2×2 Contingency Table
| Outcome + (event) | Outcome − (no event) | |
|---|---|---|
| Exposed / Treatment | ||
| Unexposed / Control |
Enter a 2×2 table to get OR, RR, absolute risk reduction, NNT, and 95% confidence intervals.
| Outcome + (event) | Outcome − (no event) | |
|---|---|---|
| Exposed / Treatment | ||
| Unexposed / Control |
In a cohort study, 30 of 100 exposed people developed the illness, compared with 15 of 100 unexposed people. Enter a = 30, b = 70 (exposed: ill, not ill) and c = 15, d = 85 (unexposed).
Both intervals exclude 1, so the association is statistically significant at the 5% level. The intervals use the standard log method (Woolf for the odds ratio, Katz for the relative risk).
Relative risk (RR) compares the probability of an event between two groups: RR = risk in exposed ÷ risk in unexposed. Odds ratio (OR) compares the odds: OR = (a·d)/(b·c). For rare outcomes the two are close; for common outcomes the OR is more extreme than the RR.
Use relative risk for cohort studies and randomized trials, where you can measure risk directly. Use the odds ratio for case-control studies (where RR can't be estimated) and logistic regression. Report the point estimate with its 95% confidence interval.
The CI is a range of plausible values for the true OR or RR. If the interval excludes 1, the association is statistically significant at α = 0.05. A CI of [1.4, 3.8] means a real, positive association; a CI of [0.8, 2.1] crosses 1 and is not significant.
Absolute risk reduction (ARR) is the plain difference in risk between groups. Number needed to treat (NNT = 1/ARR) is how many people you'd need to treat to prevent one additional bad outcome — a very intuitive measure of clinical impact.