WelchSatterthwaite
WelchSatterthwaite refers to the Welch–Satterthwaite equation, a method used in statistics to approximate the distribution of a test statistic when comparing means of two independent samples with unequal variances. The approach combines Welch's t-test for unequal variances with Satterthwaite's approximation for the degrees of freedom of a weighted sum of variances.
Historically, the method bears the names of Frank W. Welch, who proposed a version of the two-sample
The approximate degrees of freedom ν in the Welch–Satterthwaite formula are given by
ν ≈ [ (s1^2/n1 + s2^2/n2)^2 ] / [ (s1^2/n1)^2/(n1−1) + (s2^2/n2)^2/(n2−1) ],
where s1^2 and s2^2 are the sample variances and n1 and n2 are the sample sizes. The
t = (X̄1 − X̄2) / sqrt(s1^2/n1 + s2^2/n2),
with ν used to determine the critical value from the t-distribution.
Usage and limitations: The Welch–Satterthwaite adjustment is widely used for independent samples with unequal variances. It