Test statistic

Test statistic is a number derived from sample data that measures how far the observed result departs from the null hypothesis in standard-error units.

ByHoang TruongUpdated June 30, 2026

FrameworkHypothesis testing

See it move

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A formula card presents the t-test statistic: t = (x̄ − μ₀) ÷ (s ÷ √n), where x̄ is the observed sample mean, μ₀ is the null-hypothesis value, s is the sample standard deviation, and n is the sample size. A worked example shows that with x̄ = 4.3, μ₀ = 4.0, s = 0.6, and n = 25, the statistic equals (0.3) ÷ (0.12) = 2.50. A larger absolute value of t indicates stronger evidence against the null; the statistic is compared with a critical value, not with the significance level α directly.

Where it fits

SubjectData Analysis & StatisticsCoreTopicHypothesis TestingCore

The formula

LaTeX

t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}

Variables

$\overset{x}{ˉ}$: Sample mean
$μ_{0}$: Hypothesised population mean under the null hypothesis
$s$: Sample standard deviation
$n$: Sample size (observations)

One-sample t-test statistic; measures how many standard errors the sample mean lies from the null-hypothesis value. Compare the computed t against the critical value from the t-distribution at the chosen significance level and df = n − 1.

Check yourself

PracticeCORE

What does a large absolute value of a test statistic signal in a hypothesis test?

Select an answer to check your understanding.