Formula Used
Z mean: z = (x̄ - μ₀) / SE.
One sample t: t = (x̄ - μ₀) / (s / √n).
Two sample t: t = [(x̄₁ - x̄₂) - Δ₀] / SE.
Paired t: t = (d̄ - d₀) / (sᵈ / √n).
One proportion z: z = (p̂ - p₀) / √[p₀(1 - p₀) / n].
Two proportion z: z = [(p̂₁ - p̂₂) - Δ₀] / √[p̂(1 - p̂)(1/n₁ + 1/n₂)].
Chi-square: χ² = Σ[(O - E)² / E].
F statistic: F = s₁² / s₂².
Correlation t: t = r√[(n - 2) / (1 - r²)].
How to Use This Calculator
Select the test type first. Then fill only the fields required by that test. Leave unrelated fields blank.
For mean tests, enter sample mean, null mean, sample size, and the needed spread measure. For proportion tests, enter successes and sample sizes.
For chi-square, enter observed counts. Add expected counts when they are not equal. For paired t, enter differences or matching before and after lists.
Press the submit button. The result appears above the form and below the header. Use the CSV or PDF button to save the output.
Understanding the Test Statistic
A test statistic converts sample evidence into one clear number. It measures how far the observed result sits from the null claim. A large absolute value often means stronger evidence against that claim. The scale depends on the selected test. A z statistic uses the normal scale. A t statistic uses a scale with degrees of freedom. Chi-square and F statistics compare variation, counts, or model spread.
Why This Calculator Helps
Manual work can be slow when many inputs change. This calculator keeps formulas in one place. It checks sample sizes, standard errors, proportions, variances, and list lengths. It also shows the formula used for the selected method. That makes review easier for homework, reports, audits, and research notes.
Selecting the Right Test
Use a one sample mean test when one group is compared with a claimed mean. Use a two sample mean test when two independent groups are compared. Choose the paired test when each value has a natural match. Use a proportion test for success counts. Use chi-square when observed counts are compared with expected counts. Use F when two variances are compared. Use correlation t when a sample correlation is tested.
Reading the Result
The statistic is not the whole decision. Compare it with a critical value, or use the p-value. The p-value estimates how unusual the result is under the null claim. Smaller values give stronger evidence. Common cutoffs include 0.10, 0.05, and 0.01. Always match the cutoff to your study plan.
Good Input Practices
Use raw counts for proportions. Use sample standard deviations for t tests. Use known population standard deviation only for a z mean test. Keep expected chi-square counts positive. Enter paired lists in the same order. Round final reports, not internal calculations.
Important Limits
This tool supports learning and planning. It does not replace study design or professional review. Assumptions still matter. Check independence, sampling method, normality needs, and count sizes. A correct statistic can still support a weak conclusion when the data plan is poor.
For best records, save outputs with input settings. This keeps each decision traceable. It also helps readers repeat the same calculation later without guessing hidden worksheet steps or formulas.
FAQs
What is a test statistic?
A test statistic is a standardized value. It compares sample evidence with a null claim. Larger distance from zero, or larger positive values for chi-square and F tests, can show stronger evidence.
Which test type should I choose?
Choose by data structure. Use t or z for means. Use z for proportions. Use chi-square for counts. Use F for variance ratios. Use paired t when observations are matched.
Can I use standard error instead of standard deviation?
Yes, for the z mean option. Enter the known standard error directly. For t tests, use sample standard deviation and sample size, because degrees of freedom are needed.
Does the calculator give a p-value?
Yes. It estimates p-values for z, t, chi-square, and F reference distributions. Treat the value as a guide, and confirm strict reporting rules for formal work.
How do I enter chi-square data?
Enter observed counts separated by commas, spaces, or line breaks. Add expected counts when known. If expected counts are blank, the calculator uses equal expected counts.
How do paired lists work?
You may enter a list of paired differences. You may also enter before and after lists. If using before and after lists, keep values in matching order.
What does two sided mean?
A two sided test checks for a difference in either direction. It is common when the research question does not predict only a greater or only a smaller result.
Can I download the result?
Yes. After calculation, use the CSV button for spreadsheet records. Use the PDF button for a simple report with the statistic, p-value, and formula.