Stata FAQ
How do I interpret odds ratios in logistic regression?

You may also want to check out, FAQ: How do I use odds ratio to interpret logistic regression?, on our General FAQ page.

Introduction

Let's begin with probability. Probabilities range between 0 and 1. Let's say that the probability of success is .8, thus

p = .8

Then the probability of failure is

q = 1 - p = .2

Odds are determined from probabilities and range between 0 and infinity. Odds are defined as the ratio of the probability of success and the probability of failure. The odds of success are

odds(success) = p/(1-p) or p/q = .8/.2 = 4,

that is, the odds of success are 4 to 1. The odds of failure would be

odds(failure) = q/p = .2/.8 = .25.