[Phys-L] Re: infinite sig. figs.

[Michael Edmiston <edmiston@BLUFFTON.EDU>]

After reading John Mallinckrodt's recent post I think we are near
agreement.

I agree that rounding takes place immediately prior to reporting.  I
thought reporting was what we were talking about.  I keep reminding my
students to do calculations with Excel or to keep things in the
calculator registers.  When they write something down that isn't a final
result I want them to write down more digits than they think they will
ultimately need, which means they are manually acting like calculator
registers or Excel memory locations.

Thus, in this whole discussion I was assuming the calculation/analysis
are being done with as many digits as Excel or the calculator keeps.
The rub comes when the student *reports* a number that is rounded too
much, or not enough, and their question is how to determine what is too
much or not enough.

The crime of reporting too many digits strikes me as mostly a crime of
inconvenience.  After a point, the extra digits don't mean anything so
they're just excess baggage.  But the point at which that happens should
not be determined by the typical sig-fig rules.

The crime of reporting too few digits is worse because it can render the
numbers useless.  That is, the excessively rounded numbers don't show
the physics that needs to be shown.

John said,
> If the measurements showed, for instance, that v1 = (34.88 +/- .04)
> cm/s and v2 = (34.64 +/- .03) cm/s, then I'd prefer that the  student
> simply say so.

So would I, and these uncertainties are, in fact, about right for the
experiment I was describing.  However, this is the first experiment of
the term, and they haven't done error analysis in previous classes.  I
don't feel I can throw too much at them with their first experiment.
But I do feel I can tell them Denker's rules, and I can tell them that
10 digits are excess baggage while 2 digits don't communicate what the
data are capable of showing.

In fact, by using a reproducible launcher, the student run several trial
at each of several velocities.  The data clearly show what we would
expect.  At slower velocities the two velocities are closer, and as the
launch velocity increases the two velocities get further apart.  That
is, air friction gets worse at higher velocities.

John said he would reject reports of 34.879 and 34.638 if the
uncertainties are 0.04 and 0.03.  If that's the case then John would
reject many of the published numbers from NIST because they routinely
report one digit past the most significant uncertainty digit.  Denker
has referenced some of those NIST data several times in the past.

Tim Folkerts said, "I have very rarely seen a lab course where this sort
of statistical hypothesis testing was encouraged."

I spend a lot of time trying to get students to ask themselves what they
want to demonstrate and whether their data demonstrate that or something
different.  If they are not sure, I want them to think about what new
data or new experiment they could do that would help them determine what
the data are saying.  For example, sometimes when a student wonders if
the glider's loss of velocity is due to the glider going a little bit
uphill rather than from air friction, I ask if they can think of any new
data that might help answer that.  Some will think of the idea of
keeping the track the way it is, but run the glider in the opposite
direction.  Others have to be led to that idea by a series of questions
I ask them.

I sure would be happy to report that I have a lot of success turning
students into good experimentalists and good data analyzers, but I would
not be telling the truth.  I do, of course, have some successes.


Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
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