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Re: Error, a frank response!



On 14 May 97 at 1:15, Lanzafame, Frank wrote:

For chemical glassware, 1%
is pretty crude; 0.2 % is more typically the range of accuracy. The
precision should be better than the accuracy.

Ahh. Thank you. I learned something here. I had no idea that the
typical analytical chem labs performed by undergraduates were
capable of such fine precision and accuracy. (Recognizing, of
course, that the final answer will be less precise than any single
glassware precision number.)

Having read Frank's discussion, I now think that this percent
deviation sort of chem lab grading IS reasonable, as long as the
experimental random uncertainty is considerably less than the
deviation from the secret known value. But, do the students consider
the final experimental uncertainty in evaluating their results? It
sounds like they do in Frank's course. If not, then it is still an
intellectual swindle to calculate a percent deviation.

I am concluding from this useful discussion that is it appropriate,
in certain limited circumstances, to calculate a "percent error" or
percent deviation. However, it is ONLY appropriate if these
conditions apply:

1. there is an authoritative value available (definitive measurement)
2. the experimental random uncertainty is small (where small is to be
defined) with respect to the deviation from the authoritative value.

By small I mean three standard deviations of the experimental
measurement set must be several times smaller than the difference
from the authoritative value.

Situation 1. is very common. Situation 2 is very, very rare in
physics. Situation 2 may very well be common in analytical chemistry.

Given that #2 is rare in physics (I'd hazard that the situation is
almost never true in an introductory course) then it is almost never
appropriate to calculate a percent deviation in a physics course.

Calculating a percent deviation without #2 hides from students the
true meaning of uncertainty while giving them the impression that
they have taken a measure of the precision of their experiment when
they have not. (They have not because the random uncertainty of the
work is not taken into account.) As such the calculation is
misleading and a pedagogical evil.

I'm using strong language here because I think this point, while
subtle, is important and often misunderstood. I apologize if I've
stepped on some toes of some contributors here in my statements---the
discussion is helping us all sharpen our concepts.

JEG

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