Math · Statistics

T-Test Calculator

Run one-sample and two-sample Student’s t-tests — t-statistic, degrees of freedom, standard error and a p-value estimate with interpretation.

Test type

Tails

Null mean μ₀

Sample 1 data

Sample 2 data

t-statistic

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One-sample: t = (x̄ − μ₀) / (s / √n), df = n − 1
Two-sample (Welch): t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂), df via Welch–Satterthwaite
Paired: t = d̄ / (sₘ / √n), where d are the differences.

Three test types

One-sample, two-sample Welch and paired t-tests.

P-value estimate

Approximate p-value via the incomplete beta function.

Correct df

Welch–Satterthwaite degrees of freedom used.

Interpretation

Guides whether to reject the null hypothesis at α = 0.05.

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