Does this quantity related to independence have a name?

Obviously events A and B are independent iff Pr(AB) = Pr(A)Pr(B). Let’s define a related quantity Q:


So A and B are independent iff Q = 1 (assuming the denominator is nonzero). Does Q actually have a name though? I feel like it refers to some elementary concept that is escaping me right now and that I will feel quite silly for even asking this.


It’s observed to expected ratio (abbreviation: o/e).

Quoting an answer to About joint probability divided by the product of the probabilities at Math.SE (pointed out by Procrastinator):

Then, at least in the environmental, medical and life sciences literature, P(A∩B)/(P(A)P(B)) is called the observed to expected ratio (abbreviation o/e). The idea is that the numerator is the actual probability of A∩B while the denominator is what it would be if A and B were independent.

Source : Link , Question Author : Michael McGowan , Answer Author : Community

Leave a Comment