You use the Welch-Satterthwaite approximation in the QDE Toolkit: just how good is it?
2002-05-27 (Edited 2002-08-14.) The “Welch-Satterthwaite approximation” is a multi-step approach recommended by the ISO Guide to the Expression of Uncertainty in Measurement (Section G.6.4, page 64) for combining uncertainties of two (or more) additive effects each described by a standard uncertainty and degrees of freedom. Applied to comparisons, each pair difference entails subtraction rather than addition. In this context, subtraction has an uncertainty distribution about its mean that is exactly the same as for addition: to change from adding a particular variable, subtracting it instead, one need only “flip” its distribution left-to-right (about its mean) – which gives no change whatsoever with these symmetric uncertainty distributions. (Added 2002-08-14.) We follow this recommendation and use the Welch-Satterthwaite formula to approximate the distribution of the pair difference between two laboratories when the distribution for each laboratory has been given (with a standard unce
