Calculator
Example Data Table
| Use case | Test | Null value | Sample inputs | Tail | Alpha |
|---|---|---|---|---|---|
| Compare one class mean with 50 | One mean t test | 50 | x̄ = 53.2, s = 12.5, n = 64 | Two-tailed | 0.05 |
| Compare two conversion rates | Two proportions z test | 0 | 42/64 and 31/58 | Right-tailed | 0.05 |
| Test a standard deviation claim | One variance chi-square test | 12 | s = 12.5, n = 64 | Two-tailed | 0.05 |
Formula Used
The calculator chooses the formula from the selected hypothesis test.
- One mean z: z = (x̄ - μ₀) / (σ / √n)
- One mean t: t = (x̄ - μ₀) / (s / √n)
- Two means z: z = [(x̄₁ - x̄₂) - Δ₀] / √(σ₁²/n₁ + σ₂²/n₂)
- Welch t: t = [(x̄₁ - x̄₂) - Δ₀] / √(s₁²/n₁ + s₂²/n₂)
- Paired t: t = (d̄ - d₀) / (sᵈ / √n)
- One proportion z: z = (p̂ - p₀) / √[p₀(1 - p₀) / n]
- Two proportions z: z = [(p̂₁ - p̂₂) - Δ₀] / SE
- One variance: χ² = (n - 1)s² / σ₀²
- Two variances: F = (s₁² / s₂²) / R₀
How to Use This Calculator
- Select the hypothesis test that matches your research question.
- Choose the alternative tail and enter the alpha level.
- Enter the null value required by that test.
- Fill only the summary fields needed for your selected test.
- Press Calculate to show the result above the form.
- Use CSV or PDF export for reports and records.
Understanding Test Statistics
A test statistic changes sample evidence into one standard value. This value shows how far the sample stands from the null hypothesis. A large absolute value often means stronger evidence against the null claim. The exact scale depends on the selected test. A z test uses the normal curve. A t test uses sample variation and degrees of freedom. Chi-square and F tests compare variation.
Why The Calculator Helps
Manual hypothesis work can become slow. Each test has a different standard error. Each tail choice changes the p value. This calculator keeps those steps in one form. It supports one mean, two means, paired means, one proportion, two proportions, one variance, and variance ratio tests. You can enter raw summary values. The page returns the statistic, degrees of freedom, p value, critical value, decision, and useful notes.
Reading The Result
Start with the test statistic. It measures distance from the null model. Then check the p value. A small p value means the sample would be unusual if the null claim were true. Compare the p value with alpha. When p is less than alpha, reject the null hypothesis. When p is greater, do not reject it. This does not prove the null true. It only means the current sample lacks enough evidence.
Good Input Practice
Use values from a random and relevant sample. Keep units consistent. Use population standard deviation only when it is known. Otherwise choose the t test. For proportions, enter successes and total trials. For paired data, enter the mean and standard deviation of differences. For variance tests, use positive standard deviations.
Practical Reporting
A clear report should state the hypotheses, test type, statistic, p value, alpha, and conclusion. Add the sample size and degrees of freedom when available. The exported CSV and PDF help keep a record. Still, the final interpretation should match your study design. Statistical significance is not the same as practical importance. Check effect size, context, and data quality before making decisions.
Common Mistakes
Do not mix one tailed and two tailed conclusions. Do not round early. Do not ignore assumptions. Normality, independence, equal variance choices, and sample size can change the correct test. Review outliers before final reporting.
FAQs
What is a test statistic?
A test statistic converts sample evidence into a standardized value. It helps compare your result with a known probability distribution.
Which test should I choose?
Use z when population variation is known. Use t when sample variation estimates it. Use proportion tests for counts. Use chi-square or F for variance claims.
What does alpha mean?
Alpha is the chosen significance level. It is the risk of rejecting the null hypothesis when the null is actually true.
Why do tail options matter?
The tail defines the direction of the alternative hypothesis. It changes how the p value and critical value are calculated.
Can I use summary data?
Yes. This calculator is designed for summary data, including means, standard deviations, sample sizes, successes, and trial counts.
How should I read the p value?
The p value shows how unusual the sample result is under the null hypothesis. Smaller values show stronger evidence against the null.
Why use Welch t for two means?
Welch t works well when two groups may have different variances. It adjusts the degrees of freedom automatically.
Can I export my result?
Yes. Use the CSV button for spreadsheets. Use the PDF button for a compact report you can save or print.