What this calculator does
Two-proportion z-test works out tests whether two independent samples have significantly different proportions. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formulaz = (p̂₁ − p̂₂) / √(p̄(1−p̄)(1/n₁+1/n₂)), p̄ = (x₁+x₂)/(n₁+n₂)
The inputs explained
| Field | What to enter |
|---|---|
| Group 1 successes | A number. Starts at 45. |
| Group 1 size | A number. Starts at 100. |
| Group 2 successes | A number. Starts at 30. |
| Group 2 size | A number. Starts at 100. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with group 1 successes
Every other input is held at the calculator’s starting values while group 1 successes varies. Select any row to load that scenario into the calculator.