Re: what good is "percentage error"?

[gastineau@badgerden.com (John E. Gastineau)]

> 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.

This is exactly the use of percent error calculations that I worried
about after reading  instructions for the same in a commercial lab
manual. 

Let's keep using the "g" experiment as an example. Suppose a certain
apparatus yields a cluster, normally distributed but centered on 9.6
m/s^2, with a standard deviation of 2.0 m/s^2. (I'll suppress units
from now on.) Two students, correctly performing the experiment, 
happen to get these results from the rig: 9.95 and 8.02. Neither
result is any better than the other; it is only a matter of luck. By
the percent error method, one measurement is at the 1.5% level and
the other at 18%. Yet, we know that they are of exactly the same
quality. (These students have no way, notice, to determine how many 
digits to report.)

The only way to probe the precision of the experiment is to do the 
experiment enough times (or look for internal evidence such as curve 
fit uncertainties) to reveal the underlying distribution of values.

This is why I am concerned about the use of percent error in any way 
in physics classes--it conveys to the student the wrong impression 
about the information contained in a single measurement (which 
usually isn't much).


In my opinion the only way to discuss experimental precision is to 
perform multiple measurements and look at the spread of your values. 
Let's say we do a "g" experiment using a photogate and a picket 
fence. The slope of the velocity time graph might be 9.85. Alone that 
tells me nothing of its precision! I must either calculate the 
uncertainty of the fitted parameters (which, alas, most calculators 
won't do) or perform the experiment a number of times and determine 
the spread of the collection of slopes. 

Let's say we do the latter, which is more easily understood by 
students. (As another phys-l contributor said, multiple measurements 
FORCE the student to confront the issue of which is the best value?) 
That collection of values might be, ordered by value, 9.64, 9.69, 
9.76, 9.80, 9.82, 9.89. 

Even without finding the standard deviation, which I'll  admit is a 
subtle quantity for engineering students much less HS students, 
we can look at the maximum and minimum values and say that the 
experiment seems to be pointing at a value of g in the range of 9,64 
to 9.89. That's the result of the experiment. 

Of course, everyone wants to compare to the "accepted" value (in 
scare quotes since it begs the question of who accepted it!). The  
comparison is this simple: if the comparison value falls within the 
range from the experiment, we have agreement. That's all one can hope 
for--agreement. 

If you all look back at my original post, I said I wanted to stir
the pot,  and I certainly succeeded. I started this whole thread
after being troubled by the presence of what I considered wrong
thinking in a certain commercial lab manual (which I will not name!)
of the percent error calculation. My goal was to see if very many
physics teachers were in fact using this sort of calculation, and
what their reasons were. 

One poster commented that we have to start small in what we expect
students to understand, and certainly experimental uncertainty is a
difficult concept that even physics majors have a hard time with.
However, the percent error business seems to lead students in the
wrong direction, while you can at least get the concept started with
multiple measurements. 

Thanks for the comments, all.

JEG



==================
John E. Gastineau                (304) 296-1966
900 B Ridgeway Ave.              gastineau@badgerden.com
Morgantown, WV 26505
www.badgerden.com/~gastineau