Re: what good is "percentage error"?

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

On Mon, 12 May 1997, John E. Gastineau wrote:

> It's time to stir the phys-l pot again. 
>
> 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.

I totally agree with you. This misleading and nearly useless formula is
even found in some commercial *college* physics laboratory manuals.

This formula actually compares only two experimental results, the
student's and the *book* value, and ought to be called the "experimental
discrepancy." But it tells us nothing about the quality of the experiment,
for even a sloppy experiment could sometimes yield a small discrepancy.
The student still has an obligation to do an error analysis to express the
uncertainty of the results, which can be done even if there's no
*authoritiavie* value to compare with.

> 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.")

Right on!
> 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. 

A point no one has mentioned so far is that this kind of a comparison is
never done in serious scientific work. If you submitted a paper to Phys.
Rev. with such a calculation of "error" in it, the paper would likely be
rejected with extreme prejudice. We, as teachers, have some obligation to
use the standards, language, and style of our discipline, and not some
eccentric constructs introduced for dubious pedagogical purposes.

A separate issue: Percent vs. absolute measure. An absolute measure of
discrepancy or uncertainty is always appropriate. Percent measure may be
meaningful in some cases, but one ought to have a good reason for using
it. Percent measure is inappropriate or misleading in any case where the
quantity is measured on a scale with arbitrrarily chosen fixed points. For
example, you shouldn't express temperature differences as percents when
using the Celsius or Fahrenheit scales, but it's ok if you are using the
absolute (kelvin) scale. If you measured temperature to an uncertainty of
1 degree C, is that a 1% uncertainty in the boiling point? The same
absolute uncertainty in a temperature of 5 degrees C would then be 20%?
Absurd, isn't it?

Likewise, one shouldn't use percents for index of refraction, for its
scale has the arbitrarily chosen value of 1 for a vacuum.

> 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. 

Old habits die hard. They probably "learned" it in some previous course,
or perhaps a chemistry course.

> Why? What good is it? Am I missing something? 

In my opinion, it's no good, and should be purged from textbooks. You
aren't missing a thing, and students won't lose anything by throwing it
out. What is wrong with textbook authors that they allow this archaic and
misleading notion to persist this long? I was a reviewer of Bernard and
Epp's laboratory manual (6th ed) and to my surprise they changed this part
of the error discussion to something better. Perhaps because I supplied a
complete rewrite, which they used. They also changed nearly every
occurence of the ugly word "percentage" to "percent" throughout the
manual, and even in the data sheets! I urged them to eliminate the
pre-formatted data sheets, but the editors thought it would hurt sales,
for "Teachers have lots of papers to grade, and the pre-printed format
saves time."

You will find my views on this on my web page under "Laboratory" in a
document on Error Analysis (Non-Calculus). There's also a document there
on writing lab reports.

	-- 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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