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Confidence intervals and other statistical intervals in metrology

Published online by Cambridge University Press:  13 May 2013

R. Willink
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Abstract

Typically, a measurement is regarded as being incomplete without a statement of uncertainty being provided with the result. Usually, the corresponding interval of measurement uncertainty will be an evaluated confidence interval, assuming that the classical, frequentist, approach to statistics is adopted. However, there are other types of interval that are potentially relevant, and which might wrongly be called a confidence interval. This paper describes different types of statistical interval and relates these intervals to the task of obtaining a figure of measurement uncertainty. Definitions and examples are given of probability intervals, confidence intervals, prediction intervals and tolerance intervals, all of which feature in classical statistical inference. A description is also given of credible intervals, which arise in Bayesian statistics, and of fiducial intervals. There is also a discussion of the term “coverage interval” that appears in the International Vocabulary of Metrology and in the supplements to the Guide to the Expression of Uncertainty in Measurement.

Type
Research Article
Information
International Journal of Metrology and Quality Engineering , Volume 3 , Issue 3 , 2012 , pp. 169 - 178
Copyright
© EDP Sciences 2013

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References

G.J. Hahn, W.Q. Meeker, Statistical Intervals: A Guide for Practitioners (Wiley, 1991)
JCGM 200:2012, International vocabulary of metrology – Basic and general concepts and associated terms (VIM) (2012), http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2012.pdf
Joint Committee for Guides in Metrology, Evaluation of measurement data – Supplement 1 to the “Guide to the expression of uncertainty in measurement” – Propagation of distributions using a Monte Carlo method (2006)
Joint Committee for Guides in Metrology, Evaluation of measurement data – Supplement 2 to the “Guide to the expression of uncertainty in measurement” – Extension to any number of output quantities (2006)
Guide to the Expression of Uncertainty in Measurement (International Organization for Standardization, Geneva, 1995)
J. Pfanzagl, Estimation: Confidence Intervals and Regions, in International Encyclopedia of Statistics, edited by W.H. Kruskal, J.M. Tanur (The Free Press, Macmillan, 1978), pp. 259–267
G.K. Robinson, Confidence intervals and regions, in Encyclopedia of Statistical Sciences, edited by S. Kotz, N.L. Johnson, C.B. Read (Wiley, 1982), Vol. 2, pp. 120–127
S.S. Wilks, Mathematical Statistics (Wiley, 1962)
H.J. Larson, Introduction to Probability Theory and Statistical Inference, 3rd edn. (Wiley, 1982)
A.M. Mood, F.A. Graybill, Introduction to the Theory of Statistics, 2nd edn. (McGraw-Hill, 1963)
R.E. Walpole, R.H. Myers, Probability and Statistics for Engineers and Scientists, 2nd edn. (Macmillan, 1978)
R.G. Miller Jr., Simultaneous Statistical Inference, 2nd edn. (Springer-Verlag, 1980)
F.S. Acton, Analysis of Straight-Line Data (Wiley, 1959)
B.W. Lindgren, Statistical Theory (Macmillan, 1968)
Howe, W.G., Two-sided tolerance limits for normal populations – some improvements, J. Am. Stat. Assoc. 64, 610–620 (1969) Google Scholar
NIST/SEMATECH e-Handbook of Statistical Methods (2012), http://www.itl.nist.gov/div898/handbook/
H.A. David, Order Statistics, 2nd edn. (Wiley, 1981)
I. Guttman, Tolerance regions, statistical, in Encyclopedia of Statistical Sciences, edited by S. Kotz, N.L. Johnson, C.B. Read (Wiley, 1988), Vol. 9, pp. 272–287
W.F. Guthrie, H. Liu, A.L. Rukhin, B. Toman, J.C.M. Wang, N. Zhang, Three Statistical Paradigms for the Assessment and Interpretation of Measurement Uncertainty, in Data Modeling for Metrology and Testing in Measurement Science, edited by F. Pavese, A.B. Forbes (Birkhäuser, 2009), pp. 71–115
Edwards, A.W.F., Fiducial probability, The Statistician 25, 15–35 (1976) CrossRefGoogle Scholar
D.V. Lindley, Bayesian inference, in Encyclopedia of Statistical Sciences, edited by S. Kotz, N.L. Johnson, C.B. Read (Wiley, 1982), Vol. 1, pp. 197–204
Willink, R., Hall, B.D., A classical method for uncertainty analysis with multidimensional data, Metrologia 39, 361–369 (2002) CrossRefGoogle Scholar
A.P. Dawid, Invariant prior distributions, in Encyclopedia of Statistical Sciences, edited by S. Kotz, N.L. Johnson, C.B. Read (Wiley, 1983), Vol. 4, pp. 228–236