From the data
(set of observations), calculates some results for the propagation
of errors (propagation of uncertainty). Upper limit
of error ("large" but always valid) and probable error
(smaller but valid only for independent errors) are addressed.
It is assumed that, for a probability of 95 %, it is
Δ x ≅ 2 σx, from
Φ(k) − Φ(−k) ≅
95.4 % for k = 2 (Gauss). Other authors
(such as Taylor [1997]) give
Δ x ≅ σx.
A simple graph is shown with the probable error and its
limits.
| Other suggested data: |
Addition | (n = 4)
(n = 3) |
540 -72 940 -97
200 50 -20 | |
with errors 10 1 20 1
2 2 1 |
[Taylor, 1997, 50]
[ibid., 62] |
| |
Product | (n = 3)
(n = 3) |
200 5.5 10
200 50 20 |
exp.s 1 1 -1 (a division)
exp.s 1 1 -1 |
with errors 2 0.1 0.4
4 4 2 |
[Taylor, 1997, 53]
[ibid., 62] |
|
|
• Nepf, Heidi:
Propagation of Uncertainty.pdf
(accessed 2008-08-13) (=),
MIT.
• Scuro, Sante R.:
Intro.
to error theory.pdf (accessed 2008-08-13) (=),
Texas A&M Univ.).
• Err.
analysis (PennState U.).
• Wolfs, F.,
see "Error analysis"
(Univ. of Rochester).
• Weisstein, Eric W.,
"Error
propagation". From MathWorld — a Wolfram Web Resource
(2008-08-04).
• Taylor, John R.,
1997,
"An introduction to error analysis", 2.nd ed., Univ. Sci. Books
(USB), Sausalito, CA (USA)
(intro IE).
• Bevington, Philip R. and
D. Keith Robinson, 2003, "Data reduction and error analysis for the physical
sciences", 3.rd ed., McGraw-Hill, New York, NY (USA).
• Taylor, John Keenan,
1987, "Quality assurance of chemical measurements", Lewis Publishers, Inc., Chelsea, Michigan (USA).
• 1778-08-23: Wronski, Josef-Maria Hoëné de, birthday.
|
