Re: [Phys-l] quadratic uncertainty

[John Denker <jsd@av8n.com>]

On 08/30/2010 06:45 AM, LaMontagne, Bob wrote:
> 1.00   (+0.12 / -0.03)   (+0.14 i  / -0.14 i)
>
> 1.08   (+0.02 / -0.11)   (+0.14 i  / -0.14 i)

I see some effort and some cleverness went into this.

++ Two "points" are given, presumably to indicate a
bimodal distribution.  
++ The lopsided error bars indicate that each part 
of the distribution is lopsided.
++ The imaginary parts are a nice touch, too.

That gives us ten parameters (maybe less if you 
account for symmetries) to describe something where
the input had only two nontrivial variables.

Alas, it's like ants at a picnic.  If you see ten,
there might be more.

Unless I've made a mistake, the distribution on x
is worse than bimodal, and worse than skewed.  My
analysis can be found at
  http://www.av8n.com/physics/uncertainty.htm#fig-quad-roots-gcross

I take this as an object lesson in:
  a) The importance of plotting and eyeballing the
   data, rather than relying on mathematical formalisms
   such as "mean" and "standard deviation".
  b) The power of Monte Carlo to help make sense of
   situations where other methods fail.