Re: what good is "percentage error"?

[PHRP@FHSUVM.FHSU.EDU (Roger A. Pruitt)]

I agree with you that the so-called percentage error is very misleading. I
have tried to convince students to call it "percentage deviation" with the
idea that this is a better term. I suspect that someone long ago dreamed
this up as a way that students could compare quantitatively how close their
measurement came to an accepted value. However, I would like to see the
whole idea dropped.

In high school and even in college in the long ago, time usually didn't
permit multiple measurement so a single measurement was all that could be
performed. Now days with data aquisition hardware, measurements can be made
with ease, and we should strive for more sophistication in our data
analysis. You say, "I include the internal statistics from a curve fit as
'multiple measurements.'" This is good. We should also design experiments at
the beginning level that allow for some other types of easy data analysis.

There is, however, a real question about how much error analysis should be
required at the beginning level since this can consume an inordinate amount
of time which can obscure the real purpose of the experiment at this level.

Roger

> 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.
>
> 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.
>
> Why? What good is it? Am I missing something?
>
> JEG
>
> ==================
> John E. Gastineau                (304) 296-1966
> 900 B Ridgeway Ave.              gastineau@badgerden.com
> Morgantown, WV 26505
> www.badgerden.com/~gastineau
==============================================================
Roger A. Pruitt, PhD
Professor of Physics
Fort Hays State University
Hays, KS  67601
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