Confidence intervals for robust estimates of measurement uncertainty

Uncertainties arising at different stages of a measurement process can be estimated using Analysis of Variance (ANOVA) on duplicated measurements. In some cases it is also desirable to calculate confidence intervals for these uncertainties. This can be achieved using probability models that assume the measurement data are normally distributed. However, it is often the case in practice that a set of otherwise normally distributed measurement values is contaminated by a small number of outlying values, which may have a disproportionate effect on the variances calculated using the ‘classical’ form of ANOVA. In this case, robust ANOVA methods are able to provide variance estimates that are much closer to the parameters of the underlying normal distributions. A method using bootstrapping to calculate confidence intervals from robust estimates of variances is proposed and evaluated, and is shown to work well when the number of outlying values is small. The method has been implemented in a Visual Basic program.