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Definition — what does that mean?
The odds of the outcome in the exposed group divided by the odds in the unexposed group. It simplifies to the cross product ad over bc.
In Swedish: Oddskvot
OR
The odds of the outcome in the exposed group divided by the odds in the unexposed group, where odds are cases over non-cases. It simplifies to the cross product ad over bc.
OR=6
OR equals (40 times 30) divided by (20 times 10), equals 1,200 divided by 200, equals 6
You are given
a and b are the exposed with and without the outcome, c and d the unexposed with and without it. The odds of the outcome in the exposed group are a / b, in the unexposed group c / d, and the ratio of the two is (a / b) / (c / d) = ad / bc, the cross product of the table.
| Outcome | No outcome | |
|---|---|---|
| Exposed | a = 40 | b = 20 |
| Unexposed | c = 10 | d = 30 |
The exposed have odds of 40 / 20 = 2, the unexposed 10 / 30 = 1/3: OR = 2 / (1/3) = (40 · 30) / (20 · 10) = 6. The odds of the outcome are six times as high with the exposure.
The relative risk compares probabilities instead of odds: 40 / 60 against 10 / 40, a ratio of 2.67. The odds ratio of 6 is further from 1, as it always is when the outcome is common in the groups compared. The two agree when the outcome is rare, below a few per cent, which is when the odds ratio is read as a risk ratio without much harm.
In a case–control study the cases and controls are chosen by the researcher, so the share with the outcome says nothing about the population and the relative risk cannot be computed. The odds ratio can, because ad / bc is the same whether the table is read by row or by column. That symmetry is the reason the measure exists.
What is an odds ratio of 1?
No association: the outcome is as likely with the exposure as without.
Can the odds ratio be below 1?
Yes, when the exposure goes with a lower odds of the outcome: a protective factor.
Where is the diagnostic odds ratio?
The same cross product on a test’s table, TP · TN / (FP · FN), equal to LR+ / LR−, which the
calculator gives beside the likelihood ratios.
| Solve for | Rearranged | With the numbers | Comes to |
|---|---|---|---|
| OR | adbc | 40·3020·10 | 6 |
| a | ORbcd | 6·20·1030 | 40 |
| b | adORc | 40·306·10 | 20 |
| c | adORb | 40·306·20 | 10 |
| d | ORbca | 6·20·1040 | 30 |
Last reviewed October 20, 2026 ·How pages are reviewed
Statistics and probabilityAll formulas
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