To measure the correlation between two possibly related dichotomous events (E1 and E2), you use Yule's Q, given by the formula:

((ad - bc) / (ad + bc))

where, after running an experiment a certain number of times...

a = the number of times E1 happened and E2 happened
b = the number of times E1 did not happen and E2 happened
c = the number of times E1 happened and E2 did not happen
d = the number of times E1 did not happen and E2 did not happen

The result will be a real number between -1 and 1.  

When Q=1, there is a perfect positive correlation between the two events--what happens in E1 always happens in E2 and vice versa.  If E1 happens, E2 always happens.  If E2 happens, E1 always happens.  If E1 does not happen, E2 never happens.  If E2 does not happen, E1 never happens.

When Q=-1, there is a perfect negative correlation between the two events, and the occurance of one event invariably leads to the non-occurance of the other (and vice-versa).  If E1 happens, E2 never happens.  If E2 happens, E1 never happens.  If E1 does not happen, E2 always happens.  If E2 does not happen, E1 always happens.
 
When Q = 0, there is absolutely no correlation between the two events--one event happening or not happening does not influence the other event at all. Total statistical independence.


Of course, those are just the ideal conditions.  A Q value of 0.2, for instance, would indicate that there's a relatively weak positive correlation between E1 and E2--if E1 happens, it is more likely than not that E2 will happen--but you probably wouldn't want to bet the farm on it.


It's also worth noting that Yule's Q is a symmetric measure--it couldn't care less whether E1 occured first or second chronologically.



Yule's Q was first put forth in 1957, by G. V. Yule and M. G. Kendall.

Log in or registerto write something here or to contact authors.