable is affected by the combination of all your independent variables, you simply consider the two-way table where one dimension is your independent variables and the other one contains all the possible combinations of your independent variables, i.e. (young, cognitive, order1), (young, cognitive, order2), (young, motor, order1), ..., where you will obtain 4x4x2 = 32 possibilities.

Finally, you apply the Fisher test to this 6x32 table.

Of course, it is always a good idea to, in addition to the above, also consider the effect of only single independent variables (e.g. only age, resulting in a 6x4 table) and smaller combinations of independent variables (e.g. the effect of age and impairment, resulting in a 6x16 table), to find out the relevant predictors.

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  • $\begingroup$ that makes sense. My concern is the number of tests that would be run blowing up my chances of false rejections. I can correct using the Holm method (I think that is the least conservative method that I am confident I meet the assumptions for), but there will still be a loss of power for anyone of the test. $\endgroup$ Commented Feb 18, 2022 at 5:58
  • $\begingroup$ You base your decision just on one single test, the Fisher test on the 6x32 table. So no correction is necessary. The other tests I mentioned above were just for getting to know your data better. $\endgroup$
    – frank
    Commented Feb 18, 2022 at 6:31
  • $\begingroup$ Gotcha. I will have to think about how I present the results of those tests. Thanks for your help. $\endgroup$ Commented Feb 18, 2022 at 7:21

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