Difference in Proportions Interval Calculator
Constructs an unpooled normal interval for the difference between two independent proportions. The form displays (p̂1−p̂2) ± z*√(p̂1q̂1/n1+p̂2q̂2/n2) beside difference in proportions interval, using a worked condition that can be recalculated with the labeled inputs.
Enter the statistical summaries
Difference in proportions interval
The question behind difference in proportions interval
The difference in proportions interval page constructs an unpooled normal interval for the difference between two independent proportions.
Difference in proportions interval is limited to the statistical quantity named by the result panel. The difference in proportions interval calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
Reading the difference in proportions interval fields
- Group 1 successes: For difference in proportions interval, the worked value for group 1 successes is 96 successes. Treat the group 1 successes entry (96 successes) explicitly as a count, proportion, rate, estimate, or model parameter before comparing difference in proportions interval conditions. The form enforces minimum 0.
- Group 1 trials: For difference in proportions interval, the worked value for group 1 trials is 200 trials. Treat the group 1 trials entry (200 trials) explicitly as a count, proportion, rate, estimate, or model parameter before comparing difference in proportions interval conditions. The form enforces minimum 1.
- Group 2 successes: For difference in proportions interval, the worked value for group 2 successes is 70 successes. Treat the group 2 successes entry (70 successes) explicitly as a count, proportion, rate, estimate, or model parameter before comparing difference in proportions interval conditions. The form enforces minimum 0.
- Group 2 trials: For difference in proportions interval, the worked value for group 2 trials is 190 trials. Treat the group 2 trials entry (190 trials) explicitly as a count, proportion, rate, estimate, or model parameter before comparing difference in proportions interval conditions. The form enforces minimum 1.
- Critical z value: For difference in proportions interval, the worked value for critical z value is 1.96. Treat the critical z value entry (1.96) explicitly as a count, proportion, rate, estimate, or model parameter before comparing difference in proportions interval conditions. The form enforces minimum 0.
The entries used for difference in proportions interval must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid difference in proportions interval arithmetic for a nonexistent study.
Working through the difference in proportions interval formula
For difference in proportions interval, match every symbol in the relationship to a labeled field before substituting numbers. Difference in proportions interval is reported in percentage points.
While checking difference in proportions interval, inspect every denominator in (p̂1−p̂2) ± z*√(p̂1q̂1/n1+p̂2q̂2/n2). For difference in proportions interval, a zero or near-zero denominator can make difference in proportions interval undefined or unstable.
A reproducible difference in proportions interval case
The default difference in proportions interval condition is Group 1 successes = 96 successes, Group 1 trials = 200 trials, Group 2 successes = 70 successes, Group 2 trials = 190 trials, Critical z value = 1.96.
The observed difference is about 11.16 percentage points, with a 95% interval near 1.41 to 20.90.
The live calculator reports Estimate 11.157895 percentage points · Lower bound 1.4116121 percentage points · Upper bound 20.904177 percentage points · Margin 9.7462827 percentage points · Standard error 4.9725932 percentage points. Repeating one intermediate step from (p̂1−p̂2) ± z*√(p̂1q̂1/n1+p̂2q̂2/n2) provides a fixed difference in proportions interval reference check for later code changes.
What the difference in proportions interval arithmetic assumes
The interval standard error is unpooled even though an equal-proportions hypothesis test commonly pools under its null.
For difference in proportions interval, the interval is produced by a repeated-sampling procedure; it is not the probability that a fixed parameter lies inside these particular endpoints.
A nearby method may answer the next question: one-sided proportion lower bound.
How to interpret the difference in proportions interval output
When interpreting difference in proportions interval, coverage depends on the stated standard-error model, critical value, independence conditions, and any approximation used by the method.
As a second check for difference in proportions interval, reversing the numerator and denominator answers a different question, so retain the direction printed in (p̂1−p̂2) ± z*√(p̂1q̂1/n1+p̂2q̂2/n2).
Common failure modes for difference in proportions interval
Before accepting difference in proportions interval, compare every entered value with its label, unit, and allowed domain after reading the printed relationship from left to right.
For difference in proportions interval, do not move a number between fields merely because the units look compatible; each label gives the number a different statistical role.
Another difference in proportions interval failure occurs when a rounded output is reused as though it were the original measurement. Carry guard digits through calculations that depend on difference in proportions interval, then round only the reported value.
Rebuilding this difference in proportions interval calculation later
Report difference in proportions interval using (p̂1−p̂2) ± z*√(p̂1q̂1/n1+p̂2q̂2/n2), followed by the entered values, units, exclusions, and analysis date. Name the difference in proportions interval population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including Estimate 11.157895 percentage points · Lower bound 1.4116121 percentage points · Upper bound 20.904177 percentage points · Margin 9.7462827 percentage points · Standard error 4.9725932 percentage points. A later difference in proportions interval review can then distinguish a changed input from a different convention or software implementation.
Questions about difference in proportions interval
How should difference in proportions interval be rounded?
Keep the unrounded difference in proportions interval for subsequent arithmetic, then report only the precision supported by the source measurements and the decision context. Extra digits in difference in proportions interval do not correct sampling or model error.
Which input deserves the closest boundary check?
For difference in proportions interval, start with critical z value and then group 1 successes. Confirm the difference in proportions interval units and allowed domain because a valid-looking entry can still describe the wrong statistical setup.