# odds ratio

Suppose the probability of an event $A$ is not 1. The odds of the event $A$ is the ratio

 $\operatorname{odds}(A):=\frac{P(A)}{P(A^{c})}=\frac{P(A)}{1-P(A)}.$

For example, if the odds of landing a head in a coin flip is 2, then the probability of landing a head is twice as likely as that of landing a tail.

In a $2\times 2$ contingency table, with a dichotomous explanatory variable $X$ having levels 1 and 2, and a binary response variable $Y$ with success and failure as two possible levels of outcomes:

Title odds ratio OddsRatio 2013-03-22 14:41:07 2013-03-22 14:41:07 CWoo (3771) CWoo (3771) 10 CWoo (3771) Definition msc 62H20 msc 62H17 odds log-odds ratio