Title: Reporting Measurement Uncertainties According to the ISO Guide
1Reporting 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
2How 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
3Motivation
- 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
4Different 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!
5m 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
6What 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).
7ISO 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
8- 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
9ISO 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
10Determination 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
11Example 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
12Example 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
13Conclusion
- When reporting a measured value and its estimated
uncertainty, remember to include units and a
similar explanation of the uncertainty.
14Stick 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