Rostron, Peter D;
Fearn, Tom;
Ramsey, Michael H;
(2024)
Improved coverage factors for expanded measurement uncertainty calculated from two estimated variance components.
Accreditation and Quality Assurance
10.1007/s00769-024-01579-w.
(In press).
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Abstract
Measurement uncertainty (MU) arising at different stages of a measurement process can be estimated using analysis of variance (ANOVA) on replicated measurements. It is common practice to derive an expanded MU by multiplying the resulting standard deviation by a coverage factor k. This coverage factor then defines an interval around a measurement value within which the value of the measurand, or true value, is asserted to lie for a desired confidence level (e.g. 95 %). A value of k = 2 is often used to obtain approximate 95 % coverage, although k = 2 will be an underestimate when the standard deviation is estimated from a limited amount of data. An alternative is to use Student’s t-distribution to provide a value for k, but this requires an exact or approximate degrees of freedom (df). This paper explores two different methods of deriving an appropriate k in the case when two variances from an ANOVA (classical or robust) need to be combined to estimate the measurement variance. Simulations show that both methods using the modified coverage factor generally produce a confidence interval much closer to the desired level (e.g. 95 %) when the data are approximately normally distributed. When these confidence intervals do deviate from 95 %, they are consistently conservative (i.e. reported coverage is higher than the nominal 95 %). When outlying values are included at the level of the larger variance component, in some cases the method used for robust ANOVA produces confidence intervals that are very conservative.
| Type: | Article |
|---|---|
| Title: | Improved coverage factors for expanded measurement uncertainty calculated from two estimated variance components |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00769-024-01579-w |
| Publisher version: | http://dx.doi.org/10.1007/s00769-024-01579-w |
| Language: | English |
| Additional information: | Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Science & Technology, Physical Sciences, Technology, Chemistry, Analytical, Instruments & Instrumentation, Chemistry, Measurement uncertainty, Expanded uncertainty, Duplicate method, Robust ANOVA, Coverage factor, Sampling |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10191712 |
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