From: "JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL 60439" <JLU@hep.anl.gov>
Date: Mon, 12 May 1997 11:09:56 -0500 (CDT)
Hi John-
Yes, and it's even worse than that. The "percentage error"
calculation presupposes that the quantity measured is identical to the
quantity compared with, which is often not the case (this is a bit different
from "systematic error").
The exercise, which is done in all physics labs I'm familiar with
except my own, is supposed to acquaint the student with the idea that
all measurements are inexact. It doesn't work, as you can tell by walking
into a doctor's office and watching how the height, weight, temperature and
blood pressure measurements are done and evaluated (was the last weight
measurement done while you were wearing your winter coat?).
The guiding principle should be, I think, don't teach anything until
there is a payoff from learning it. Courses involving high precision
instrumentation (usually more advanced courses) may involve multiple
measurements of a quantity, in which case the results will differ from
measurement to measurement. In that case the student must resolve the
issue: which measurement do I accept? In that case, a major part of the
course can be devoted to the study of statistics and statistical concepts,
which can be used to help answer the students' question.
There was an earlier thread on this topic.
Regards, Jack
*******************************************************
Today I was looking through a commercial high school physics level lab
manual, and came across the instruction to perform an experiment once
and then determine the "percentage error" by calculating
(accepted - measured)/accepted * 100%.
Is this quantity even being taught? How can it be used? It seems to me
that it is useless at best and misleading at worst, and should never
be used.
It does not measure the precision of a measurement in any way, being
based on a single measurement. A small error could be due to a high
quality experiment or it could be due to luck. Only multiple
measurements can establish the precision of the experiment. (I include
the internal statistics from a curve fit as "multiple measurements.")
It does not measure systematic error, again since it is based on a
single measurement. The deviation from an accepted value is not useful
since the random error is also present.
It does imply to the students that it is a measure of the quality of
the experiment, or of their skill. Since the "percentage error"
measures neither of these, it is a misleading quantity.
Even after discussing concepts of random errors, standard deviations,
and such, I've had to work to keep many students in freshman-level
university physics from including the calculation in their lab reports
as a measure of their experimental success, so I know that the
quantity is being taught and emphasized out there.