Calculator Inputs
Choose a test type. Fill the fields needed for that test. Leave unused fields blank.
Example Data Table
| Test | Input values | Formula focus | Expected output |
|---|---|---|---|
| One Sample Mean Z | x̄ = 52, μ₀ = 50, σ = 6, n = 36 | Known population deviation | z statistic and p value |
| One Sample Mean T | x̄ = 52, μ₀ = 50, s = 6.5, n = 36 | Unknown population deviation | t statistic and degrees of freedom |
| One Proportion Z | x = 48, n = 100, p₀ = 0.40 | Single proportion claim | z statistic and decision |
| Two Proportion Z | x₁ = 56, n₁ = 120, x₂ = 49, n₂ = 115 | Difference between two rates | z statistic and p value |
Formula Used
One mean z: z = (x̄ - μ₀) / (σ / √n)
One mean t: t = (x̄ - μ₀) / (s / √n)
One proportion z: z = (p̂ - p₀) / √[p₀(1 - p₀) / n]
Two means z: z = [(x̄₁ - x̄₂) - Δ₀] / √(σ₁²/n₁ + σ₂²/n₂)
Welch two means t: t = [(x̄₁ - x̄₂) - Δ₀] / √(s₁²/n₁ + s₂²/n₂)
Pooled t: t = [(x̄₁ - x̄₂) - Δ₀] / [sₚ√(1/n₁ + 1/n₂)]
Paired t: t = (d̄ - Δ₀) / (sᵈ / √n)
Two proportions z: z = [(p̂₁ - p̂₂) - Δ₀] / SE
How to Use This Calculator
- Select the test type that matches your hypothesis test.
- Choose two tailed, right tailed, or left tailed direction.
- Enter alpha, such as 0.05 or 0.01.
- Fill only the input fields required for the selected test.
- Press Calculate to show the statistic above the form.
- Review the p value, critical value, and decision.
- Use CSV or PDF download for reports and records.
Article
Understanding Standardized Test Statistics
A standardized test statistic converts sample evidence into one comparable score. It measures how far an estimate is from the null value. The distance is measured in standard error units. This makes different tests easier to compare. A large positive value supports an upper tail claim. A large negative value supports a lower tail claim. A value near zero usually shows weak evidence.
Why This Calculator Helps
Manual hypothesis testing can be confusing. Many formulas look similar. Yet each test needs the correct standard error. This calculator separates common cases. It supports means, proportions, paired samples, and two sample designs. It also reports p value logic. The output gives the statistic, standard error, degrees of freedom, and decision. That makes review faster and cleaner.
Choosing the Right Test
Use a one sample mean z test when the population standard deviation is known. Use a one sample t test when it is unknown. Use a one proportion z test for a single rate or percentage. Use a two mean test when two independent groups are compared. Use a paired t test when the same subject is measured twice. Use a two proportion z test when two rates are compared.
Interpreting the Result
The sign of the statistic shows direction. The size shows strength. A two tailed test checks for any difference. A right tailed test checks for a higher result. A left tailed test checks for a lower result. The p value is compared with alpha. If the p value is less than or equal to alpha, reject the null hypothesis.
Best Practices
Always verify sample size first. Check that standard deviations are positive. Make sure proportions stay between zero and one. Do not mix paired and independent data. Select the alternative hypothesis before looking at results. Use the exported report for study notes or audit records. The calculator is a support tool. Statistical judgment is still needed.
Common Mistakes
Do not enter a percentage as both a percent and a decimal. Use 0.42 for forty two percent. Do not use sample deviation in a z test unless it is an accepted approximation. Keep hypotheses clear. Record assumptions with every result for safer interpretation each time.
FAQs
What is a standardized test statistic?
It is a score that shows how far a sample estimate is from a hypothesized value. The distance is measured in standard error units.
When should I use a z statistic?
Use a z statistic when the population deviation is known, or when testing proportions with suitable sample conditions.
When should I use a t statistic?
Use a t statistic when the population deviation is unknown and sample deviation is used instead.
What does the p value mean?
The p value measures how likely the sample evidence is under the null hypothesis. Smaller values give stronger evidence against it.
What does alpha mean?
Alpha is the significance level. It is the cutoff used to decide whether the p value is small enough.
Can this calculator compare two groups?
Yes. It supports independent mean tests, pooled mean tests, paired tests, and two proportion tests.
Why are degrees of freedom shown?
Degrees of freedom are needed for t tests. They affect the shape of the t distribution and the p value.
Can I export the result?
Yes. After calculation, use the CSV or PDF button to save the results for reports, homework, or records.