StatReason

Difference in Proportions Confidence Interval

Estimate how far apart two independent proportions, such as two conversion rates or two event rates, actually are, with an interval built from each group's own Wilson score interval rather than a plain Wald approximation.

What this answers

This calculator answers "by how much do these two rates actually differ, and how precisely can that gap be pinned down?" reporting an absolute risk difference (Group A's rate minus Group B's rate), not a ratio. Report the ratio instead with the Risk Ratio Confidence Interval Calculator if that framing fits your question better.

How it is calculated

Rather than using the classic Wald interval (which performs poorly near 0 or 1 and with small samples), this calculator builds a Newcombe-Wilson interval: each group's own Wilson score confidence bound is computed first, and those bounds are then combined to bracket the difference. This is the same construction used inside the site's Two-Proportion z-Test, exposed here as its own standalone estimation engine for when you want the interval without running a formal significance test.

Worked example

For 5 successes out of 10 trials in Group A and 3 out of 10 in Group B, the observed difference is .5 minus .3, or .2. With such small samples, the resulting 95% interval is wide, typically spanning both negative and positive values, a useful reminder that a 20 percentage-point observed gap from only 10 trials per group carries substantial sampling uncertainty.

Assumption audit

Calculated from your data: each group's observed proportion, the absolute difference, and each group's own Wilson score bounds feeding into the combined interval.
Evidence to review: whether both groups have a reasonably large sample size; with very small trial counts in either group, this interval will be wide enough that almost any conclusion beyond "inconclusive" is premature.
You must verify: that each group's trials are independent of one another and that the two groups were exposed to genuinely comparable conditions except for whatever difference you are estimating.

What this interval does not mean

An interval that excludes 0 suggests a real difference between the two rates at your chosen confidence level, but it does not by itself say whether that difference is practically meaningful; a technically significant but tiny percentage-point gap may not matter for your decision. An interval that includes 0 does not prove the two rates are equal, only that the data cannot rule out equality at this sample size.

Limitations

This interval reports an absolute risk difference, which can be harder to compare across studies with very different baseline rates than a relative measure like a risk ratio or odds ratio; consider reporting both when baseline rates differ substantially between contexts you are comparing.