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



Ludwik,

I have no problem with people expressing experimental uncertainty in term of a bar = +- 1 SD. Simply stating your choice (and +-1 SD is by no means universal, neither is +-1 SE) seems sensible.
In this case, supposing one had a physical system where the roots represent a quantity of mass or some such (to take Ludwik's example),
the question remains this: what bands of uncertainty in this particular arrangement allow us to conclude that the experimenter knows what (s)he is doing?

For all three coefficients given to the SAME uncertainty for simplicity's sake, it turns out that an SD = 0.00032 provides reasonable assurance of delivering positive real roots from this pathological quadratic - I find less than than 1 per 1000 trials in error i.e going complex at this level)
Important to recall that double precision is advised when modeling it. In other words, an experimenter reporting an error bar
for the coefficients as 1.000 +-0.0001, 2.08 +- 0.01 , 1.08 +- .01 in a system whose roots are expected to be positive real, is not playing with the requisite deck of cards in this matter.

Brian W

On 8/30/2010 6:30 PM, ludwik kowalski wrote:
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