The odds ratio is the ratio of the odds of an event in two groups. If the event probabilities satisfy 
, then
 |
For a 
contingency
table having event and nonevent counts 
in the first group and 
in the second, this becomes 
when all four counts are positive.
An odds ratio of 1 indicates equal event odds in the two groups. The odds ratio is unchanged if the roles of group and outcome are interchanged in the table. It differs from relative risk; the two measures can be close when the event is rare but need not be close otherwise.
