🧮 Odds Ratio Calculator
Calculate the odds ratio (OR) and 95% confidence interval (Woolf method) from a 2×2 case-control table. Includes interpretation of whether the exposure is a risk factor or protective.
Enter your 2×2 table (cases/controls × exposed/unexposed):
| Exposed | Unexposed | |
|---|---|---|
| Cases | ||
| Controls |
a = cases & exposed, b = cases & unexposed, c = controls & exposed, d = controls & unexposed
Odds Ratio Formulas
Frequently Asked Questions
An odds ratio compares the odds of an exposure among cases to the odds of the same exposure among controls. OR > 1 means the exposure is associated with increased odds of being a case (potential risk factor); OR < 1 means protective.
Odds ratios are typically used in case-control studies where you select on outcome status. Relative risk is used in cohort studies. For rare outcomes (prevalence < 10%), OR ≈ RR. For common outcomes, OR can substantially overestimate RR.
The Woolf (or Woolf-Haldane) method calculates the confidence interval for the odds ratio by working on the log scale. SE_ln(OR) = √(1/a + 1/b + 1/c + 1/d). The 95% CI is then back-transformed by exponentiation.
If the 95% CI for the OR includes 1.0, the result is not statistically significant at α = 0.05. This means you cannot rule out that the true OR = 1 (no association) based on the available data.
In a case-control study, OR is the appropriate measure. In a cohort study, relative risk (RR) is preferred. However, OR is still valid and calculable from any 2×2 table — it just may not be the most natural measure for the study design.
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