# Two Proportion Z Test Calculator

Compare two independent proportions with a pooled two-proportion Z test and confidence interval

> Canonical page: https://elysiatools.com/en/tools/two-proportion-z-test-calculator

- **Category:** Math & Numbers

- **Keywords:** two proportion z test, proportion difference, ab test, conversion rate, p value, calculator

## Overview

The Two Proportion Z Test Calculator allows you to compare two independent proportions to determine if there is a statistically significant difference between them. By inputting the number of successes and trials for two groups, you can instantly calculate the Z-statistic, P-value, and evaluate your null hypothesis using a pooled variance approach.

## Inputs

- **Group 1 Successes** (number)
- **Group 1 Trials** (number)
- **Group 2 Successes** (number)
- **Group 2 Trials** (number)
- **Hypothesized Difference** (number)
- **Alternative Hypothesis** (select)
- **Alpha** (number)
- **Decimal Places** (number)

## When to use

- When evaluating the results of an A/B test to see if a new variation significantly outperforms the control group.
- When comparing conversion rates, click-through rates, or success metrics between two independent demographic segments.
- When determining if the difference between two observed sample proportions is due to random chance or a true underlying effect.

## How it works

- Enter the number of successes and total trials for Group 1 and Group 2.
- Set your hypothesized difference (usually 0), alternative hypothesis (two-sided, greater, or less), and alpha level.
- The calculator computes the sample proportions, the pooled proportion, and the standard error.
- Review the resulting JSON output, which includes the Z-statistic, P-value, and a boolean indicating whether to reject the null hypothesis.

## Use cases

- Marketing teams analyzing A/B test data to decide which email subject line yields a higher open rate.
- Product managers comparing user conversion rates between a new checkout flow and the legacy system.
- Researchers evaluating the effectiveness of two different treatments based on the proportion of successful outcomes.

## Frequently asked questions

### What is a pooled two-proportion Z-test?

It is a statistical test used to determine if the difference between two independent sample proportions is significant, assuming the null hypothesis that the proportions are equal.

### What does the alpha value represent?

The alpha value, or significance level, is the probability of rejecting the null hypothesis when it is actually true. A common default is 0.05 (5%).

### Can I test for a specific difference other than zero?

Yes, you can adjust the 'Hypothesized Difference' input to test if the difference between the two proportions equals a specific non-zero value.

### What does 'rejectNull: true' mean in the output?

It means the calculated P-value is less than your specified alpha level, indicating a statistically significant difference between the two groups.

### What is the difference between a two-sided and one-sided test?

A two-sided test checks for any difference (greater or less) between the proportions, while a one-sided test checks for a difference in one specific direction.

## Related tools

- [Active Earth Pressure (Rankine)](https://elysiatools.com/en/tools/active-earth-pressure): Calculate the Rankine active earth pressure on a smooth vertical wall backfilled with cohesionless soil. K_a = tan²(45°−φ/2). Optional uniform surcharge q. Returns the base pressure p₀, the total force P, and the resultant height.
- [Bayes Theorem Calculator](https://elysiatools.com/en/tools/bayes-theorem-calculator): Calculate posterior probability P(A given B) using prior, likelihood, and false-positive rate
- [Bending Stress Calculator](https://elysiatools.com/en/tools/bending-stress-calculator): Calculate the maximum bending (flexural) stress σ_max = M·c/I = M/Z at the outermost fiber of a beam section. Supports solid circle, rectangle, hollow tube, and I-beam; computes I, section modulus Z, and distance c automatically. Stress in MPa.
- [Cantilever Beam Calculator](https://elysiatools.com/en/tools/cantilever-beam-calculator): Calculate the maximum bending moment M_max, maximum shear force V_max and free-end deflection δ_max of a cantilever beam under a free-end point load P or a uniformly distributed load q. Point load: δ = PL³/(3EI); UDL: δ = qL⁴/(8EI).
- [Factorial Calculator](https://elysiatools.com/en/tools/factorial-calculator): Calculate n! for a non-negative integer with exact BigInt output, optional steps, and related values such as trailing zeros
- [Fisher Exact Test Calculator](https://elysiatools.com/en/tools/fisher-exact-test-calculator): Run Fisher exact test for a 2 x 2 contingency table with exact one-sided or two-sided p-values
- [Kruskal-Wallis Calculator](https://elysiatools.com/en/tools/kruskal-wallis-calculator): Compare three or more independent groups with the nonparametric Kruskal-Wallis H test
- [Mann-Whitney U Test Calculator](https://elysiatools.com/en/tools/mann-whitney-u-test-calculator): Compare two independent samples with the nonparametric Mann-Whitney U rank-sum test

## Samples

- [Android Image Processing Java Samples](https://elysiatools.com/en/samples/android-image-processing-java): Android Java image processing examples including reading/saving images, scaling, and format conversion
- [Android Image Processing Kotlin Samples](https://elysiatools.com/en/samples/android-image-processing-kotlin): Android Kotlin image processing examples including reading/saving images, scaling, and format conversion
- [Web Image Processing Python Samples](https://elysiatools.com/en/samples/web-image-processing-python): Web Python image processing examples using PIL/Pillow including reading, saving, resizing, and format conversion
- [Web Image Processing Rust Samples](https://elysiatools.com/en/samples/web-image-processing-rust): Web Rust image processing examples including image read/save, scaling, and format conversion

## Related content

- [A/B Experiment Design, Sample Size, and Statistical Power](https://elysiatools.com/en/hubs/ab-testing-experiment-design-and-statistical-power): Plan an A/B experiment, size its evidence, select the right test, and review effect size and uncertainty before treating a result as actionable.