It is defined as the ratio of the odds of an event
occurring in one group to the odds of it occurring
in another group, or to a sample-based estimate of
The odds ratio compares the relative odds in each
One advantage of the odds ratio is that it is not
dependent on whether we focus on the event's
occurrence or its failure to occur. If the odds ratio
for an event deviates substantially from 1.0, the
odds ratio for the event's failure to occur will also
deviate substantially from 1.0, though in the
Shown below is the typical 2 by 2 table.
You can understand the odds ratio by first noticing
what the odds are in each row of the table. The
odds for row Y- are a/b. The odds for row Y+ are
c/d. The odds ratio (OR) is simply the ratio of the
which can be simplified to
Notice that if the odds are the same in
each row, then the odds ratio is 1.
An odds ratio of 1 indicates that the condition or
event under study is equally likely in both groups.
An odds ratio greater than 1 indicates that the
condition or event is more likely in the first group.
And an odds ratio less than 1 indicates that the
condition or event is less likely in the first group.
Consider the following data on survival of
passengers on the Titanic. There were 462 female
passengers: 308 survived and 154 died. There were
851 male passengers: 142 survived and 709 died
(see table below).
DEAD ALIVE TOTAL
MALE 709 142 851
FEMALE 154 308 462
TOTAL 863 450 1,313
Clearly, a male passenger on the Titanic was more
likely to die than a female passenger.
The odds ratio compares the relative odds of
death in each group.
For males, the odds were 5:1 in favor of death
For females, the odds were exactly 2:1 against
dying (154X142= 21,868)
The odds ratio (218,372/21,868= 9.986 ). There is a
ten fold greater odds of death for males than for
suppose that in a sample of 100 men, 60 have
drunk wine in the previous week, while in a sample
of 100 women only 20 have drunk wine in the same
WHO WHO DIDN’T TOTAL
MEN 60 40 100
WOMEN 30 70 100
TOTAL 90 110 200
The odds of a man drinking wine are 60 to 40, or 2:1
the odds of a woman drinking wine are only 20 to
80, or 1:2
Now, (60X70 =4200) for men
and (30X40 = 1200 ) for women
so the odds ratio is 4, showing that men are much
more likely to drink wine than women.
the odds ratio is commonly used as a means of
expressing the results in some forms of clinical trials,
in survey research, and in epidemiology, such as in