Nobody so far has addressed Warren's actual question, which seems to raise the problem of how well it is ultimately possible to even define such physical constants. A more conveniently macroscopic example is the length of a day. Variations in the earth's orbit limit the accuracy to which the length of individual days can be treated as a constant. Averaging over an entire year (itself subject to smaller variations) permits greater accuracy, but involves redefining the meaning of "day" in a more sophisticated fashion. Digging further down encounters alarming philosophical questions concerning (for example) the definition of measurement, and the universe within which it is legitimate to take an average --- over a sufficiently long period, the "day" is progressively lengthening. Fred Lunnon On 11/24/13, meekerdb <meekerdb@verizon.net> wrote:
If it's in a table it should tell you what it means. In a paper think it is usually three standard deviations, but NIST tables quote the std dev and relative uncertainty (std dev/mean value).
Brent
On 11/24/2013 4:05 AM, Dan Asimov wrote:
I just want to know what the number after the ± means.
--Dan
On 2013-11-23, at 10:16 PM, Rowan Hamilton wrote:
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?
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