Math
Two-sided z-test p-value
Calculate a two-sided standard-normal tail probability from a z statistic.
Calculators / Math / Two-proportion z statistic
Two-proportion z statistic calculator
Compare two independent observed proportions using a pooled normal-approximation statistic.
On this page
First minus second proportion20percentage points
Pooled z statistic2.83
Pooled standard error0.07
Calculator controls
How to calculate
Compare two independent observed proportions using a pooled normal-approximation statistic.
First minus second proportion =
(x1/n1-x2/n2)*100 percentage pointsPooled z statistic =
(x1/n1-x2/n2)/(sqrt(((x1+x2)/(n1+n2))*(1-((x1+x2)/(n1+n2)))*(1/n1+1/n2)))Pooled standard error =
sqrt(((x1+x2)/(n1+n2))*(1-((x1+x2)/(n1+n2)))*(1/n1+1/n2))Worked example
- First successes: 60
- First sample size: 100
- Second successes: 40
- Second sample size: 100
- First minus second proportion: 20 percentage points
- Pooled z statistic: 2.83
- Pooled standard error: 0.07
Assumptions and limits
Successes cannot exceed sample size. The null model assumes equal population proportions; small expected counts or dependent samples need other methods.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Compare two independent observed proportions using a pooled normal-approximation statistic. The z statistic is signed. Assess sample adequacy and the intended hypothesis before using a separate p-value calculator.
When this tool is useful
The z statistic is signed. Assess sample adequacy and the intended hypothesis before using a separate p-value calculator.
Understanding your inputs
| Input | Example |
|---|---|
First successes x1 | 60 |
First sample size n1 | 100 |
Second successes x2 | 40 |
Second sample size n2 | 100 |
Frequently asked questions
Which assumptions matter for this result?
Successes cannot exceed sample size. The null model assumes equal population proportions; small expected counts or dependent samples need other methods.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.