Re: [Phys-l] each error bar == one standard deviation

[ludwik kowalski <kowalskil@mail.montclair.edu>]

Like most people, I usually express uncertainties as +/- one standard  
deviation. But Brian made a different choice and I followed his  
example. In True Basic X=rnd will select a random number from a  
distribution which is uniform between  -1 and +1.

Suppose Y is the sum of 12 such numbers. Then Z=Y-6 is a random number  
whose mean value is 0 and whose standard deviation is 1.

R=A+B*Z

is a random number whose means value is A, and whose standard  
deviation is B. My Monte Carlo problem uses a subroutine delivering R  
for any specified A and B. I do not remember where I copied it from,  
when I was a postdoc, about 40 years ago.

Ludwik




On Aug 30, 2010, at 5:19 PM, Folkerts, Timothy J wrote:

> > Unless otherwise specified very explicitly:
> > -- For a Gaussian, each error bar is one standard deviation.
> > Note that this is approximately equal to the HWHM.
> > The + and - error bars together cover 68% of the probability.
> > -- For a triangular distribution, each error bar is exactly
> >  one HWHM.  The + and - error bars together cover 75% of the
> >  probability.
> > -- For a square distribution, each error bar is exactly one
> >  HWHM.  The + and - error bars together cover 100% of the
> >  probability.
>
> There are other common conventions.  For example, NIST sticks with  
> +/- 1 standard deviation for all of these.  (http://physics.nist.gov/cuu/Uncertainty/typeb.html 
> )
>
> "The following figure schematically illustrates the three  
> distributions described above: normal, rectangular, and triangular.  
> In the figures, µt is the expectation or mean of the distribution,  
> and the shaded areas represent ± one standard uncertainty u about  
> the mean. For a normal distribution, ± u encompases about 68 % of  
> the distribution; for a uniform distribution, ± u encompasses about  
> 58 % of the distribution; and for a triangular distribution, ± u  
> encompasses about 65 % of the distribution."
>
>
> I'm not saying one convent is better than another -- I'm just saying  
> varying conventions are out there.
>
> Tim Folkerts
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Ludwik

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