Two Proportion Test Calculator

Calculator

Group 1 Label

Group 1 Successes

Group 1 Sample Size

Group 2 Label

Group 2 Successes

Group 2 Sample Size

Alternative Hypothesis

Null Difference

Alpha Level

Confidence Level Percent

Test Standard Error

Continuity Correction

Use count correction

Example Data Table

Group	Successes	Sample Size	Sample Proportion	Use Case
Treatment	58	200	0.2900	New landing page conversions
Control	42	190	0.2211	Old landing page conversions
Suggested setup	Two sided test, alpha 0.05, null difference 0, confidence 95%

Formula Used

Sample proportions: p1 = x1 / n1 and p2 = x2 / n2.

Pooled proportion: p = (x1 + x2) / (n1 + n2).

Pooled standard error: SE = sqrt[p(1 - p)(1 / n1 + 1 / n2)].

Unpooled standard error: SE = sqrt[p1(1 - p1) / n1 + p2(1 - p2) / n2].

Z statistic: z = [(p1 - p2) - null difference] / SE.

Confidence interval: (p1 - p2) ± z critical × unpooled SE.

Cohen h: h = 2asin(sqrt(p1)) - 2asin(sqrt(p2)).

How to Use This Calculator

Enter the success count and total sample size for both groups.
Choose a two sided or one sided alternative hypothesis.
Set the alpha level and confidence level.
Select pooled, unpooled, or automatic standard error handling.
Use continuity correction when you need a conservative count adjustment.
Press calculate and review the result above the form.
Download the CSV or PDF for your report.

Understanding a Two Proportion Test

A two proportion test compares two independent sample proportions. It asks whether the observed difference is likely from chance. The method is useful for surveys, experiments, audits, and quality checks. Each group must have a success count and a total count. The calculator turns those counts into sample proportions.

When to Use It

Use this test when the outcome has two categories. Examples include pass or fail, yes or no, clicked or did not click, and defective or acceptable. The samples should be independent. One person or item should not appear in both groups. Large samples work best. Small samples may need exact methods.

What the Result Means

The z score measures how far the observed difference is from the null difference. The p value shows the chance of seeing a result this extreme, assuming the null claim is true. A small p value gives evidence against the null hypothesis. The confidence interval gives a practical range for the difference between proportions.

Advanced Controls

This page includes one sided and two sided alternatives. It also supports pooled and unpooled standard errors. The pooled method is common when the null difference is zero. The unpooled method is often used for confidence intervals. A continuity correction can make the test more conservative for count data.

Practical Reading

Statistical significance is not the same as practical importance. A very large sample can make a tiny difference significant. Always review the effect size and the confidence interval width. The difference in proportions is often the clearest measure. Relative risk and odds ratio can also help when groups represent risk or conversion.

Data Quality Notes

Check your counts before using the result. Successes cannot exceed totals. The groups should be collected in similar ways. Biased sampling can create a misleading p value. Rounding can also affect reports. Keep the original counts with your exported result.

Reporting the Test

A good report includes both sample proportions, the difference, z score, p value, confidence interval, alternative hypothesis, and decision level. Mention whether a pooled or unpooled test was used. Add the context of the study. This makes the conclusion easier to review later. Use exports to keep the decision traceable for audits.

FAQs

What is a two proportion test?

It is a statistical test that compares two independent sample proportions. It checks whether their difference is larger than expected by random sampling variation.

When should I use the pooled standard error?

Use the pooled standard error when testing a zero difference between proportions. This is the common setup for a standard two proportion z test.

When should I use the unpooled standard error?

Use the unpooled standard error for confidence intervals. It is also helpful when testing a nonzero null difference between two proportions.

What does the p value mean?

The p value estimates how unusual the observed result is under the null hypothesis. Smaller values give stronger evidence against the null claim.

What is a good alpha level?

Many reports use 0.05. Some fields use 0.01 or 0.10. Choose alpha before reviewing the result to avoid biased conclusions.

What does the confidence interval show?

It gives a likely range for the true difference between the two population proportions. Wide intervals show more uncertainty.

What is continuity correction?

Continuity correction adjusts the observed difference for discrete count data. It usually makes the test more conservative.

Can this test prove causation?

No. The test shows statistical evidence for a difference. Causation depends on study design, randomization, controls, and data quality.