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Two Proportion Z-Test Calculator

Compare success rates in two independent groups using a pooled two-proportion z-test.

Data stays on this deviceConvention explained below
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Data explorer

Check the dataset and sample convention before interpreting results.

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Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter successes in a, trials in a, successes in b, trials in b, alternative hypothesis, significance level.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

Input reference and sample values

Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.

InputFormat and unitsSample
Successes in AWhole numbers only. Zero or positive. Maximum: 1000000.50
Trials in AWhole numbers only. Minimum: 1. Maximum: 1000000.100
Successes in BWhole numbers only. Zero or positive. Maximum: 1000000.35
Trials in BWhole numbers only. Minimum: 1. Maximum: 1000000.100
Alternative hypothesisChoose Two-sided: different / One-sided: greater / One-sided: less.Two-sided: different
Significance levelNumeric value. Minimum: 0.0001. Maximum: 0.2.0.05

Result for these sample inputs

0.0319052552 probability
Test statistic
2.14559562
Degrees of freedom
Normal approximation
Decision at chosen alpha
Reject the null hypothesis
Success rate A
0.5
Success rate B
0.35
Difference in percentage points
15

The p-value is not the probability that the null hypothesis is true. Choose the hypothesis and significance level before inspecting the result; statistical significance does not measure practical importance.

Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.

The method, explained

Pool successes across both groups. SE = sqrt[p pooled × (1−p pooled) × (1/nA+1/nB)]. z = (pA−pB)/SE.

A WORKED EXAMPLE

Using successes in a = 50, trials in a = 100, successes in b = 35, trials in b = 100, alternative hypothesis = two, significance level = 0.05, the result is 0.0319052552 probability. Change these example inputs to match your task; use the method above to check each step.

What to keep in mind

Independent binomial groups, no repeated users across groups, no continuity correction. Repeatedly checking results during a running experiment changes false-positive behavior. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Reference: NIST: statistical methods handbook

Common questions

Can I use this for conversion-rate comparisons?

Yes, when observations are independent and each group has a success count and trial count. Ensure the same user is not counted repeatedly as independent evidence.

Why does it pool the two rates?

The null model assumes equal population proportions. The pooled success rate estimates that common proportion for the standard error used by this test.

Methodology maintained by ClarityKit. How these tools are built and checked.