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

[John Denker <jsd@av8n.com>]

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