Abstract
This article considers the problem of uncertainty evaluation when there are repeated measurements of a small quantity known to be non-negative. A solution to this problem has recently been put forward by the Analytical Methods Committee of the Royal Society of Chemistry (Accred Qual Assur 13:29–32). The Bayesian statistical basis of this solution is explained and discussed. It is shown that the performance of this procedure can be poor in an important subset of measurement situations.
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Analytical Methods Committee, The Royal Society of Chemistry (2008) Accred Qual Assur 13:29–32
ISO (2006/1999) BS ISO 3534 (Parts 1–3) Statistics—vocabulary and symbols, International Organization for Standardization
ISO (1994/1998) BS ISO 5725 (Parts 1–6) Accuracy (trueness and precision) of measurement methods and results, International Organization for Standardization
Mandel J (1980) The statistical analysis of experimental data. Dover, New York
Taylor JR (1997) An introduction to error analysis, 2nd edn. University Science Books, Sausalito
Coleman HW, Steele WG (1999) Experimentation and uncertainty analysis for engineers, 2nd edn. Wiley, New York
Armstrong N, Hibbert DB (2009). Chemom Intell Lab Syst 97:194–210
Hibbert DB, Armstrong N (2009). Chemom Intell Lab Syst 97:211–220
Marriott FHC (1990) A dictionary of statistical terms, 5th edn. International Statistical Institute, Longman, Harlow
Lindley DV (1982) Bayesian inference. In: Kotz S, Johnson NL, Read CB (eds) Encyclopedia of statistical sciences, vol 1. Wiley, New York
Ehrlich C, Dybkaer C, Wöger W (2007). Accred Qual Assur 12:201–218
Lee P M (1989) Bayesian statistics: an introduction. Oxford University Press, New York
O’Hagan A (1994) Kendall’s advanced theory of statistics, vol. 2B: Bayesian inference. Edward Arnold, London
Gelman A, Carlin JB, Stern HS, Rubin DB (1995) Bayesian data analysis. Chapman & Hall, London
Analytical Methods Committee (2008) AMCTB 26A Measurement uncertainty and confidence intervals near natural limits (re-issued September 2008). http://www.rsc.org/images/brief%2026A_tcm18-134929.pdf
Hall BD (2008). Metrologia 45:L5–L8
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Willink, R. Uncertainty in repeated measurement of a small non-negative quantity: explanation and discussion of Bayesian methodology. Accred Qual Assur 15, 181–188 (2010). https://doi.org/10.1007/s00769-009-0595-7
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DOI: https://doi.org/10.1007/s00769-009-0595-7