Reporting Measurement Uncertainties According to the ISO Guide

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Reporting Measurement Uncertainties According to
the ISO Guide

• Duane Deardorff
• Dept. of Physics and Astronomy
• The University of North Carolina at Chapel Hill
• Contributed Paper EK06 presented at
• 127th National Meeting of the AAPT
• Madison, WI
• August 6, 2003

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How many of you

• Have reported measurements from an experimental
  physics lab (teaching or research)
• Use or encourage students to use SI units
• Are familiar with the book An Introduction to
  Error Analysis by John Taylor
• Are familiar with the ISO Guide to the Expression
  of Uncertainty in Measurement
• Know the difference between Type A and Type B
  components used to evaluate the standard
  uncertainty of a measurement

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Motivation

• Physics relies on empirical data that is
  inherently subject to measurement uncertainties
• Reporting of uncertainties must be standardized
  in order for values to be interpreted correctly
• Students should learn these standards
• (just like they should learn and use SI
  notation)
• Outcome of my dissertation research on students
  treatment of uncertainties

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Different conventions have been used to report
measurement uncertainties

• Difficult to compare results for agreement
• Confuses students (and experts!)
• Many scientists may not even realize the
  differences in notation!

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m 75 5 g What is the meaning of 5 ?

• Best guess by experimenter
• Half the smallest division of measurement
• Standard deviation ?
• Standard error ?m ?/?n
• Expanded uncertainty of 2? or 3? (95 or
  99 confidence interval)
• Standard uncertainty u
• Combined standard uncertainty uc

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What does x u mean?

• Physicists generally report 1? (68 CI)
• Chemists report 2? or 3? (95 or 99 CI)
• Survey/poll margin of error is 95 CI
• Accuracy tolerances are often 95 or 99
• NIST Calibration certificate is usually 99

Conclusion The interpretation of u is not
consistent within a field, let alone between
fields, and the meaning is generally not
specified (except in NIST publications).
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ISO Guide to the Expression of Uncertainty in
Measurement

• In 1993 the International Organization for
  Standardization published new guidelines for
  industry and research GUM
• NIST version physics.nist.gov/cuu/Uncertainty
• Use combined standard uncertainty uc that
  includes both Type A and Type B components
• use term uncertainty not error
• avoid use of ambiguous notation without
  explanation

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• The format should be avoided whenever
  possible because it has traditionally been used
  to indicate an interval corresponding to a high
  level of confidence and thus may be confused with
  an expanded uncertainty.
• -ISO Guide, p. 7

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ISO Guide recommendationClearly define
uncertainty values.

• Ex. m 100.021 47 g with a combined standard
  uncertainty uc 0.35 mg
• or m 100.021 47(35) g, where the number in
  parentheses is the numerical value of uc and
  refers to the corresponding last digits of the
  quoted result
• or m (100.021 47 0.000 35) g, where the
  number following the symbol is the numerical
  value of uc and not a confidence interval

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Determination of combined standard uncertainty
uc

• Type A component random, evaluated
  statistically
• (e.g. standard deviation or standard error)
• Type B component scientific judgment based on
  all available information, a priori
• (e.g. instrument precision, rated accuracy of
  instrument, variation in previous data, physical
  factors, etc.)
• Combined standard uncertainty

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Example 1

• A meter stick is used to measure the width of a
  table
• Width (cm) 56.2, 56.7, 56.3, 56.9, 56.5
• uA 0.13 cm (standard error)
• uB 0.1 cm (resolution and assumed
  accuracy)
• uC 0.16 cm
• Average width 56.52 cm with uC 0.16 cm
• Typical intro physics W 56.6 0.2 cm

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Example 2

• A DMM is used to measure the current in a
  circuit.
• Type A component
• Meter readings (mA) 1.426 to 1.428
• Uncertainty from fluctuations 0.001 mA
• Type B component
• Accuracy rating of meter 1 (assume 99 CI)
• Corresponding uncertainty (0.014 mA)/2.576
• Combined standard uncertainty uc 0.006 mA

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Conclusion

• When reporting a measured value and its estimated
  uncertainty, remember to include units and a
  similar explanation of the uncertainty.

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Stick with the ISO Guide (GUM)!

• ISO Guide to the Expression of Uncertainty in
  Measurements (1993)
• NIST physics.nist.gov/cuu/Uncertainty
• For more information about the expression of
  measurement uncertainty by and for introductory
  physics students, go to
• www.physics.unc.edu/deardorf/uncertainty