odds ratio

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

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

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
Canonical name	OddsRatio
Date of creation	2013-03-22 14:41:07
Last modified on	2013-03-22 14:41:07
Owner	CWoo (3771)
Last modified by	CWoo (3771)
Numerical id	10
Author	CWoo (3771)
Entry type	Definition
Classification	msc 62H20
Classification	msc 62H17
Defines	odds
Defines	log-odds ratio