Pooled Proportion Calculator
Combines successes and trials from two groups into one pooled proportion. The form displays ppool = (x1 + x2) / (n1 + n2) beside pooled proportion, using a worked condition that can be recalculated with the labeled inputs.
Enter the planning assumptions in this example
Pooled proportion
Interpreting the requested pooled proportion
The pooled proportion page combines successes and trials from two groups into one pooled proportion.
Pooled proportion is limited to the statistical quantity named by the result panel. The pooled proportion calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
Measurements required for pooled proportion
- Group 1 successes: For pooled proportion, the worked value for group 1 successes is 160 successes. Treat the group 1 successes entry (160 successes) explicitly as a count, proportion, rate, estimate, or model parameter before comparing pooled proportion conditions. The form enforces minimum 0.
- Group 1 size: For pooled proportion, the worked value for group 1 size is 400 observations. Treat the group 1 size entry (400 observations) explicitly as a count, proportion, rate, estimate, or model parameter before comparing pooled proportion conditions. The form enforces minimum 1.
- Group 2 successes: For pooled proportion, the worked value for group 2 successes is 119 successes. Treat the group 2 successes entry (119 successes) explicitly as a count, proportion, rate, estimate, or model parameter before comparing pooled proportion conditions. The form enforces minimum 0.
- Group 2 size: For pooled proportion, the worked value for group 2 size is 350 observations. Treat the group 2 size entry (350 observations) explicitly as a count, proportion, rate, estimate, or model parameter before comparing pooled proportion conditions. The form enforces minimum 1.
The entries used for pooled proportion must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid pooled proportion arithmetic for a nonexistent study.
Following the pooled proportion relationship
For pooled proportion, match every symbol in the relationship to a labeled field before substituting numbers. Pooled proportion is reported in %.
While checking pooled proportion, inspect every denominator in ppool = (x1 + x2) / (n1 + n2). For pooled proportion, a zero or near-zero denominator can make pooled proportion undefined or unstable.
A reproducible pooled proportion case
The default pooled proportion condition is Group 1 successes = 160 successes, Group 1 size = 400 observations, Group 2 successes = 119 successes, Group 2 size = 350 observations.
A total of 279 successes among 750 observations gives a pooled proportion of 37.2 percent.
The live calculator reports Pooled proportion 37.2 % · Total successes 279 · Total observations 750. Repeating one intermediate step from ppool = (x1 + x2) / (n1 + n2) provides a fixed pooled proportion reference check for later code changes.
The surrounding workflow may also require difference in proportions standard error and cluster design effect.
Limits on interpreting pooled proportion
Pooling is appropriate only for a question that treats both groups as sharing one proportion, such as the null standard error in a two-proportion test.
For pooled proportion, a planning or survey quantity is only as defensible as its frame, response assumptions, clustering, and population definition.
How to interpret the pooled proportion output
When interpreting pooled proportion, changing a design effect, allocation rule, response rate, or finite-population boundary can matter more than another displayed decimal.
As a second check for pooled proportion, reversing the numerator and denominator answers a different question, so retain the direction printed in ppool = (x1 + x2) / (n1 + n2).
Varying a single pooled proportion input at a time
Change group 1 successes while holding the remaining entries fixed, then state why the direction and size of the pooled proportion change are plausible from ppool = (x1 + x2) / (n1 + n2).
Repeat the pooled proportion exercise with group 2 size. If a modest defensible change materially alters the interpretation, report both conditions rather than presenting that pooled proportion scenario as exact.
Mistakes to avoid in the pooled proportion setup
Before accepting pooled proportion, compare every entered value with its label, unit, and allowed domain after reading the printed relationship from left to right.
For pooled proportion, do not move a number between fields merely because the units look compatible; each label gives the number a different statistical role.
Another pooled proportion failure occurs when a rounded output is reused as though it were the original measurement. Carry guard digits through calculations that depend on pooled proportion, then round only the reported value.
Documenting the pooled proportion result
Report pooled proportion using ppool = (x1 + x2) / (n1 + n2), followed by the entered values, units, exclusions, and analysis date. Name the pooled proportion population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including Pooled proportion 37.2 % · Total successes 279 · Total observations 750. A later pooled proportion review can then distinguish a changed input from a different convention or software implementation.
Questions about pooled proportion
Why could another program report a different pooled proportion?
A different convention for rounding, tails, ties, interpolation, parameterization, or missing values can change pooled proportion. Compare the printed pooled proportion formula and its input definitions before treating either output as wrong.
What does pooled proportion represent on this page?
It is the quantity produced by ppool = (x1 + x2) / (n1 + n2) from the displayed group 1 successes, group 1 size, group 2 successes, group 2 size. This page combines successes and trials from two groups into one pooled proportion.
What should be saved with pooled proportion?
Save the entered values and units for group 1 successes, group 1 size, group 2 successes, group 2 size, along with the analysis date, exclusions, software or formula version, and the relationship ppool = (x1 + x2) / (n1 + n2). That record is sufficient to rebuild this specific pooled proportion calculation.