Confidence intervals for robust estimates of measurement uncertainty

Rostron, Peter D, Fearn, Tom and Ramsey, Michael H (2020) Confidence intervals for robust estimates of measurement uncertainty. Accreditation and Quality Assurance. ISSN 0949-1775

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Abstract

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.

Item Type: Article
Additional Information: The notations Fp,ν1,ν2 and χ2 p,ν in Eqs. (1), (2) and (3) correspond to that of Graybill [8], for whom the probability p is that in the upper tail. Thus they correspond to the inverse cumulative distribution functions of the respective distributions evaluated for a probability of 1−p and not for a probability p as stated in the paragraph immediately above these equations. The correct interpretation was used in coding the RANOVA3 software and in all the other computations reported in the paper. The originally published text at the top of the third page is: Fp, ν1, ν2 is the inverse cumulative distribution function (cdf) of the F probability distribution with degrees of freedom ν1, ν2 for a probability p, and χ2 p,ν is the inverse cdf of the chi-squared distribution with degrees of freedom ν for probability p. The corrected text therefore is: Fp, ν1, ν2 is the inverse cumulative distribution function (cdf) of the F probability distribution with degrees of freedom ν1, ν2 for a probability 1−p, and χ2 p,ν is the inverse cdf of the chi-squared distribution with degrees of freedom ν for probability 1−p.
Keywords: Measurement uncertainty, bootstrap, confidence interval, confidence limit, robust ANOVA, duplicate method
Schools and Departments: School of Life Sciences > Evolution, Behaviour and Environment
Subjects: Q Science > QA Mathematics > QA0276 Mathematical statistics
Q Science > QD Chemistry > QD0071 Analytical chemistry
Depositing User: Michael Ramsey
Date Deposited: 04 Dec 2019 08:13
Last Modified: 11 Mar 2021 10:04
URI: http://sro.sussex.ac.uk/id/eprint/88375

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