Fisher's exact test in more than 2 variables 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.

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.
