B D Hall and R Willink 2001 Metrologia 38 9 doi:10.1088/0026-1394/38/1/2
B D Hall and R Willink
Show affiliationsThe 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.
06.20.Dk Measurement and error theory
02.50.-r Probability theory, stochastic processes, and statistics
Issue 1 (February 2001)
B D Hall and R Willink 2001 Metrologia 38 9
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