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Let's say I've got two classes of individuals, "Mutants" and "Non-mutants". Let's say I have 50 Mutants and 120 Non-mutants, so 170 individuals total.

Now I want to study how these two groups may differ in some preferences.

Let's say I find that 32 of the Mutants like to eat cheese (64%), while 50 of the Non-mutants like to eat cheese (42%).

Let's say I find that 20 of the Mutants are tired (40%), while only 2 of the Non-mutants are tired (~2%).

I can do some univariate statistics and conclude that it seems that there is a statistically significant difference between the Mutants and Non-mutants in their cheese liking, and also a statistically significant difference between the Mutants and Non-mutants in their tiredness.

What I want to know is what statistical tests can I do to figure out if these differences are INDEPENDENT of each other. For instance, is the difference between the % of mutants who like cheese and % of non-mutants who like cheese really due to "mutant"/"non-mutant"? Or is it actually a product of the differences in tiredness (do tired people in general just like cheese?)

Is this even possible to answer with the information given? What sort of "multivariate statistics" do I need to do to sort something like this out?

Thank you so much in advance, and ask me any clarifying questions you need to. Thanks!