t-Test (One/Two Sample, Paired, Welch)
Family of tests for means under normality assumption — using the t-distribution as reference.
Also known as: Student's t-test, Welch's t-test, paired t-test
The t-test is the classic mean-comparison test. It uses the t-distribution to check whether one or two observed means are compatible with a target or with each other.
- One-sample t-test — H₀: μ = μ₀; tests whether a single mean deviates from a target
- Two-sample t-test — H₀: μ₁ = μ₂; assumes equal variances
- Welch t-test — two-sample without variance equality; more robust, often the default in practice
- Paired t-test — before/after measurements on the same objects; tests the differences
See also
Used in
In the Algorithm Lab
Sources
- Student — The Probable Error of a Mean, Biometrika, 6(1), 1908
- Welch, B. L. — The Generalization of Student's Problem when Several Different Population Variances are Involved, Biometrika, 34(1/2), 1947
- Fahrmeir, L. et al. — Statistik, Springer