“the ratio of the probability of an event’s occurring to the probability of its not occurring the likelihood of the occurrence of one thing rather than the occurrence of another thing, as in a contest” (American Heritage Dictionary, 2012)Īn odds ratio (OR) is a measure of association between a certain property A and a second property B in a population.“the probability that one thing is so or will happen rather than another the ratio of the probability of one event to that of an alternative event” (Merriam-Webster Dictionary, 2012).“the chances of something happening” (Macmillan British Dictionary, 2012).The statistical definition of odds is quite precise compared to dictionary definitions, which are inconsistent and have different meanings, even in a plain language sense instead of a statistical one : One major differences between odds and probability is that while odds range from 0 and infinity, probability ranges from 0 to 1. The odds of the horse winning a race is 1/3 (1 win to 3 losses) and the probability is 1/4 (1 win out of 4 races). For example, let’s say the horse runs 4 races and wins 1. When there are a very small number of events, odds and probability are very similar. In the horse example, the probability of a win is 20/100. The odds definition is very similar to the definition of probability, which is the fraction of times an event occurs in a certain number of trials. For our racehorse example, that would be 80 to 20, or 4 to 1. This is defined as the number of ways an event does not happen against the number of ways an event does happen. But there is another way to define odds in statistics- odds against an event happening. The above odds definition is the odds in favor of an event. As an example, if a racehorse runs 100 races and wins 20 times, the odds of the horse winning a race is 20/80 = 1/4. In other words, it’s a ratio of successes (or wins) to losses (or failures). Odds is usually defined in statistics as the probability an event will occur divided by the probability that it will not occur.
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