Difference in Proportions Interval Calculator
Constructs an unpooled normal interval for the difference between two independent proportions. The example keeps the method and inputs visible so the result can be checked independently.
Enter the statistical summaries
Difference in proportions interval
Meaning of the displayed bounds before the result is reused
Constructs an unpooled normal interval for the difference between two independent proportions. The displayed result follows (p̂1−p̂2) ± z*√(p̂1q̂1/n1+p̂2q̂2/n2), with every symbol tied to a labeled input. That step separates arithmetic from interpretation.
The observed difference is about 11.16 percentage points, with a 95% interval near 1.41 to 20.90. This worked condition is a reproducible arithmetic check, not evidence that the model fits every dataset. That choice determines which comparison is defensible.
Interpretation of difference in proportions interval should follow the design that produced the inputs. Random assignment, random sampling, repeated measurements, matched pairs, and convenience observations support different conclusions even when they happen to produce the same statistic on this page.
Where the model applies during independent review
The interval standard error is unpooled even though an equal-proportions hypothesis test commonly pools under its null. This definition should travel with the copied result.
The unit of analysis, sampling frame, dependence structure, and treatment of missing values remain outside the final number. Record those choices before interpreting this interval. A reverse calculation can expose an inconsistency here.
Before accepting difference in proportions interval, compare the result with the scale of the raw measurement or event rate. A numerically small difference can matter on a tightly controlled scale, while a larger difference may be uninformative when ordinary variation is much wider. The substantive benchmark belongs beside the statistical calculation.
Which values belong in the fields
Check that counts are whole observations, scales refer to the same measurement, and standard errors or deviations come from the population or sample named on the page. A percentage and a proportion differ by a factor of 100. The calculation alone cannot supply that missing context.
If a critical value is entered, it must match the intended tail convention and reference degrees of freedom. Changing confidence level without changing that value creates a mislabeled result. The numerical precision does not override that requirement.
A boundary-case check under the stated design
Recalculate one intermediate quantity from (p̂1−p̂2) ± z*√(p̂1q̂1/n1+p̂2q̂2/n2) and then work backward from the displayed endpoint or statistic. This catches swapped groups, reversed quantiles, and copied denominators. The labeled fields make the assumption auditable.
Vary one credible input while holding the rest fixed. The direction and size of the change should agree with the formula before the result is carried into a report. This check belongs before rounding.
Coverage, evidence, and context in the worked condition
A confidence interval describes a procedure’s long-run coverage under its assumptions; it is not the probability that this fixed interval contains the parameter. The report should state this boundary plainly.
Practical importance requires the effect size, measurement scale, uncertainty, and consequences of a decision. A threshold crossing by itself does not supply that context. That distinction remains visible in the worked case.
A nearby procedure is one-sided proportion lower bound.
A method choice made from design before the result is reused
Sparse cells, strong skew, influential observations, clustering, pairing, estimated nuisance parameters, or unequal variances can change the reference distribution. The interval standard error is unpooled even though an equal-proportions hypothesis test commonly pools under its null. This point matters before the result enters another model.
Do not choose among methods by selecting the answer that looks most favorable. Choose from the data-generating design, then preserve the method name and convention. The answer should retain that convention.
Questions about the method for the stated inputs
When should difference in proportions interval be repeated?
Repeat it when an input, exclusion, group definition, confidence level, tail choice, or model assumption changes. For this page, the reported quantity is difference in proportions interval.
While checking group order, how many digits should be reported?
Retain guard digits during checking, then round to a level justified by the source measurement and the decision that follows. For this page, the reported quantity is difference in proportions interval.
When the result is reused, can a missing value be entered as zero?
Only when zero was observed. Missingness and a measured zero have different statistical meanings. For this page, the reported quantity is difference in proportions interval.
When the sample changes, does a narrow interval prove the estimate is unbiased?
No. Precision under a model does not repair selection, measurement, nonresponse, or specification bias. For this page, the reported quantity is difference in proportions interval.
For this result, what belongs in a reproducible record?
Save the input summaries or data, unit of analysis, formula convention, exclusions, unrounded output, and software or table method used. For this page, the reported quantity is difference in proportions interval.