| Chronology | Current Month | Current Thread | Current Date |
| [Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
Date: Tue, 10 Oct 2000 12:57:42 -0400<PHYS-L@lists.nau.edu>
From: Michael Edmiston <edmiston@BLUFFTON.EDU>
Reply-To: "phys-l@lists.nau.edu: Forum for Physics Educators"
To: PHYS-L@lists.nau.edu
Subject: Re: systematic error and statistical error
I agree with John Denker's statements, and I like his ruler example.
I especially like his statements about *labeling* what type of error is
being reported. A similar problem arises in distinguishing between the
sample standard deviation, and the standard error of the mean. When a
person reports the result of several measurements and indicates the result
in the format 3.45 +- 0.03, what is the meaning of this number? Is it the
standard deviation, or is it the standard error of the mean, or something
else? I think several different meanings are commonly used, and the only
way for the reader to know is for the writer to specify.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817
John Denker said:
1) In a word, no, there is no "right" order.
1a) If you state a statistical uncertainty, it must be labelled as such.
1b) If you state a systematic uncertainty, it must be labelled as such.
..) In any case, the overall uncertainty should be stated (and labelled as
such if there is any doubt).
2) As I have written before: there is no clear-cut, principled distinction
between systematic uncertainty and other types of uncertainty.
For example, suppose the rulers in the classroom expand and contract as a
function of temperature. At any given moment, this leads to a systematic
error. But if the experiment is repeated at different times of the year
(i.e. at different ambient temperatures) the systematic error becomes a
random error. Also if the ruler is randomly selected from an ensemble
(metal, wood, plastic, ...) another element of randomness is
introduced. The point is that it's not worth obsessing over the details.
At the end of the task you want to understand and communicate the _physics_
of each process that introduces significant uncertainty; applying
adjectives like "systematic" to the various processes is of secondary
importance or less.
========
For low-quality measurements, the distinctions between accuracy / precision
/ systematic error / statistical error don't matter very much. For
high-quality
measurements, you need to worry about a lot more than that.
The pros typically just talk about "uncertainty" and give a detailed
analysis of the many contributions to the uncertainty.
As it says on
http://physics.nist.gov/cuu/Uncertainty/international2.html
% The end result of the work of ISO/TAG 4/WG 3 is the 100-page _Guide
% to the Expression of Uncertainty in Measurement_ (or GUM as it is
% now often called)