Propagated Error Bars
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of errors is essential to be able to judge the relevance of observed trends. Below, a brief definition of the main concepts and a discussion of propagation of error division generic ways to obtain error estimates is provided. [1] [2] Of
Error Propagation Physics
course, any particular measuring device generally requires specific techniques. Contents 1 The measurement process 2 Calibration error propagation calculator 3 Error estimate (experimental error known) 4 Systematic and random errors 5 Error estimate (experimental error unknown) 6 Test of statistical validity of the model 7 Fluctuations and
Error Propagation Chemistry
noise 8 Non-Gaussian statistics 9 Integrated data analysis 10 Summary 11 References The measurement process The measuring device performs measurements on a physical system P. As a result, it produces estimates of a set of physical parameters {p}. One may think of p as loose numbers (e.g., a confinement time), data along a spatial chord at error propagation square root a single time (e.g., a Thomson scattering profile), data at a point in space with time resolution (e.g., magnetic field fluctuations from a Mirnov coil), or data having both time and space resolution (e.g., tomographic data from Soft X-Ray arrays). The actual measurement hardware does not deliver the parameters {p} directly, but produces a set of numbers {s}, usually expressed in Volts, Amperes, or pixels. Calibration The first task of the experimentalist is to translate the measured signals {s} into the corresponding physical parameters {p}. The second task is to provide error estimates (discussed below). Generally, the translation of {s} into {p} requires having a (basic) model for the experiment studied and its interaction with the measuring device. In the simplest cases, the relation between {s} and {p} is linear (e.g. conversion of the measured voltages from Mirnov coils to magnetic fields). Taking s and p to be vectors, such a conversion can be written as $ p = A \cdot(s - b), $ wher
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Ask Question _ Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it error propagation definition only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top error propagation with different plus and min errors http://wiki.fusenet.eu/wiki/Error_propagation and data fitting up vote 3 down vote favorite 1 I am refreshing my memory on error propagation and data fitting (Levenberg-Marquadt). You have the absolute (measurement) error, the relative (measurement) error, the population/sample standard deviation and the population/sample standard error. These are typically written down as: $$a \pm b = a (+b, -b)$$ But suppose you have different errors in the plus and min direction? $$a (+b, -c)$$ What are the rules here http://physics.stackexchange.com/questions/151444/error-propagation-with-different-plus-and-min-errors-and-data-fitting again and how are the formula for error propagation modified? Also, how is this taken into account in data fitting? Any good resource on this is welcome. error-analysis share|cite|improve this question edited Dec 9 '14 at 20:43 John M 5041519 asked Dec 9 '14 at 18:47 user965972 1162 Interesting question. Asymmetric errors seem terribly complicated compared to our familiar errors, see page 28: phas.ubc.ca/~oser/p509/Lec_10.pdf . –jinawee Dec 9 '14 at 19:15 "Asymmetric errors: Quite honestly, the typical physicist doesn't have a clue." That's me alright. :( –user965972 Dec 9 '14 at 20:31 @jinawee The resource you posted is interesting, I had not come across the Barlow method. However, at least for the examples given, the results are extremely similar to propagating the positive and negative uncertainties separately. Are the differences worth worrying about unless you are very certain of the form of the pdf? But if you were, why use error propagation? Need to read the Barlow paper. arxiv.org/pdf/physics/0406120v1.pdf –Rob Jeffries Dec 9 '14 at 23:22 add a comment| 1 Answer 1 active oldest votes up vote 1 down vote I think what you could do is treat the quoted value as the most likely value and the two uncertainties as semi-gaussian probability distributions. So for example in error propagation you would have to propagate the
a given measurement can be made is determined by variations in the thing being measured. For instance, a number of measurements of the diameter of a baseball would probably show that the ball is not a perfect sphere and consequently the measured values would http://www.mcm.edu/~bykov.tikhon/lab09/Error%20Propagation.htm be distributed over a range of values. Sometimes the accuracy with which a measurement can be made is determined by the accuracy with which the scale on the instrument can be read. For example, it is hardly possible to read a meter stick more closely than + 0.5mm. The limits of accuracy may be set either by the precision of the scale of the instrument or by the ability and/or skill of the observer. But limits always exist. It error propagation is also possible to have systematic error due to faulty instruments, for example, a meter stick which is not exactly one meter long. Then all measurements made with the instrument are in error, usually by a constant factor. Uncertainty is not the failure of the observer to read the instruments correctly. If the observer records a 99.5 when the value should have been 89.5, this is not uncertainty, but is a mistake. It is always of interest and usually propagated error bars necessary to know just how dependable are the results of an experiment and it is usually not the absolute uncertainty that is important but the percent uncertainty between the measured value and the ``true'' value (a.k.a. the ``accepted value'') . For example, a 1000 km uncertainty in measuring the distance from Abilene to Moscow is much worse than a 1000 km uncertainty in measuring the distance from Abilene to the Sun. When an accepted answer exists, the percent error is calculated from the difference divided by the accepted value: If large enough number of measurements for the same physical quantity is performed then the average between all the measurements can be taken as the accepted value for this quantity. A satisfactory way to estimate absolute uncertainty of the final result would be by taking the maximum of absolute uncertainties for each of the measurements of this quantity. The precision of the measuring device and limitations on the scale reading also have to be taken into account. If it so happens that limitations of the scale and reading are larger than the uncertainty predicted based of the spread of your measurements then instrumental uncertainty due to the measuring device has to be taken as the final estimate of the absolute uncertainty. II. Propagation of Uncertainty Along with knowing the percent error of experimental result, it is also necessary sometimes to know whether the experimental
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