Transcript Reporting measurement uncertainties according to the ISO GUM

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
How many of you:
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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
Motivation
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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)
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Outcome of my dissertation research on
students’ treatment of uncertainties
Different conventions have
been used to report
measurement uncertainties
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Difficult to compare results for
agreement
Confuses students (and experts!)
Many scientists may not even realize
the differences in notation!
m = 75 ± 5 g
What is the meaning of ± 5 ?
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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
What does x ± u mean?
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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).
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
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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
“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
ISO Guide recommendation:
Clearly 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
Determination of combined
standard uncertainty: uc
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Type A component: random, evaluated statistically
(e.g. standard deviation or standard error)
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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.)
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Combined standard uncertainty:
uC  u  u
2
A
2
B
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
Example 2
A DMM is used to measure the current in a circuit.
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Type A component
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Type B component
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Meter readings (mA): 1.426 to 1.428
Uncertainty from fluctuations = 0.001 mA
Accuracy rating of meter = ± 1% (assume 99% CI)
Corresponding uncertainty = (0.014 mA)/2.576
Combined standard uncertainty:
uc = 0.006 mA
Conclusion
When reporting a measured
value and its estimated
uncertainty, remember to
include units and a similar
explanation of the uncertainty.
“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