StatisticsFree

Test Statistic Calculator

Use this free test statistic calculator to compute the t-statistic, z-statistic for proportions, or chi-square statistic from your data. Select the test type, enter values, and get the test statistic with degrees of freedom and interpretation.

Enter Values

Statistic Type

Choose the type of test statistic to compute

Sample Mean

For t-statistic: the sample average

Sample Standard Deviation

For t-statistic: sample std dev

Sample Size

For t and z: number of observations

Null Value (mu0)

For t-statistic: hypothesized mean

Sample Proportion (p-hat)

For z-proportion: observed proportion

Null Proportion (p0)

For z-proportion: hypothesized proportion

Observed 1

For chi-square: observed count 1

Observed 2

For chi-square: observed count 2

Observed 3

For chi-square: observed count 3

Observed 4

For chi-square: observed count 4

Expected 1

For chi-square: expected count 1

Expected 2

For chi-square: expected count 2

Expected 3

For chi-square: expected count 3

Expected 4

For chi-square: expected count 4

Result

Enter values above and click Calculate to see your result.

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Formula

Core Formula

\text{t-statistic: } t = \frac{\bar{x} - \mu_0}{s \,/\, \sqrt{n}} \\[6pt] \text{z-statistic: } z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \\[6pt] \text{Chi-square: } \chi^2 = \sum \frac{(O - E)^2}{E}

How it works: Each test statistic measures how far the observed result is from the null hypothesis, standardized by variability. Larger absolute values indicate stronger evidence against the null.

Review and Methodology

Updated Mar 26, 2026

This calculator runs locally in your browser. Inputs are converted into the units required by the formula, and the result is paired with supporting references so you can verify the method before using it for planning or estimates.

Worked Example

Test: One-sample t. Mean = 52, s = 10, n = 25, mu0 = 50

1Step 1: SE = 10 / sqrt(25) = 2

2Step 2: t = (52 - 50) / 2 = 1.00

3Step 3: df = 24

Result: t = 1.00 with 24 degrees of freedom.

What Is a Test Statistic?

A test statistic is a standardized value that measures how far sample data deviates from what the null hypothesis predicts. It converts raw data into a single number comparable against a known probability distribution.

The t-statistic compares a sample mean to a hypothesized value (unknown population std dev)
The z-statistic for proportions tests if an observed proportion differs from a hypothesized one
The chi-square statistic measures how well observed categorical frequencies match expected ones
All test statistics share the same logic: larger values mean stronger evidence against H0
The test statistic plus degrees of freedom determines the p-value

Understanding test statistics is the key to hypothesis testing across all fields of data analysis.

You can also calculate changes using our T-Test Calculator, Z-Test Calculator, Chi-Square Calculator or Degrees of Freedom Calculator.

Frequently Asked Questions

What is a test statistic in simple terms?

A "surprise score" that summarizes how different your data is from what the null hypothesis predicts. Large values mean the data is very surprising under H0.

How do I choose which statistic?

Use t for comparing means (unknown sigma). Use z for proportions. Use chi-square for categorical count data.

Does this return p-values?

This tool focuses on the statistic value and df. For full hypothesis test results with p-values, use the dedicated T-Test, Z-Test, or Chi-Square calculators.

What does a negative test statistic mean?

For t and z, negative means the sample result is below the hypothesized value. Chi-square is always non-negative.

How large must it be to be significant?

For z: |z| > 1.96 at alpha = 0.05. For t: depends on df. For chi-square: depends on df, always positive.

Can I use this Test Statistic Calculator on my own web page?

You can. Look for the "Embed" button near the top of this calculator. It lets you pick a size, border style, and color palette, then gives you an iframe tag to paste into any webpage. The widget is responsive, loads fast, and costs nothing. More details at calculory.com/services/embed-calculators.

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