Conditional Entropy:

Joint Entropy:

A non-symmetric measure of association (“uncertainty coefficient”?) between and measures the percentage of entropy reduced from if is given:

Or the percentage of entropy reduced from if is given:

Where , the

*mutual information*of and , is non-negative and symmetric.

Anyway, equals 0 if no association, 1 if knowing fully predicts (i.e. is a function of ).

A

*symmetric*measure can be made of

*a weighted average*of and :

Relation to or measures like Cramer’s V etc.:

No obvious relation. Generated some 2×2 contigency tables and plotted their vs Cramer’s V: