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Abstract
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Basic Statistical Calculations
Analysis of Uncertainty -Spreadsheet Model
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A Beginner's Guide to Uncertainty of Measurement

Profile image of Stephanie A. BellStephanie A. Bell

Abstract

The ,aim of this ,Beginner’s Guide is to introduce ,the subject of measurement uncertainty. Every measurement,is subject to some,uncertainty. A measurement,result is only complete,if it is accompanied ,by a ,statement of the ,uncertainty in the ,measurement. Measurement uncertainties can come from the measuring instrument, from the item being measured, from the environment, from the operator, and from other sources. Such uncertainties can be estimated using statistical analysis of a set of measurements, and using other kinds of information about the measurement,process. There are established rules for how to calculate an

Figures (14)
Figure 1. ‘Blob plot’ illustrating an example set of values and showing the mean If there is variation in readings when they are repeated, it is best to take many readings and take an average. An average gives you an estimate of the ‘true’ value. An average or arithmetic mean is usually shown by a symbol with a bar above it, e.g. x (‘x-bar’) is the mean value of x. Figure 1 shows an illustration of a set of values and their mean value. Example 1 shows how to calculate an arithmetic mean. | How many readings should you average? Figure | shows an illustration of a set of values and their mean value. Example | shows how to
Figure 1. ‘Blob plot’ illustrating an example set of values and showing the mean If there is variation in readings when they are repeated, it is best to take many readings and take an average. An average gives you an estimate of the ‘true’ value. An average or arithmetic mean is usually shown by a symbol with a bar above it, e.g. x (‘x-bar’) is the mean value of x. Figure 1 shows an illustration of a set of values and their mean value. Example 1 shows how to calculate an arithmetic mean. | How many readings should you average? Figure | shows an illustration of a set of values and their mean value. Example | shows how to
Figure 6. How long is a piece of string?
Figure 6. How long is a piece of string?
*Here the (+) half-width divided by V3 is used. Table 1. Spreadsheet model showing the ‘uncertainty budget’
*Here the (+) half-width divided by V3 is used. Table 1. Spreadsheet model showing the ‘uncertainty budget’
13.2 Calculator and software errors moderate numbers of readings, you would not use @,,. estimate of uncertainty: oO, gives the standard deviation of the sample itself, and does not
13.2 Calculator and software errors moderate numbers of readings, you would not use @,,. estimate of uncertainty: oO, gives the standard deviation of the sample itself, and does not

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References (11)

  1. BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML. Guide to the Expression of Uncertainty in Measurement. International Organization for Standardization, Geneva. ISBN 92-67- 10188-9, First Edition 1993, corrected and reprinted 1995. (BSI Equivalent: BSI PD 6461: 1995, Vocabulary of Metrology, Part 3. Guide to the Expression of Uncertainty in Measurement. British Standards Institution, London.)
  2. BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML. International Vocabulary of Basic and General Terms in Metrology Second Edition 1993. International Organization for Standardization, Geneva.
  3. Chatfield, C. (1983) Statistics for Technology. Third Edition. (New York: Chapman and Hall.)
  4. Dietrich, C.F. (1991), Uncertainty, calibration and probability. Second Edition. (Bristol: Adam Hilger.)
  5. EA-4/02 Expression of the Uncertainty of Measurement in Calibration, 1999, European co-operation for Accreditation.
  6. International Standard ISO 3534-1 Statistics -vocabulary and symbols -Part I: Probability and General Statistical Terms, First Edition 1993, International Organization for Standardization, Geneva.
  7. PD 6461 : Part 1 : 1995 Vocabulary of Metrology, Part 1. Basic and general terms (international), British Standards Institution, London.
  8. EURACHEM/CITAC Guide: Quantifying Uncertainty in Analytical Measurement, Second Edition 2000.
  9. UKAS publication M 3003 The Expression of Uncertainty and Confidence in Measurement Edition 1, December 1997.
  10. International Standard ISO/IEC 17025 General Requirements for the competence of testing and calibration laboratories, First Edition 1999, International Organization for Standardization, Geneva.
  11. At the time of publication, the following websites contained useful information on estimating uncertainty of measurement: http://physics.nist.gov/cuu/Uncertainty/index.html http://www.ukas.com/new_docs/technical-uncertain.htm

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