In statistics and uncertainty analysis, the Welch–Satterthwaite equation is used to calculate an approximation to the effective degrees of freedom of a linear combination of independent sample variances, also known as the pooled degrees of freedom, corresponding to the pooled variance.
For n sample variances si2 (i = 1, ..., n), each respectively having νi degrees of freedom, often one computes the linear combination
where
There is no assumption that the underlying population variances σi2 are equal. This is known as the Behrens–Fisher problem.
The result can be used to perform approximate statistical inference tests. The simplest application of this equation is in performing Welch's t test.