Re: what good is "percentage error"?

[Doug Craigen <dcc@cyberspc.mb.ca>]

On Sun, 12 May 1996, N.Pete Lohstreter wrote:

> My students are allowed to use ERROR only when there is a known value to
> compare their lab results to.  If they attempt to determine the
> acceleration due to gravity in the lab, they can report that they found
> it to be 9.71 m/s/s  an absolute error of 0.10 m/s/s or that they
> measured the value to within 1% of the accepted value, or that their
> value only had a 1% error.
>
> If there is not an accepted value to compare to, then an uncertanty is
> expected on the report.

Excuse me for using your words above as a springboard for replying to
several people's comments.

In a case such as this, where there is a value that we already have a high
degree of confidence in, such as "g", then I will admit that there is a
certain amount of semantic justification to calling the result an "error"
- more so than an "uncertainty".  If we truly believe that g = 9.81 and
the experiment is only being done for practice etc etc etc, then yes a
student who gets 9.71 is actually wrong by 0.1.  However, using the words
"error" or "uncertainty" here only confuses the student about real error
analysis.  

I believe that from the outset students need to be taught that
an experiment without an estimate of the accuracy ("uncertainty" or
"error" analysis) is not worth doing at all.  If your student gets a value
of 9.71 they should have an idea of how precise they believe this number
to be independent of whether they know what anybody else has ever measured
for this number.  So if they have 9.71 +/- 0.2 (which then becomes 
9.7 +/- 0.2) they know that they have pinpointed the value of g to be
somewhere in the vicinity of 9.5 to 9.9.  They then compare this with the
accepted value of 9.81 and say that there is no cnotradiction between
their experiment and that number.  This sort of thinking should be among
the ABCs of laboratory work, proper statistical errors etc are a topic
left for college.

Finally, because students are usually measuring previously established
quantities, there is a real danger of giving them the impression that
science is about running an experiment that will find a desired answer.
Watch a group of students perform an experiment to measure 'g'.
Everything they do is driven by a desire to get the answer of 9.8.  By
teaching them that the difference between their answer and somebody else's
answer is their "error" or "uncertainty", we reinforce this misconception
about experimental science. 

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| Doug Craigen                                                 |
|                                                              |
| If you think Physics is no laughing matter, think again .... |
|    http://cyberspc.mb.ca/~dcc/phys/humor.html                |
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