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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

Choose the type of test statistic to compute

For t-statistic: the sample average

For t-statistic: sample std dev

For t and z: number of observations

For t-statistic: hypothesized mean

For z-proportion: observed proportion

For z-proportion: hypothesized proportion

For chi-square: observed count 1

For chi-square: observed count 2

For chi-square: observed count 3

For chi-square: observed count 4

For chi-square: expected count 1

For chi-square: expected count 2

For chi-square: expected count 3

For chi-square: expected count 4

Result

Enter values above and click Calculate to see your result.

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Formula

t = (x-bar - mu0) / (s / sqrt(n)), z = (p-hat - p0) / sqrt(p0(1-p0)/n), chi-square = sum((O-E) squared / E)

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.

Worked Example

Test: One-sample t. Mean = 52, s = 10, n = 25, mu0 = 50 Step 1: SE = 10 / sqrt(25) = 2 Step 2: t = (52 - 50) / 2 = 1.00 Step 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.

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T-Test CalculatorZ-Test CalculatorChi-Square CalculatorDegrees of Freedom Calculator

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