<Dd> d . f . = (s 1 2 n 1 + s 2 2 n 2) 2 (s 1 2 / n 1) 2 n 1 − 1 + (s 2 2 / n 2) 2 n 2 − 1 . (\ displaystyle \ mathrm (d.f.) = (\ frac (\ left ((\ frac (s_ (1) ^ (2)) (n_ (1))) + (\ frac (s_ (2) ^ (2)) (n_ (2))) \ right) ^ (2)) ((\ frac (\ left (s_ (1) ^ (2) / n_ (1) \ right) ^ (2)) (n_ (1) - 1)) + (\ frac (\ left (s_ (2) ^ (2) / n_ (2) \ right) ^ (2)) (n_ (2) - 1)))).) </Dd> <P> This is known as the Welch--Satterthwaite equation . The true distribution of the test statistic actually depends (slightly) on the two unknown population variances (see Behrens--Fisher problem). </P> <P> This test is used when the samples are dependent; that is, when there is only one sample that has been tested twice (repeated measures) or when there are two samples that have been matched or "paired". This is an example of a paired difference test . </P> <Dl> <Dd> t = X _̄ D − μ 0 s D n . (\ displaystyle t = (\ frac ((\ bar (X)) _ (D) - \ mu _ (0)) (\ frac (s_ (D)) (\ sqrt (n)))).) </Dd> </Dl>

What does an independent sample t test measure