Odds ratio - Definition and Overview

The odds-ratio is a statistical measure, particularly important in Bayesian statistics and logistic regression.

It is defined as the ratio of the odds of an event occurring in one group to the odds of it occurring in another group, or to a data-based estimate of that ratio. These groups might be men and women, an experimental group and a control group, or any other dichotomous classification. So if the probabilities of the event in each of the groups are p and q respectively then the odds-ratio is

<math>{ p/(1-p) \over q/(1-q)}=\frac{\;p(1-q)\;}{\;(1-p)q\;}.<math>

The logarithm of the odds-ratio is the difference of the logits of the probabilities.

The increased use of logistic regression in medical and social science research means that the odds-ratio is commonly used as a means of expressing the results in some forms of clinical trials, such as case-controlled trials, and in survey research.