Two Proportion Z Test Calculator

Select null and alternative hypotheses:

Sample 1

Number of Successes

How many in Sample 1 had the outcome you're testing for.

Sample Size

Total number of people or items in Sample 1.

Sample 2

Number of Successes

How many in Sample 2 had the outcome you're testing for.

Sample Size

Total number of people or items in Sample 2.

Significance Level (α)

Your risk tolerance for a false positive — 0.05 is standard.

About This Test

What Is the Two-Proportion Z-Test?

The two-proportion Z-test compares the proportion of a binary outcome — success or failure, yes or no — between two independent groups, to check whether the difference you're seeing is real or just random variation.

When to Use It

Comparing conversion rates between two landing pages or campaigns (A/B testing)
Comparing response rates between two treatment groups in a clinical trial
Comparing defect rates between two production lines
Any situation with two independent samples and a yes/no outcome

The Formula

\[ Z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\bar{p}(1-\bar{p})\left(\dfrac{1}{n_1}+\dfrac{1}{n_2}\right)}} \] \[ \bar{p} = \frac{x_1+x_2}{n_1+n_2} \]

Worked Example

A team compares conversion rates on two landing pages. Page A converts 50 out of 500 visitors. Page B converts 65 out of 500 visitors. At α = 0.05, is the difference significant?

\( \hat{p}_1 = 50/500 = 0.10, \ \hat{p}_2 = 65/500 = 0.13 \)
Pooled proportion: \( \bar{p} = (50+65)/(500+500) = 0.115 \)
Standard error ≈ 0.0202
\( Z \approx -1.49 \), two-tailed p-value ≈ 0.137
Since 0.137 > 0.05, we fail to reject H₀ — the difference isn't statistically significant at this sample size.

Your Results

Use it when there are two proportion values given!

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Two Proportion Z Test Calculator

Sample 1

Sample 2

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