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.