Re: [Phys-L] teaching error analysis in high school

[Jeff Bigler <jcb@mit.edu>]

On 9/30/2012 2:44 PM, John Denker wrote:
> On 09/30/2012 07:33 AM, Jeff Bigler wrote:
> > I taught them how > to estimate uncertainty 
>
> Good.
>
> > and how to propagate uncertainties through their
> > calculations. 
>
> Not so good.
>
> > I based what I teach them on an error analysis tutorial from Columbia
> > University, at <http://phys.columbia.edu/~tutorial/>. 
>
> The "propagation" ideas presented there are wrong in theory and
> unsafe in practice.  For example, it says:
>
> > > Therefore, we arrive at the general rule for the error in the case of
> > > sums and differences: The absolute error of the result is the sum of
> > > the absolute errors of the original quantities. Remember, even if you
> > > subtract two quantities you still add their absolute errors.
>   http://phys.columbia.edu/~tutorial/propagation/tut_e_4_1.html
>
> That is *NOT* the general rule.  That only works in theory if the
> addends are uncorrelated ... which in rarely if ever the case in
> practice.  All similar propagation rules suffer from similar problems.
>
> Constructive suggestion:  Use the _Crank Three Times_™ method.
> It is easier and in every way better.
>   http://www.av8n.com/physics/uncertainty.htm#sec-crank3

Hmm.  In the lecture, I used Crank Three Times in a simple area (length
x width) calculation to illustrate how adding relative errors gives the
same result.

Agreed that the variables need to be uncorrelated, but as you say in
your discussion, the same needs to be true for C3T.  I'm explicitly
having them assume that the variables are uncorrelated because most of
my students don't have the statistics background to deal with anything
else.  (Yes, I do mention that just like other assumptions that we make
at different points in the course, this is a simplification.)

My educational goal is for them to think of uncertainty as something
quantifiable, to understand in basic terms about how they might be able
to quantify it, and to practice doing so every time they perform an
experiment where they measure something.
-- 
Jeff Bigler
Lynn English HS; Lynn, MA, USA
"Magic" is what we call Science before we understand it.