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.

中文翻译：

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稳健估计测量不确定度的置信区间

在测量过程的不同阶段产生的不确定性可以使用重复测量的方差分析 (ANOVA) 进行估计。在某些情况下，还需要计算这些不确定性的置信区间。这可以使用假设测量数据呈正态分布的概率模型来实现。然而，在实践中，一组其他正态分布的测量值经常会受到少量异常值的污染，这可能会对使用“经典”形式的 ANOVA 计算的方差产生不成比例的影响。在这种情况下，稳健的方差分析方法能够提供更接近基础正态分布参数的方差估计。提出并评估了一种使用自举法从稳健的方差估计计算置信区间的方法，并且在离群值的数量很少时显示效果很好。该方法已在可视化基本程序中实现。