http://en.wikipedia.org/wiki/Odds_ratioDefinition in terms of group-wise odds
The odds ratio is the ratio of the odds of an event occurring in one group to the odds of it occurring in another group, or to a sample-based estimate of that ratio.
Suppose that in a sample of 100 men, 90 have drunk wine in the previous week, while in a sample of 100 women only 20 have drunk wine in the same period. The odds of a man drinking wine are 90 to 10, or 9:1, while the odds of a woman drinking wine are only 20 to 80, or 1:4 = 0.25:1. The odds ratio is thus 9/0.25, or 36, showing that men are much more likely to drink wine than women.
Relation to statistical independence
If X and Y are independent, their joint probabilities can be expressed in terms of their marginal probabilities. In this case, the odds ratio equals one, and conversely the odds ratio can only equal one if the joint probabilities can be factored in this way. Thus the odds ratio equals one if and only if X and Y are independent.
Source
incanter/stats.clj:2671
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