Calculate a Risk Difference with a Newcombe Interval

Define the direction of subtraction

Write the first group, second group, binary event, and common follow-up window. The risk difference is the first probability minus the second. A negative value can favor the first group for an undesirable event, while the interpretation reverses for a desirable outcome.

Check that both denominators represent the intended populations. Different follow-up opportunities, missing outcomes, or changes in event definitions can make a simple comparison misleading. Counts from matched observations or clustered samples do not satisfy the independent-binomial setup used by this calculator.

Name the uncertainty method

The statsmodels documentation for independent proportions distinguishes several confidence-interval approaches, including Newcombe. Specify the selected method rather than relying on a software default that might differ between implementations or versions.

The Newcombe approach used here combines the separate Wilson limits through square-root combinations of their distances from the observed proportions. It does not simply subtract one pair of Wilson endpoints. Keep the method description with the input counts and confidence level so another analyst can reproduce the result.

Recalculate a fictional comparison

Suppose group A has 40 events among 100 observations and group B has 20 among 100. The risk difference A minus B is 0.20, or 20 percentage points. It is not a 20% relative increase: the risk ratio for these numbers is 2, corresponding to a 100% relative increase.

For these fictional independent counts, the two-sided 95% Newcombe interval without continuity correction is approximately 0.07312 to 0.31851, or 7.31 to 31.85 percentage points. The risk-difference tool reproduces the calculation. This example concerns arithmetic, not a real treatment recommendation.

Audit reporting and limits

Use the effect-measure worksheet to preserve group order, event status, counts, uncertainty method, and exclusions. Report the underlying risks beside the difference; readers should not need to infer the baseline probability from an isolated contrast.

A confidence interval that does not include zero addresses a statistical comparison under the model. It does not determine whether the difference is clinically important, whether the comparison is causal, or whether a missing-data assumption is credible. Those judgments require the research context and a defensible analysis plan.

If considering a reciprocal measure such as number needed to treat, inspect the event direction, time horizon, and interval behavior before transforming. An interval crossing zero creates complications that a single reciprocal number can hide. Keep the original risk difference visible even when an additional measure is useful.

Finish with a reproducible statement of the two risks, signed difference, interval, and intended population. Explain any adjusted or design-specific analysis separately rather than implying this unadjusted calculator has accounted for it.

Source checked on 3 November 2026; fictional interval independently recalculated.