Calculator
Formula Used
One mean z: z = (x̄ - μ0) / (σ / √n).
One mean t: t = (x̄ - μ0) / (s / √n), df = n - 1.
Two mean Welch t: t = ((x̄1 - x̄2) - Δ0) / √(s1²/n1 + s2²/n2).
One proportion z: z = (p̂ - p0) / √(p0(1 - p0) / n).
Two proportion z: z = (p̂1 - p̂2) / √(p pooled(1 - p pooled)(1/n1 + 1/n2)).
Chi square variance: χ² = (n - 1)s² / σ0².
F variance: F = s1² / s2².
How To Use This Calculator
Select the test method first. Choose the tail that matches your alternative hypothesis. Enter alpha as a decimal value. Fill only the fields needed for your selected test. Manual modes need the statistic and degrees of freedom. Press calculate. Read the statistic, p value, and decision above the form. Use the CSV or PDF button to save the result.
Example Data Table
| Test | Input Example | Use Case |
|---|---|---|
| One sample t | Mean 52.4, μ0 50, s 8.2, n 36 | Check whether a sample mean differs from a claim. |
| Two proportion z | x1 56, n1 100, x2 44, n2 95 | Compare two conversion rates or success rates. |
| F variance | s1 8.2, n1 36, s2 7.8, n2 40 | Compare variation between two independent groups. |
Why This Calculator Helps
Hypothesis testing can feel slow when every test uses a different statistic. This calculator brings common tests into one place. You can compare a sample with a claimed value. You can compare two groups. You can also enter a known statistic directly. The result gives the statistic, distribution, degrees of freedom, p value, and decision.
Better Testing Workflow
A good test starts with a clear null hypothesis. The null states the value or equality being checked. The alternative states the expected direction. Choose two tailed when any difference matters. Choose left tailed when smaller values support the claim. Choose right tailed when larger values support the claim.
Supported Methods
The tool supports z tests for means when population standard deviation is known. It supports t tests when sample standard deviation is used. It supports proportion tests with counts. It also supports chi square variance tests and F variance ratio tests. The manual mode helps when a textbook or software already provides the statistic.
Reading The P Value
The p value measures how unusual the observed statistic is if the null hypothesis is true. A small p value gives stronger evidence against the null. Compare it with the chosen alpha level. Many studies use 0.05. Sensitive work may use 0.01 or another planned level.
Practical Checks
Always check assumptions before trusting a result. Large samples make z proportion tests more stable. Small mean tests need roughly normal data. Two sample t tests often work best with Welch degrees of freedom. F tests can react strongly to nonnormal data. Use the output as a guide, not as automatic proof.
Export And Review
The CSV option stores the main fields in a spreadsheet friendly format. The PDF option makes a compact report for notes or sharing. Keep the report with your data source, test purpose, and chosen alpha. This makes the analysis easier to audit later. It also helps explain decisions to readers.
Common Mistakes
Do not switch tails after seeing the result. Do not mix population standard deviation with sample standard deviation. Avoid rounding too early. Enter counts for proportion tests, not percentages. Report the statistic and p value together, because both describe the evidence clearly.
FAQs
What is a test statistic?
A test statistic converts sample evidence into a standardized value. It shows how far the observed result is from the null hypothesis under the chosen test model.
What is a p value?
A p value is the probability of getting evidence this extreme, or more extreme, when the null hypothesis is true.
When should I use a z test?
Use a z test for means when the population standard deviation is known. Use it for proportions when sample counts support normal approximation.
When should I use a t test?
Use a t test when the population standard deviation is unknown and sample standard deviation estimates spread. It is common for mean tests.
What does two tailed mean?
Two tailed means the alternative checks for difference in either direction. Large positive and large negative statistics can both count as evidence.
What alpha should I choose?
Many analyses use 0.05. Choose alpha before testing. Use stricter values when false positives carry higher risk.
Does a small p value prove the claim?
No. A small p value shows evidence against the null. It does not prove causation, importance, or data quality.
Can I download the result?
Yes. Use the CSV button for spreadsheet use. Use the PDF button for a compact report.