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Confidence intervals for robust estimates of measurement uncertainty
Version 2 2023-06-12, 09:16
Version 1 2023-06-09, 19:49
journal contribution
posted on 2023-06-12, 09:16 authored by Peter D Rostron, Tom Fearn, Michael H RamseyUncertainties 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.
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0949-1775Publisher
SpringerExternal DOI
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- Evolution, Behaviour and Environment Publications
Notes
The notations Fp,?1,?2 and ?2 p,? 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, ?1, ?2 is the inverse cumulative distribution function (cdf) of the F probability distribution with degrees of freedom ?1, ?2 for a probability p, and ?2 p,? is the inverse cdf of the chi-squared distribution with degrees of freedom ? for probability p. The corrected text therefore is: Fp, ?1, ?2 is the inverse cumulative distribution function (cdf) of the F probability distribution with degrees of freedom ?1, ?2 for a probability 1-p, and ?2 p,? is the inverse cdf of the chi-squared distribution with degrees of freedom ? for probability 1-p.Full text available
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Legacy Posted Date
2019-12-04First Open Access (FOA) Date
2020-02-24First Compliant Deposit (FCD) Date
2019-12-03Usage metrics
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