Difference of Proportions Confidence Interval
Estimate an interval for one population proportion minus another.
How the difference of proportions confidence interval works
A difference-of-proportions interval compares two independent rates while retaining the direction of group one minus group two. Each sample proportion contributes its own binomial variance divided by sample size. The square root of their sum is the unpooled standard error, which is multiplied by a z critical value and placed around the observed difference.
The defaults have 60 successes from 100 in group one and 45 from 100 in group two. Their observed proportions are 0.60 and 0.45, giving difference 0.15. The verified 95 percent standard error is about 0.069821 and margin 0.136850, producing endpoints 0.013150 and 0.286850.
Reading difference of proportions confidence interval results privately
Both samples should be independent, and success and failure counts should be large enough for a normal approximation. Sparse counts call for exact or score-based methods. The interval is unpooled because it estimates a difference; hypothesis-test standard errors may pool under a null equality assumption. Group order controls the sign but not interval width. This difference of proportions confidence interval calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
Why is this standard error unpooled?
An interval estimates each population proportion separately, so each observed proportion supplies its own variance term.
What does an interval containing zero mean?
Zero difference remains compatible with the data at the selected confidence level under this approximation.
Is the difference of proportions confidence interval private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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