Definition

A measure of the odds of one event relative to another. It is calculated as the ratio of the odds of one event to the odds of the other. It is often used to compare the odds of an outcome in one (say treatment) group versus its odds in another (say control) group. Odds ratios are used in Logistic Regression and Loglinear Models to describe the effect a predictor variable has on the output variable.

Examples

where

p1 = Probability that the event occurs in group A

p2 = Probability that the event occurs in group B

Suppose that the probability that a new car will work consistently for the next 5 years is 0.99 and the corresponding probability for a used car is 0.6.

Odds ratio (new car vs. used car) = [0.99/(1-0.99)]/[0.6/(1-0.6)] = 66

Thus, the odds of working consistently for the next five years for a new car are 66 times the odds for a used car.

Application

An Odds ratio > 1 indicates the odds are higher for the group in the numerator. Odds ratio < 1 indicates the odds are higher for the group in the denominator. Odds ratio = 1 indicates the odds are the same for the two groups. Odds ratios can take any value between zero and infinity.