Odds Ratio Calculator
Enter the four counts of a 2x2 table: exposed and unexposed groups, each split into those with and without the outcome. You get the odds ratio, its 95% confidence interval and a p-value.
Updated
Report a problem
Formula
- Odds ratio:
OR = (a x d) / (b x c) - Standard error:
SE = sqrt(1/a + 1/b + 1/c + 1/d)on the log scale - 95% CI:
exp(ln(OR) +/- 1.959964 x SE) - z and p:
z = ln(OR) / SE,p = 2 x (1 - Phi(|z|)) - Zero cells: add 0.5 to every cell (Haldane-Anscombe)
Worked example
Table a=20, b=80, c=10, d=90. OR = (20 x 90) / (80 x 10) = 2.25. SE = sqrt(1/20 + 1/80 + 1/10 + 1/90) = 0.4167. The 95% CI is 0.9943 to 5.0915, z = 1.9462 and p = 0.0516, so just short of significance at 5%.
Frequently asked questions
How do you calculate an odds ratio?
Divide the odds of the outcome in the exposed group, a/b, by the odds in the unexposed group, c/d, which simplifies to (a x d) / (b x c). For 20, 80 / 10, 90 that is (20 x 90) / (80 x 10) = 2.25.
How is the 95% confidence interval found?
The log method works on ln(OR) with standard error sqrt(1/a + 1/b + 1/c + 1/d), then exponentiates ln(OR) +/- 1.96 x SE. For 20, 80 / 10, 90 SE = 0.4167, giving 0.9943 to 5.0915. Because the interval includes 1, the result is not significant at 5%.
What does an odds ratio of 1, above 1 or below 1 mean?
An odds ratio of 1 means equal odds in both groups. Above 1 means higher odds of the outcome in the exposed group, below 1 lower odds. 30, 10 / 10, 30 gives 9, so the exposed odds are nine times higher.
What if one of the cells is zero?
A zero cell makes the odds ratio zero or undefined, so the Haldane-Anscombe correction adds 0.5 to every cell before calculating. The result says when this was applied. A whole row or column of zeros cannot be analysed.