Calculator Form
Example Data Table
| Scenario | Test Type | x1 | n1 | x2 | n2 | Null Value | Tail | Alpha |
|---|---|---|---|---|---|---|---|---|
| Survey approval versus claim | One sample | 56 | 100 | - | - | p0 = 0.50 | Two sided | 0.05 |
| A/B conversion comparison | Two sample | 122 | 500 | 98 | 480 | d0 = 0 | Greater than | 0.05 |
| Defect rate below target | One sample | 7 | 250 | - | - | p0 = 0.04 | Less than | 0.01 |
Formula Used
One Sample Proportion Test
Sample proportion: p̂ = x / n
Test statistic: z = (p̂ - p0) / sqrt(p0(1 - p0) / n)
Wald interval: p̂ ± z* sqrt(p̂(1 - p̂) / n)
Two Sample Proportion Test
Sample proportions: p̂1 = x1 / n1 and p̂2 = x2 / n2
Pooled proportion: p̂ = (x1 + x2) / (n1 + n2)
Pooled standard error: sqrt(p̂(1 - p̂)(1 / n1 + 1 / n2))
Test statistic: z = ((p̂1 - p̂2) - d0) / SE
P Value Rules
Two sided: p = 2 × P(Z ≥ |z|)
Greater than: p = P(Z ≥ z)
Less than: p = P(Z ≤ z)
How To Use This Calculator
- Select one sample or two sample proportion testing.
- Choose the alternative hypothesis used in your problem.
- Enter successes and total observations for each required sample.
- Enter the null proportion or hypothesized difference.
- Set alpha and confidence level.
- Select pooled standard error when comparing two proportions with zero null difference.
- Press Calculate and read the z statistic, p value, and decision.
- Use the CSV or PDF button to save your report.
Understanding Proportion Tests
A proportion test checks whether a sample share supports a claimed population share. It is useful when each observation has two outcomes. Examples include pass or fail, yes or no, defect or good. This calculator turns counts into a z statistic, a p value, and a plain decision.
Why This Calculator Helps
Manual proportion testing can be slow. You must convert counts, choose the correct standard error, select a tail, and compare the p value with alpha. This tool keeps those steps together. It supports one sample tests and two sample comparisons. It also shows confidence intervals, effect size, and warning notes when assumptions may be weak.
One Sample Testing
Use a one sample test when one group is compared with a claimed rate. Enter successes, total trials, and the null proportion. The calculator estimates the sample proportion. Then it measures how far that estimate sits from the claim. A large distance produces a large absolute z score.
Two Sample Testing
Use a two sample test when two independent groups are compared. The calculator subtracts the second sample proportion from the first. It can use a pooled standard error for a zero difference null. It can also use an unpooled error for estimation work. This helps with classroom problems, quality checks, surveys, and A/B test reviews.
Interpreting Results
The p value measures how unusual the observed result is under the null hypothesis. A small p value gives stronger evidence against the null. If the p value is less than or equal to alpha, reject the null. If it is larger, do not reject it. This does not prove the null true. It means the evidence is not strong enough.
Good Practice
Use random samples when possible. Keep groups independent. Check expected successes and failures before trusting the normal approximation. Very small samples may need exact methods. Also compare statistical significance with practical importance. A tiny difference can be significant with a large sample, yet unimportant in real decisions.
Export And Record
After calculating, download a CSV file for spreadsheets. You can also create a simple PDF report. The exported report helps document inputs, formulas, and decisions for study notes, audits, and project files during future later review.
FAQs
What is a proportion test statistic?
It is a z score that measures how far a sample proportion is from a claimed proportion or another sample proportion.
When should I use a one sample proportion test?
Use it when one sample is compared with one claimed population proportion, such as a target approval rate.
When should I use a two sample proportion test?
Use it when comparing two independent groups, such as two campaigns, two products, or two survey groups.
What does the p value mean?
The p value shows how unusual the observed result is if the null hypothesis is true.
What does alpha mean?
Alpha is the rejection cutoff. Common values are 0.05, 0.01, and 0.10.
Should I use pooled standard error?
Use pooled standard error for a two sample test when the null difference is zero and groups are independent.
What is continuity correction?
It adjusts a discrete count test toward the null. It can be useful with smaller samples.
Can this replace exact binomial testing?
No. If expected counts are small, exact binomial or exact two proportion methods may be better.