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An Introduction to Measurement Uncertainty and Error Analysis

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Science relies on empirical data, which is inherently subject to measurement error ... Similar findings in other studies (Sere; Garratt) 9. Student Difficulties ... – PowerPoint PPT presentation

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Title: An Introduction to Measurement Uncertainty and Error Analysis


1
An Introduction to Measurement Uncertaintyand
Error Analysis
  • New TA Orientation, Fall 2003
  • Department of Physics and Astronomy

The University of North Carolina at Chapel Hill
2
Are these time measurements significantly
different?
  • t1 1.86 s
  • t2 2.07 s
  • Yes
  • No
  • Cant tell

3
Are these time measurements significantly
different?
  • t1 1.86 s
  • t2 2.07 s
  • Student responses (N 44)
  • Yes 43
  • No 27 ???
  • Cant tell 30

4
Purpose and Challenges
  • Science relies on empirical data, which is
    inherently subject to measurement error
  • Uncertainty estimates are necessary for
  • assessing quality of data
  • comparison of data
  • verify/refute theoretical predictions
  • Students often have difficulty analyzing errors
  • Guidelines for reporting uncertainties vary
  • Terminology and notation is not consistent
  • International standard exists but is not well
    known

5
Student Difficulties
  • 1) Uncertainty is rarely estimated and stated,
    even when required (true for experts too!).
  • 2) Even if found, most students do not use
    uncertainties to justify their conclusions.
  • 3) Calculated values are often reported with too
    many (in)significant digits.
  • 4) Students have difficulty identifying the
    primary source of error in an experiment.

6
Student Difficulties
  • 1) Students often fail to report a quantitative
    uncertainty estimate, even when requested.
  • Overall reporting rates from this study
  • 0 to 50 of students reported uncertainty
  • 30 to 70 of TAs reported uncertainty

7
Student Difficulties
  • Task Use a ruler to measure the diameter of a
    penny as accurately as possible.

8
Student Difficulties
  • 2) Even if stated, most students do not justify
    their conclusions based on the uncertainty
  • Judgements are made based on arbitrary criteria
  • Our percent error was only 4, so our experiment
    proved the theory.
  • I decide by how much two measurements differ in
    order to see if they agree.
  • The result should be accurate as long as the
    error is less than 10.
  • Similar findings in other studies (Sere
    Garratt)

9
Student Difficulties
  • 3) Students tend to overstate precision
    (too many significant figures) of calculated
    values and to a lesser extent for directly
    measured values.

Typical student values
L
L 2.35 cm ( 0.05 cm) W 1.85 cm ( 0.05 cm)
W
A LW 4.3475 cm2 (Expert A 4.3
0.1 cm2 )
10
Student Difficulties
  • 4) Students have difficulty identifying the
    primary source of error in an experiment.
  • Are nickel coins made of nickel? Find density
  • Median density from 76 students 7.1 g/cm3
  • (standard deviation 10 g/cm3 )
  • Density of pure nickel 8.912 g/cm3
  • Density of nickel coin 8.9 0.4 g/cm3
  • (alloy of 25 nickel, 75 copper)

11
Sources of Error for Nickel Density
12
  • Students often focus on the details of error
    analysis and miss the big picture, losing sight
    of the forest for the sake of the trees.

13
Student t1 (s) t2 (s) 1.86 2.07 1.74 1.89
2.15 2.20 Average 1.92 2.05
t1 (s) t2 (s) Std. Dev. 0.21 0.16 Std.
Error 0.12 0.09
The numbers are close, but
different.
Expert
These time measurements agree with each other.
14
Teaching Tips
  • Remind students of the big picture view of why
    uncertainty estimates are important.
  • Show examples of how to decide whether results
    agree or disagree within their uncertainty using
    error bars on number line.
  • Require students to justify their conclusions
    based on uncertainty estimates, no general
    statements like
  • Our results only had a 5 error, so this proved
    the theory. - wrong, for more than one reason!
  • Teach concepts consistent with ISO Guide

15
ISO Guide to the Expression of Uncertainty in
Measurement (GUM)
  • International Organization for Standardization
    published new guidelines in 1993 for industry and
    research
  • NIST version physics.nist.gov/cuu/Uncertainty
  • Use standard uncertainty
  • Type A component random, evaluated
    statistically
  • Type B component systematic, judgement, a
    priori
  • use terms uncertainty and error appropriately
  • explain meaning of notation and uncert. value

16
It is better to be roughly right than precisely
wrong.
  • - Alan Greenspan
  • U.S. Federal Reserve Chairman

For more on measurement uncertainty research, go
to www.physics.unc.edu/deardorf/uncertainty
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