What is satterthwaite approximation?

The Satterthwaite approximation is a statistical method used to calculate the effective degrees of freedom (df) in a t-test when the variances of the two groups being compared are not equal and/or the sample sizes are relatively small. The method is named after its developer, Charles Satterthwaite.

When conducting a t-test, the degrees of freedom reflect the number of independent pieces of information available for estimating the population standard deviation. The effective degrees of freedom, calculated using the Satterthwaite approximation, take into account differences in sample sizes and variances between the two groups being compared, resulting in a more accurate estimate of the true degrees of freedom.

The Satterthwaite approximation involves complex calculations, but it can be easily obtained using statistical software packages like R or SPSS. It is commonly used in research areas such as psychology, biology, and social sciences where sample sizes are relatively small and/or variances are not equal between groups.