Statistics in
Crosstabulations  Odds Ratio
An odds ratio is a statistical measure of dependence between 2 binary
variables in a 2x2 table. An odds ratio of 1 indicates independence. A
typical example involves comparing two groups with respect to an event
of interest occurring or not occurring.
The following table is from Agresti (1990)
Categorical Data Analysis. It
shows the breakdown of participants in a clinical trial testing whether
aspirin taken regularly reduces the likelihood of heart attack.

Heart Attack 
No Heart
Attack 
Placebo 
189 
10,845 
Aspirin 
104 
10,933 
The odds of an individual in the placebo group experiencing heart attack
is 189/10,845 = 0.01742739
The odds of an individual in the aspirin group experiencing heart attack
is 104/10,933 = 0.009512485
Odds ratio = 0.01742739 / 0.009512485 = 1.832054, the odds of experiencing
a heart attack is 1.83 times greater for the placebo group than for the
aspirin group.
Asymptotic large sample confidence interval = [1.440042
2.330780]
Formulas
For the following 2x2 table:
Odds ratio (or) = ad / bc
Large sample CI = exp ( ln (or) +/ zcrit * sqrt(1/a+1/b+1/c+1/d) )
zcrit = 1alpha/2 quantile from the standard normal distribution where
alpha = 1confidence level