Z Test Proportion Calculator

Calculator Form

Test Type

Alternative Hypothesis

Alpha

Confidence Level

Sample One Successes

Sample One Size

Hypothesized Proportion

Sample Two Successes

Sample Two Size

Null Difference

Continuity Correction

Apply correction

Example Data Table

Example	Successes	Sample Size	Null Value	Use Case
One sample	56	100	0.50	Check if a pass rate differs from 50%.
Two sample group one	56	100	0	Compare group one against group two.
Two sample group two	42	95	0	Measure the difference in sample proportions.

Formula Used

One Sample Proportion Test

The sample proportion is calculated as successes divided by sample size.

p̂ = x / n

SE = sqrt(p0 × (1 - p0) / n)

z = (p̂ - p0) / SE

Two Sample Proportion Test

The two sample test uses a pooled proportion for the test statistic.

p1 = x1 / n1

p2 = x2 / n2

pooled p = (x1 + x2) / (n1 + n2)

SE = sqrt(pooled p × (1 - pooled p) × (1/n1 + 1/n2))

z = ((p1 - p2) - null difference) / SE

P Value Rule

For a two tailed test, the p value doubles the upper tail area beyond the absolute z score.

How to Use This Calculator

Select one sample or two sample test.
Choose the alternative hypothesis.
Enter success counts and sample sizes.
Enter the null proportion or null difference.
Set alpha and confidence level.
Apply continuity correction only when needed.
Press the calculate button.
Download the result as CSV or PDF.

Understanding the Z Test Proportion Calculator

A z test for proportion checks whether a sample share supports a claimed population share. It also compares two independent sample shares. This calculator gives the z score, standard error, p value, confidence interval, and decision. It is useful when outcomes are binary. Examples include pass or fail, yes or no, defect or no defect.

When to Use It

Use a one sample test when you have one count and one claimed proportion. Use a two sample test when you compare two groups. The groups should be independent. Each sample should be large enough for a normal approximation. A common check is at least five expected successes and failures.

Why the Inputs Matter

The success count defines the observed sample proportion. The sample size controls precision. A larger sample gives a smaller standard error. The hypothesized proportion or null difference defines the value being tested. The alternative hypothesis controls the tail of the p value. The alpha value sets the rejection rule.

Reading the Results

The z score shows how far the observed result is from the null value. It is measured in standard errors. A large positive value supports a greater alternative. A large negative value supports a less alternative. The p value shows how unusual the result is if the null claim is true. If the p value is less than alpha, reject the null hypothesis.

Confidence Interval Notes

The confidence interval estimates a reasonable range for the true proportion or difference. It uses the unpooled standard error. The test for two proportions uses a pooled standard error under the null. This is standard because the null assumes equal proportions when the null difference is zero.

Practical Advice

Check your data before trusting the result. Counts must be whole numbers. Counts cannot exceed sample sizes. Avoid using this test for very small samples. Consider exact methods when expected counts are low. Use continuity correction only when you want a conservative adjustment for discrete counts.

For reporting, include the test type, alternative, z score, p value, confidence level, and final decision. Keep the original counts in your notes. Percentages alone hide the sample size and can make weak evidence look stronger than expected.

FAQs

What is a z test for proportion?

It is a hypothesis test for a population proportion. It compares an observed sample proportion with a claimed value or compares two independent sample proportions.

When should I use a one sample test?

Use it when one sample is compared with one claimed population proportion. For example, test whether a survey approval rate differs from 50%.

When should I use a two sample test?

Use it when two independent groups are compared. For example, compare conversion rates, pass rates, defect rates, or approval rates between two samples.

What does the z score mean?

The z score shows how many standard errors the observed proportion is from the null value. Larger absolute values show stronger evidence.

What does the p value mean?

The p value shows how unusual the result is under the null hypothesis. A smaller p value gives stronger evidence against the null.

What alpha value should I use?

A common alpha value is 0.05. It means you reject the null when the p value is below five percent.

Should I use continuity correction?

Continuity correction can make results more conservative. It is sometimes used because proportions are based on discrete success counts.

Can I download the results?

Yes. After calculation, use the CSV or PDF button. Both options save the main results for records or reports.