One Proportion Z Test Calculator
Tests an observed binomial proportion against a null proportion using the null standard error. The form displays z=(p̂−p0)/√(p0(1−p0)/n) beside one-proportion z test, using a worked condition that can be recalculated with the labeled inputs.
Enter the statistical summaries before reporting
One-proportion z test
The question behind one-proportion z test
The one proportion z test page tests an observed binomial proportion against a null proportion using the null standard error.
One-proportion z test is limited to the statistical quantity named by the result panel. The one-proportion z test calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
Reading the one proportion z test fields
- Successes: For one-proportion z test, the worked value for successes is 118 successes. Treat the successes entry (118 successes) explicitly as a count, proportion, rate, estimate, or model parameter before comparing one-proportion z test conditions. The form enforces minimum 0.
- Trials: For one-proportion z test, the worked value for trials is 220 trials. Treat the trials entry (220 trials) explicitly as a count, proportion, rate, estimate, or model parameter before comparing one-proportion z test conditions. The form enforces minimum 1.
- Null proportion: For one-proportion z test, the worked value for null proportion is 50 %. Treat the null proportion entry (50 %) explicitly as a count, proportion, rate, estimate, or model parameter before comparing one-proportion z test conditions. The form enforces minimum 0.0001, maximum 99.9999.
The entries used for one-proportion z test must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid one-proportion z test arithmetic for a nonexistent study.
Working through the one proportion z test formula
For one-proportion z test, match every symbol in the relationship to a labeled field before substituting numbers. One-proportion z test is reported in the scale implied by the inputs and formula.
While checking one-proportion z test, inspect every denominator in z=(p̂−p0)/√(p0(1−p0)/n). For one-proportion z test, a zero or near-zero denominator can make one-proportion z test undefined or unstable.
For a related comparison, continue with pooled two sample t test.
Worked values for one-proportion z test
The default one-proportion z test condition is Successes = 118 successes, Trials = 220 trials, Null proportion = 50 %.
The example estimate is 53.64%, giving z≈1.08 and a two-sided p-value near 0.280.
The live calculator reports Observed proportion 53.636364 % · z statistic 1.0787198 · Two-sided p-value 0.28071274. Repeating one intermediate step from z=(p̂−p0)/√(p0(1−p0)/n) provides a fixed one-proportion z test reference check for later code changes.
What the one proportion z test arithmetic assumes
Expected successes and failures under the null should be large enough for the normal approximation.
For one 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 one-proportion z test
When interpreting one 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 one-proportion z test, reversing the numerator and denominator answers a different question, so retain the direction printed in z=(p̂−p0)/√(p0(1−p0)/n).
Testing how stable one-proportion z test is
Change successes while holding the remaining entries fixed, then state why the direction and size of the one-proportion z test change are plausible from z=(p̂−p0)/√(p0(1−p0)/n).
Repeat the one-proportion z test exercise with null proportion. If a modest defensible change materially alters the interpretation, report both conditions rather than presenting that one-proportion z test scenario as exact.
Where a plausible one-proportion z test can go wrong
Before accepting one-proportion z test, compare every entered value with its label, unit, and allowed domain after reading the printed relationship from left to right.
For one-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 one-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 one-proportion z test, then round only the reported value.
Rebuilding this one proportion z test calculation later
Report one-proportion z test using z=(p̂−p0)/√(p0(1−p0)/n), followed by the entered values, units, exclusions, and analysis date. Name the one-proportion z test population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including Observed proportion 53.636364 % · z statistic 1.0787198 · Two-sided p-value 0.28071274. A later one-proportion z test review can then distinguish a changed input from a different convention or software implementation.
Questions about one-proportion z test
What should be saved with one-proportion z test?
Save the entered values and units for successes, trials, null proportion, along with the analysis date, exclusions, software or formula version, and the relationship z=(p̂−p0)/√(p0(1−p0)/n). That record is sufficient to rebuild this specific one-proportion z test calculation.
Does one-proportion z test establish a causal or population conclusion?
No. The displayed one proportion z test value is conditional on the entered data and named method. The one-proportion z test design, measurement process, and assumptions determine what can be concluded beyond those values.
How should one-proportion z test be rounded?
Keep the unrounded one-proportion z test for subsequent arithmetic, then report only the precision supported by the source measurements and the decision context. Extra digits in one-proportion z test do not correct sampling or model error.