It means a great deal more than that. There are statistical errors (usually calculated assuming a Poisson distribution) but there are also systematic errors, which are very complicated to study. The systematic errors come from many sources, some of which may be correlated. It is necessary to understand these systematic errors in a linear algebra sense. You need to think of the solution space a manifold, and the errors live in a tangent space near the measurement point. Correlated errors represent non-orthogonal basis vectors in this tangent space. If you have removed all correlations from your errors, then you have an orthogonal basis for your tangent space, and then you can add your errors in quadrature and be sure that you have an accurate error analysis. I spent years studying this in great detail in grad school. On Sat, Nov 23, 2013 at 8:34 PM, Dan Asimov <dasimov@earthlink.net> wrote:
This is my chance to ask: When a physicist writes a measurement like
548.57990943 ± 0.00000023,
does the number after the ± represent the standard deviation (root-mean-squared error), or something else?
Thanks,
Dan
On 2013-11-23, at 7:57 PM, Rowan Hamilton wrote:
Physicists spend a great deal of time and effort on understanding the errors in any physical measurement. A particle physics PhD involves about 2 years of classes, 2 years of slave labor, 1 year of measurement and then 3 years of error analysis. This is no joke. Since particle physics is an inherently statistical field, particle physicists are experts at error analysis.
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