Does "Welch-Satterthwaite" make a good uncertainty estimate?

Abstract

The Welch-Satterthwaite (W-S) formula is a classical, approximate method for combining several sample estimates of normal population variances. However, the W-S formula is routinely applied to the results of physical measurements even though uncertainties may include those of Type B. This paper considers the validity of the W-S formula as a means of obtaining a confidence interval for the measurand. The classical concept of a confidence interval provides performance criteria that can be used to assess the W-S formula by simulation. Examples presented include the combination of two Type A uncertainties, and the combination of one Type A and one Type B uncertainty. The results show that the W-S formula performs very well. This finding contrasts with the findings of other recent studies which did not apply classical performance criteria.

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