Odds ratio from a 2×2 table
The odds ratio (OR) compares the odds of an outcome between an exposed group and an unexposed or comparison group. Enter the four cells of a 2×2 table.
Formula
For cells a, b, c and d, OR = (a × d) ÷ (b × c). The approximate 95% confidence interval is calculated on the logarithmic scale using the standard error √(1/a + 1/b + 1/c + 1/d), then transformed back to the OR scale.
Interpretation
OR = 1 indicates equal odds in the two groups. OR greater than 1 indicates higher odds in the first group, while OR below 1 indicates lower odds. Interpretation must consider the study design, confidence interval and possible confounding.
If any cell is zero, this calculator applies a 0.5 continuity correction to all four cells to permit estimation.
Frequently asked questions
Is an odds ratio the same as relative risk?
No. They are different effect measures and can diverge when outcomes are common.