Re: [Phys-l] formatting uncertainties (was: New gravitational constant)

[Rick Tarara <rtarara@saintmarys.edu>]

----- Original Message ----- 
From: "John Denker" <jsd@av8n.com>
> OK, we all agree that students *are* taught in high school
> not to report numbers like that.
>
> My question is, _why_ are they taught that?  I don't see
> anything wrong with such an expression, and indeed there
> are situations where such an expression is entirely
> appropriate, as discussed below.

My answer is that these ARE high school students--and high school teachers. 
All of the experimental and statistical subtleties that John brings up are 
beyond the HS curriculum.  I know JD thinks they shouldn't be, but they are. 
There are too many conceptual and critical thinking concerns at this level 
to tackle them all, and I suspect that the primary thing most instructors 
are dealing with is students multiplying two values on their calculators and 
then writing down every digit that appears.

Let me put it another way...when did each of us actually have a statistics 
course?  If like me---never.  (It is possible that HS certification may 
require such, whereas getting a Ph.D. in physics does not.)  I had 9 
semesters of undergraduate math, but no stats.  What stats I know, I learned 
in grad school while doing 'real' experiments and dealing with determining 
uncertainties for nuclear energy levels as measured in complex 
experiments--lots of levels of experimental and statistical uncertainties. 
How many HS teachers have had that level of background?  How many of their 
students can deal with the differences between the uncertainty of a given 
measurement and the statistical uncertainty based on a series of 
measurements -- especially when most intro lab experiments may have only 3-5 
trials.

> When I plot the distributions in the usual way, the difference
> between .67255 ± 0.001 and .6726 ± 0.001 is readily perceptible
> to the naked eye.  If somebody is unable to perceive the difference,
> that's his problem, not mine.

I confess to having the above problem--OK, maybe if I actually saw the 
plots--but I don't know from this what I should expect to see.  Sure, that's 
my problem, but I suspect one shared by many here.  ;-)

Rick

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Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN
rtarara@saintmarys.edu
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