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Re: what good is "percentage error"?





On Tue, 13 May 1997, Richard W. Tarara wrote:

An example of why getting students to think in terms of percentage
differences (uncertainties, errors) is important can be illustrated using a
simple experiment. In the first lab of the year, I have students
determining densities and hence the material of several objects. One of
those objects is a long (50-60 cm) copper wire with a diameter in the 1-2
mm range. The wires have been bent for storage. The students use a dial
caliper to get the diameter and a meter stick for the length and generally
don't get a very good match to copper for the density even though (from the
color) many do suspect that the wire is copper. When asked to comment on
their findings, most will blame the length measurement for the problems
they had with the wire--it was hard to straighten and they had to use a
meter stick--while the diameter measurement seems quite accurate to them
(after all, the dial caliper can be read to .01 cm!) The teaching moment
then presents itself to have them calculate the percent uncertainty in the
length measurement even if it is only good to +/- 1 cm, versus the
uncertainty in the diameter if good to +/- 0.1 cm. The absolute
uncertainty in the diameter may be 1/10 that of the length but the
percentage uncertainty is 5 times greater.


Rick


A good example, Rick. This gets at the *reason* for dealing with
experimental uncertainties. They allow us to make meaningful statements
about the probable uncertainty of results *and* to understand functionally
*how much* each source of uncertainty contributed to that. Such
considerations allow one to redesign the experiment to improve it in many
cases. If uncertainty analysis is seen as a sterile computational
exercise, students will dismiss it as more busy-work drudgery. We need to
design experiments in which uncertainty analysis is an integral part of
carrying out the experiment to achieve the best possible results with the
given (imperfect) apparatus. Hardly any commercial lab manuals support
this objective.

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
Home page: http://www.lhup.edu/~dsimanek FAX: 717-893-2047
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