From a randomly
generated (G) or user-supplied (S) sample (set of observations),
calculates some common statistics: average (x-bar),
standard deviation (s), average deviation (δ).
The graph shows: for G, δ simulated
for random samples of size 2k trials, with (integer)
k = 1..log2(ntrial)
(log2100000 = 16.6 → 16); for S, the user data,
without the (possible) outlier.
An extreme (smallest or largest) value in the sample is
assessed to estimate whether it is an outlier (to be rejected).
The decision on what is an outlier is a delicate question.
See, for example, Barnett and Lewis [1998].
Excel:
t = Studinv([(1+prob)/2, ν] becomes
TINV[(1-prob, ν] Typically,
ν = n − 1. (Here, n had already been
reduced, so ν = noriginal − 2 .)
Other suggested data:
26.6 26.8 26.2 26.9 27.1 27.0 (smallest)
26.6 26.9 26.7 26.6 26.7 26.6 (largest) |
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• Scuro,
Sante R.: Error
theory.pdf (Texas A&M Univ.).
• Err.
analysis (P. C. Eklund, PennState U.).
• Petridis, A.
(Drake Univ.).
• Wolfs,
F., see "Error analysis" (Univ. of
Rochester).
• Weisstein, Eric W.,
"Error
propagation". From MathWorld — a Wolfram Web Resource
(accessed 2008-08-04).
• Barnett, Vic and
Toby Lewis, 1998, "Outliers in statistical data",
3.rd ed. (=1994, 1978), Wiley,
New York, NY (USA). (At ISEG Library: 1994.)
• 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).
• Google search: simulation
"Monte Carlo" "Chemical Engineering"…
• Kurtosis, skewness.xls
• Descriptive
statistics (SAS v7 doc., Oklahoma State Univ., Stillwater).
• Student's
t (this site).
• Taylor, John R.,
1997,
"An introduction to error analysis", 2.nd ed., Univ. Sci. Books
(USB), Sausalito, CA (USA)
(intro IE).
• [Lyons, 1991]
• [J. K. Taylor, 1987]
• Weisstein, Eric W.,
"Student's
t-distribution". From MathWorld — a Wolfram
Web Resource (accessed 2008-08-04).
• Chauvenet, William, 1820–1870
("Chauvenet's
criterion").
• 1805-08-04: Hamilton, Sir William Rowan, birthday.
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