Calculator
Enter two groups. The calculator tests whether their proportions differ significantly using a two-proportion z test.
Example Data Table
Use this sample to try the calculator quickly.
| Scenario | Successes | Sample Size | Observed Proportion |
|---|---|---|---|
| Landing Page A | 54 | 200 | 27.00% |
| Landing Page B | 38 | 210 | 18.10% |
| Observed difference | 8.90 percentage points | ||
Formula Used
The calculator compares two independent sample proportions. Group 1 is always subtracted from Group 2 as p1 - p2.
- The pooled proportion is used for the hypothesis test under the null hypothesis.
- The interval uses the unpooled standard error, which is standard practice.
- For one-tailed tests, the calculator shows a one-sided confidence bound.
- Continuity correction slightly shrinks the observed difference before computing z.
How to Use This Calculator
- Type a label for each group so the result is easier to read.
- Enter the number of successes and total sample size for both groups.
- Choose an alpha level, such as 0.05 for a 5% significance test.
- Select whether your test is two-tailed, right-tailed, or left-tailed.
- Optional: enable continuity correction for a slightly more conservative z statistic.
- Pick the number of decimal places you want in the output.
- Click Calculate Difference Test to show the result above the form.
- Review the decision, p value, interval, assumption note, and chart.
- Use the CSV or PDF buttons to export the summary for reports.
FAQs
1. What does this calculator test?
It tests whether two independent sample proportions differ significantly. Examples include conversion rates, pass rates, defect rates, or response rates across two groups or treatments.
2. When should I use a two-proportion z test?
Use it when each observation falls into success or failure, the groups are independent, and both samples are large enough for the normal approximation to be reasonable.
3. Why does the calculator use a pooled proportion?
The pooled proportion matches the null hypothesis that the two population proportions are equal. It gives the standard error used in the z test statistic.
4. What does a p value mean here?
The p value measures how unusual your observed difference would be if the null hypothesis were true. Smaller values provide stronger evidence against equal proportions.
5. What if the confidence interval includes zero?
If zero lies inside the interval, the data do not show a clear difference at that confidence level. The observed gap may be due to sampling variation.
6. Should I use continuity correction?
Continuity correction makes the z statistic slightly more conservative. It is optional, but some instructors or analysts prefer it for count-based proportion tests.
7. What does Cohen’s h tell me?
Cohen’s h describes practical effect size. It helps you judge whether the difference is tiny, small, medium, or large beyond simple statistical significance.
8. Can I trust results with very small samples?
Be cautious. Small counts can weaken the normal approximation. When success or failure counts are below 5, exact methods are often better than z-based methods.