📚 Trusted by students, educators & researchers since 2017.
Z-Test for Proportions Calculator
Determine if the difference between percentage-based outcomes is statistically significant. Select your test type, enter your sample sizes and successes, and instantly calculate the Z-statistic and p-value.
How to use this calculator
- Select your test type:
- Two-Sample (Independent): Compares the proportions of two separate groups (e.g., Group A had a 12% success rate, Group B had a 15% success rate. Is that difference real?).
- One-Sample: Compares the proportion of a single sample against a known or hypothesized population proportion.
- Enter your data: Enter the total number of trials or observations ($n$) and the number of “successes” ($x$). A success is just the event you are measuring (e.g., a click, a vote, a purchase).
- Set your parameters: Choose your significance level ($\alpha$) and whether you are running a one-tailed or two-tailed test. Two-tailed at $\alpha = 0.05$ is the default for most standard research and A/B testing.
Z-Test for Proportions
Determine statistical significance between percentages.
Z-Statistic
0
P-Value
0
Difference
0%
*Technical note: This test relies on the normal approximation to the binomial distribution. Ensure your sample is sufficiently large (typically np ≥ 5 and n(1-p) ≥ 5).
Understanding Your Results
A Z-test for proportions helps you determine if a difference in percentages is mathematically significant or just the result of random chance.
- Z-Statistic ($z$): A measure of how many standard deviations the observed proportion is away from the expected proportion (or how far the two samples are from each other). A larger absolute Z-score indicates a more significant difference.
- P-Value: The probability of observing this difference (or larger) if the null hypothesis were true.
- Conclusion: If the p-value is less than your chosen significance level, you reject the null hypothesis and conclude that the difference between the proportions is statistically significant.