Re: [Phys-L] propagation of erroneous techniques

[John Denker <jsd@av8n.com>]

On 03/11/2014 10:23 AM, rjensen@ualberta.ca wrote:
> Physicists should love either the sig figs method or propagation of
> error. 

You're kidding, right?  The sig figs rules are a lot of work, and
almost guarantee getting the wrong answer, both as to the nominal
value and the uncertainty.

The "propagation of error" rules are even more laborious, so much
so as to be wildly inappropriate to the introductory course ... 
and are by no means guaranteed to get the right answer.

  For starters: Try using propagation-of-error to calculate the 
  correction factor /and the uncertainty thereof/ associated with 
  the obliquity of the moon's orbit, as applied to the moonrise 
  photo that was recently discussed in this forum.

  Compare to the actual distribution (to a good approximation):
     http://www.av8n.com/physics/probability-intro.htm#fig-moon-dec-error-density-adaptive

> I have students coming to my class saying that they were taught
> to report all answers to 3 sig digits.

That's actually a pretty good starting point.  That's dramatically 
less work than fooling with sig figs, and a lot more likely to get 
the right answer for the nominal value.

It says nothing about the uncertainty, which is often the correct
thing to say.  There are lots of situations where the raw data
never had any error bars to begin with, and/or you don't care 
about the error bars, and/or the uncertainty could not possibly
be expressed in terms of error bars.

Reference:
  http://www.av8n.com/physics/uncertainty.htm

Note:  The first couple of pages should be understandable to and
relevant to just about everybody.  Later pages delve into the
gory details.