As a clearly contrived example of what the information correlation functions indicate, consider the three binary variables 
, i=1,2,3. Let 
. Then 
, i.e. it is zero unless all three have the same value.
Consider the full information correlation function, 
of equation 3.29. It is straightforward to show that
Thus the information between the reduced distributions is log(2) (the n of section 3.14 is odd), as might be expected from the fact that there is one bit determined by the full distribution not determined by the any of the reduced distributions. Again, we must warn the reader that care must be used in interpreting the information correlation functions.