Test Statistic Value Calculator

Find z, t, chi-square, and F statistics with confidence. Enter sample values, deviations, and counts. Review formulas, exports, and examples in one simple workspace.

Calculator

One Sample z Test

One Sample t Test

Proportion z Test

Welch Two Sample t Test

Chi-Square Test

Use comma separated values. Example: 18, 22, 20

F Variance Ratio Test

Formula Used

One sample z: z = (x̄ - μ₀) / (σ / √n)

One sample t: t = (x̄ - μ₀) / (s / √n)

Proportion z: z = (p̂ - p₀) / √(p₀(1 - p₀) / n)

Welch t: t = ((x̄₁ - x̄₂) - Δ₀) / √(s₁²/n₁ + s₂²/n₂)

Chi-square: χ² = Σ((O - E)² / E)

F ratio: F = s₁² / s₂²

How to Use This Calculator

Select the statistic type first. Enter the values requested for that method. Press calculate to show the result above the form. Use CSV or PDF buttons to save the current calculation. For chi-square work, enter observed and expected counts as comma separated lists.

Example Data Table

Test Type Example Inputs Formula Focus Example Statistic
One sample z x̄=105, μ₀=100, σ=15, n=36 Mean with known population deviation 2.0000
One sample t x̄=84, μ₀=80, s=10, n=25 Mean with sample deviation 2.0000
Proportion z x=64, n=100, p₀=0.50 Sample proportion against null share 2.8000
Welch t x̄₁=52, x̄₂=47, s₁=8, s₂=7 Two independent means 2.5390
Chi-square Observed 18,22,20 and expected 20,20,20 Category count mismatch 0.4000
F ratio s₁=12, s₂=9 Variance comparison 1.7778

Understanding Test Statistic Values

A test statistic turns sample evidence into one standard number. That number shows how far observed data sits from a null claim. A larger absolute value usually means stronger evidence against that claim. The meaning depends on the selected test, sample design, and tail direction.

Why This Calculator Helps

This calculator supports common hypothesis testing needs. It can compute one sample z values, one sample t values, proportion z values, Welch two sample t values, chi-square values, and F ratios. Each method uses fields that match its formula. This keeps entry clear. It also reduces mistakes during study, reporting, or classroom work.

Choosing the Right Method

Use a z mean test when the population standard deviation is known. Use a t mean test when the population deviation is unknown and sample deviation is used. Use a proportion z test for counts, rates, or conversion shares. Use Welch t when two independent groups have different variation. Use chi-square for observed and expected category counts. Use F when comparing two variances.

Reading the Output

The output gives the statistic value first. It also shows degrees of freedom when that detail is useful. For z tests, the value is measured in standard errors. For t tests, it is measured with sample based uncertainty. For chi-square tests, higher positive values show more total mismatch across categories. For F tests, values compare variance size between two groups.

Good Practice

Always review assumptions before using any statistic. Check sample independence. Check expected counts for chi-square work. Check whether a one tail or two tail decision is planned. The calculator does not replace statistical judgment. It gives a transparent calculation path. You can export the results for records. You can also compare the example table before entering your own data.

Exporting Your Work

The export tools are useful when calculations must be saved, checked, or shared. The CSV file stores inputs and the final statistic in rows. The PDF file creates a simple summary. Keep both with your worksheet or report. This helps reviewers trace the selected method, entered values, formula, and result without repeating the full calculation by hand later. That record also supports careful audits and future corrections when needed later.

FAQs

What is a test statistic?

A test statistic is a standardized value created from sample data. It helps compare observed evidence with a null hypothesis.

Which test statistic should I choose?

Choose z for known population deviation, t for sample deviation, chi-square for counts, and F for comparing variances.

Does this calculator give p-values?

This page focuses on the test statistic value. You can compare the value with a critical value or use it for p-value lookup.

What does degrees of freedom mean?

Degrees of freedom describe how many values can vary after restrictions are applied. They are important for t, chi-square, and F tests.

Can I use decimals?

Yes. Decimal values are accepted for means, deviations, proportions, and null differences. Counts should match the selected method.

How do I enter chi-square data?

Enter observed counts in one comma separated list. Enter expected counts in another list with the same number of categories.

What is Welch t used for?

Welch t compares two independent group means. It is useful when the groups may have different variances or sample sizes.

Can I export the result?

Yes. Use the CSV button for spreadsheet records. Use the PDF button for a simple printable result summary.

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