Calculator
Example Data Table
| Scenario | Successes | Sample Size | Null Value | Suggested Test |
|---|---|---|---|---|
| Website conversion check | 58 | 100 | 0.50 | One sample, two tailed |
| Two landing pages | 42 and 33 | 100 and 100 | 0 difference | Two sample, two tailed |
| Defect rate improvement | 21 | 300 | 0.10 | One sample, left tailed |
Formula Used
One Sample Proportion Test
Sample proportion: p̂ = x / n
Standard error under the null: SE = sqrt[p0(1 - p0) / n]
Z statistic: z = (p̂ - p0) / SE
Two Sample Proportion Test
Group proportions: p̂1 = x1 / n1 and p̂2 = x2 / n2
Pooled proportion: pc = (x1 + x2) / (n1 + n2)
Pooled standard error: SE = sqrt[pc(1 - pc)(1 / n1 + 1 / n2)]
Z statistic: z = [(p̂1 - p̂2) - d0] / SE
P Value
The p value is found from the standard normal curve. The selected tail controls the area used.
How to Use This Calculator
- Select one sample or two sample testing.
- Choose the alternative hypothesis direction.
- Enter alpha, counts, sample sizes, and null values.
- Select the confidence interval method.
- Use continuity correction when a conservative normal test is preferred.
- Press Calculate to show results above the form.
- Use CSV or PDF buttons to save your report.
About Proportion Stat Tests
What Is a Proportion Test?
A proportion test checks whether observed sample counts support a claim about a population rate. It works with events that have two outcomes. Examples include pass or fail, yes or no, and defective or good. The calculator converts successes and sample size into a sample proportion. Then it compares that value with the null claim. Always report assumptions, alpha, sample design, and practical meaning.
Why This Calculator Helps
Manual proportion testing can be slow. Small setup errors can change the result. This tool keeps each step visible. It shows the sample rate, standard error, z score, p value, confidence interval, effect size, and decision. It also checks basic assumptions, such as expected successes and failures.
One Sample Testing
Use the one sample option when one group is compared with a known or claimed proportion. Enter successes, total observations, and the null proportion. Choose a left, right, or two tailed test. The tool uses the null standard error for the test statistic. It can also apply a continuity correction when you want a more conservative normal approximation.
Two Sample Testing
Use the two sample option when two independent groups are compared. Enter successes and totals for both groups. The calculator finds the difference between sample proportions. It can use pooled or unpooled standard error for the test. Pooled error is common when the null difference is zero.
Interpreting Results
The p value measures how unusual the observed result is under the null hypothesis. A small p value gives evidence against the null claim. The decision compares the p value with alpha. A confidence interval shows a reasonable range for the population proportion or difference. If a two tailed interval excludes the null value, it supports rejection at the matching level.
Good Practice
Use counts from a random or well designed sample. Keep groups independent. Avoid treating repeated measures as separate people or items. Check that expected counts are not too small. When counts are low, exact methods may be better. This calculator is intended for normal approximation testing and clear educational reporting.
FAQs
What is a proportion test?
A proportion test checks whether a sample proportion supports or rejects a claim about a population proportion. It uses counts, sample size, and a null value.
When should I use a one sample test?
Use it when one sample is compared with a known or claimed rate. For example, compare a pass rate with a stated target value.
When should I use a two sample test?
Use it when you compare two independent groups. Examples include two ads, two treatments, two stores, or two product versions.
What does the p value mean?
The p value shows how unusual the observed result is if the null hypothesis is true. Smaller values give stronger evidence against the null.
What alpha value should I use?
Many reports use 0.05. You can enter another value when your study, class, policy, or risk level requires a different cutoff.
What is continuity correction?
Continuity correction adjusts a discrete count problem before using a normal curve. It can make the test more conservative in some cases.
Which confidence interval method is best?
Wilson is often a strong default for one proportion. Wald is simple, but it can perform poorly with small samples or extreme proportions.
Can this replace exact tests?
No. This calculator uses normal approximation methods. If counts are very small, exact binomial or Fisher methods may be more suitable.