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  • Current: Nov 22, 2023

Odds ratio

An odds ratio is a ratio of two odds. When the probability of an event occuring in the population A is p, odds in the population A are:

OddsA = p/(1 - p)


Assume that the probability of the same event occuring in population B is q. In this case, odds in the population B:

OddsB = q/(1 - q)


The odds ratio is:

Odds ratio = OddsA/OddsB = p(1 - q)/q(1 - p)



Definitions in the literature

  • An odds ratio (OR) is a measure of association between an exposure and an outcome [1].
  • The odds ratio is a measure of the magnitude of an association (statistical effect, nonindependence) between two binary (or dichotomous) variables [2].