Ztest Proportions Calculator
Free Ztest proportions Calculator for hypothesis tests. Enter values to get step-by-step solutions with formulas and graphs.
Formula
z = (pฬโ - pฬโ) / โ(pฬ(1-pฬ)(1/nโ + 1/nโ))
The z-statistic is calculated by dividing the difference in sample proportions by the pooled standard error. The pooled proportion p-hat combines both samples under the null hypothesis assumption that the true proportions are equal.
Worked Examples
Example 1: A/B Test for Website Conversion
Problem: Version A: 120 conversions out of 1,500 visitors. Version B: 155 conversions out of 1,500 visitors. Test at ฮฑ = 0.05 (two-tailed).
Solution: p1 = 120/1500 = 0.0800, p2 = 155/1500 = 0.1033\nPooled p = (120+155)/(1500+1500) = 0.0917\nSE = โ(0.0917 ร 0.9083 ร (1/1500 + 1/1500)) = 0.01055\nz = (0.0800 - 0.1033) / 0.01055 = -2.209\np-value = 0.0272 (two-tailed)\n0.0272 < 0.05 โ Reject Hโ
Result: z = -2.209 | p-value = 0.027 | Significant โ Version B has higher conversion rate
Example 2: Clinical Trial Drug Effectiveness
Problem: Treatment group: 85 recoveries out of 200 patients. Control group: 60 recoveries out of 200 patients. Test at ฮฑ = 0.01 (right-tailed).
Solution: p1 = 85/200 = 0.425, p2 = 60/200 = 0.300\nPooled p = (85+60)/(200+200) = 0.3625\nSE = โ(0.3625 ร 0.6375 ร (1/200 + 1/200)) = 0.04808\nz = (0.425 - 0.300) / 0.04808 = 2.600\np-value = 0.0047 (right-tailed)\n0.0047 < 0.01 โ Reject Hโ
Result: z = 2.600 | p-value = 0.005 | Significant โ Treatment group has higher recovery rate
Frequently Asked Questions
How do I interpret the p-value in a proportions z-test?
The p-value represents the probability of observing a difference in sample proportions as extreme as (or more extreme than) the one calculated, assuming the null hypothesis is true (that the population proportions are actually equal). A small p-value, typically below 0.05, indicates that such an extreme result would be very unlikely if there were truly no difference, leading us to reject the null hypothesis. For example, a p-value of 0.03 means there is only a 3% chance of seeing the observed difference (or a larger one) if the proportions were actually equal. Importantly, the p-value does not tell you the probability that the null hypothesis is true, the magnitude of the practical effect, or whether the result is meaningful in a real-world context. Always consider the confidence interval and effect size alongside the p-value, as statistically significant results with very large samples may represent trivially small practical differences.
What formula does Ztest Proportions Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
Can I share or bookmark my calculation?
You can bookmark the calculator page in your browser. Many calculators also display a shareable result summary you can copy. The page URL stays the same so returning to it will bring you back to the same tool.
Can I use the results for professional or academic purposes?
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
Can I use Ztest Proportions Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.