Two Proportion Z Test Calculator
Tests equality of two independent proportions with a pooled null standard error. The form displays z=(p̂1−p̂2)/√(p̄(1−p̄)(1/n1+1/n2)) beside two-proportion z test, using a worked condition that can be recalculated with the labeled inputs.
Describe the observed sample during an independent check
Two-proportion z test
Interpreting the requested two-proportion z test
The two proportion z test page tests equality of two independent proportions with a pooled null standard error.
Two-proportion z test is limited to the statistical quantity named by the result panel. The two-proportion z test calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
Measurements required for two-proportion z test
- Group 1 successes: For two-proportion z test, 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 two-proportion z test conditions. The form enforces minimum 0.
- Group 1 trials: For two-proportion z test, 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 two-proportion z test conditions. The form enforces minimum 1.
- Group 2 successes: For two-proportion z test, 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 two-proportion z test conditions. The form enforces minimum 0.
- Group 2 trials: For two-proportion z test, 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 two-proportion z test conditions. The form enforces minimum 1.
The entries used for two-proportion z test must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid two-proportion z test arithmetic for a nonexistent study.
When the analysis changes, compare one proportion z test and chi square goodness of fit.
Working through the two proportion z test formula
For two-proportion z test, match every symbol in the relationship to a labeled field before substituting numbers. Two-proportion z test is reported in the scale implied by the inputs and formula.
While checking two-proportion z test, inspect every denominator in z=(p̂1−p̂2)/√(p̄(1−p̄)(1/n1+1/n2)). For two-proportion z test, a zero or near-zero denominator can make two-proportion z test undefined or unstable.
Checking the displayed example
The default two-proportion z test condition is Group 1 successes = 96 successes, Group 1 trials = 200 trials, Group 2 successes = 70 successes, Group 2 trials = 190 trials.
The example difference gives z≈2.23 and a two-sided p-value near 0.026.
The live calculator reports Observed difference 11.157895 percentage points · z statistic 2.2275543 · Two-sided p-value 0.02591016 · Pooled proportion 42.564103 %. Repeating one intermediate step from z=(p̂1−p̂2)/√(p̄(1−p̄)(1/n1+1/n2)) provides a fixed two-proportion z test reference check for later code changes.
Limits on interpreting two-proportion z test
The pooled standard error belongs to the null test; interval estimation ordinarily uses the separate observed proportions.
For two proportion z test, a p-value measures compatibility with a stated null model; it is not the probability that the null hypothesis is true and it does not measure practical importance.
A second check on two-proportion z test
When interpreting two proportion z test, pair the test result with the effect direction, effect size, uncertainty, sampling design, and the rule used for one-sided or two-sided inference.
As a second check for two-proportion z test, reversing the numerator and denominator answers a different question, so retain the direction printed in z=(p̂1−p̂2)/√(p̄(1−p̄)(1/n1+1/n2)).
Varying a single two proportion z test input at a time
Change group 1 successes while holding the remaining entries fixed, then state why the direction and size of the two-proportion z test change are plausible from z=(p̂1−p̂2)/√(p̄(1−p̄)(1/n1+1/n2)).
Repeat the two-proportion z test exercise with group 2 trials. If a modest defensible change materially alters the interpretation, report both conditions rather than presenting that two-proportion z test scenario as exact.
Mistakes to avoid in the two proportion z test setup
Before accepting two-proportion z test, compare every entered value with its label, unit, and allowed domain after reading the printed relationship from left to right.
For two-proportion z test, do not move a number between fields merely because the units look compatible; each label gives the number a different statistical role.
Another two-proportion z test failure occurs when a rounded output is reused as though it were the original measurement. Carry guard digits through calculations that depend on two-proportion z test, then round only the reported value.
A reproducible record of two-proportion z test
Report two-proportion z test using z=(p̂1−p̂2)/√(p̄(1−p̄)(1/n1+1/n2)), followed by the entered values, units, exclusions, and analysis date. Name the two-proportion z test population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including Observed difference 11.157895 percentage points · z statistic 2.2275543 · Two-sided p-value 0.02591016 · Pooled proportion 42.564103 %. A later two-proportion z test review can then distinguish a changed input from a different convention or software implementation.
Questions about two-proportion z test
Why could another program report a different two-proportion z test?
A different convention for rounding, tails, ties, interpolation, parameterization, or missing values can change two-proportion z test. Compare the printed two-proportion z test formula and its input definitions before treating either output as wrong.
What does two-proportion z test represent on this page?
It is the quantity produced by z=(p̂1−p̂2)/√(p̄(1−p̄)(1/n1+1/n2)) from the displayed group 1 successes, group 1 trials, group 2 successes, group 2 trials. This page tests equality of two independent proportions with a pooled null standard error.