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Tri-variate independence test.

So I've just done the chi-squared test in further maths which allows one to test for independence between qualities as sets of 2 qualities and was wondering if anyone could recommend like a 3D version of that?
E.g. Gender, age and height of all Olympic skiers, or would one have to combine 2 sets into one and then look at it?
Original post by Aph
So I've just done the chi-squared test in further maths which allows one to test for independence between qualities as sets of 2 qualities and was wondering if anyone could recommend like a 3D version of that?
E.g. Gender, age and height of all Olympic skiers, or would one have to combine 2 sets into one and then look at it?


Yes, you can extend the chi-squared procedure to n-way tables, where n>2. Chi-squared, in its basic form, will work whenever you can compute an "expected" with which to compare an observed.

The problem with simply using Chi-squared in this way is that when you go to more dimensions than two, the dependence/independence structure gets more complicated. Chi-squared can tell you that X, Y, Z and T are not independent - but it tells you nothing about how they are not independent. So X and Y may be dependent, with Z & T mutually independent and with Z jointly independent of X & Y etc. etc!

So when you get onto this sort of data you usually use a class of models called "log-linear" models that allow you to understand what's going on in the dependence/independence structure.

Agresti's "Introduction to Categorical Data Analysis" is the standard undergraduate text for this sort of stuff.

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