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Current issue   Ukr. J. Phys. 2017, Vol. 62, N 2, p.184-191
https://doi.org/10.15407/ujpe62.02.0184    Paper

Rode G.G.

Institute of Physics, Nat. Acad. of Sci. of Ukraine
(46, Prosp. Nauky, Kyiv 03680, Ukraine; e-mail: ifanrode@gmail.com)

Propagation of the Measurement Errors and Measured Means of Physical Quantities for the Elementary Functions x2 and x

Section: Physics Experiment Techniques
Original Author's Text:  Ukrainian

Abstract: Rules for the propagation of the error and mean value obtained for a measured physical quantity x onto another one, which is coupled to the former by means of the x2 or x functional relation, have been derived. Those rules are inherently based on the Gaussian weight scheme, so that they should provide correct results in the framework of the latter with discrete data, which is typical of a real physical experiment (with samplings). The obtained analytical form that represents the mentioned rules (the “analytical propagation rules”) and their exact character allow the processing and analysis of experimental data to be simplified and accelerated.

Key words: propagation of error, propagation of uncertainty.

References:

  1. D.J. Hudson, Statistics. Lectures on Elementary Statistics and Probability (CERN, 1964).
  2. G.G. Rode. The propagation of measurement errors and measured means of a physical quantity for the elementary functions cos x and arccos x. Ukr. J. Phys. 61, 345 (2016).
    https://doi.org/10.15407/ujpe61.04.0345
  3. I.S. Gradshtein, I. M. Ryzhik. Table of Integrals, Series, and Products (Academic Press, 1980) [ISBN: 0122947606].
  4. Propagation of uncertainty (Wikipedia) [https:// en.wikipedia.org/wiki/Propagation_of_uncertainty].
  5. H.H. Ku. Notes on the use of propagation of error formulas. J. Res. Nat. Bur. Stand. 70C, 263 (1966).
    https://doi.org/10.6028/jres.070C.025
  6. Ph.R. Bevington, D.K. Robinson. Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 2002) [ISBN: 0-07-247227-8].
  7. J.R. Taylor. An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements (University Science Books, 1997)[ISBN: 0-935702-75X].
  8. B.N. Taylor, C.E. Kuyatt. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results (NIST Technical Note 1297) (National Institute of Standards and Technology, 1994).
  9. P.K. Sinervo. Definition and treatment of systematic uncertainties in high energy physics and astrophysics. In Proceedings of the PHYSTAT2003 Conference, SLAC, Stanford, CA, September 8–11 (2003), p. 122.
  10. J. Denker. Nonlinear least squares [http://www.av8n.com/physics/nonlinear-least-squares.htm].
  11. E.W. Weisstein. Standard deviation entry at mathworld. [http://mathworld.wolfram.com/StandardDeviation.html].
  12. Evaluation of measurement data – An introduction to the "Guide to the expression of uncertainty in measurement" and related documents. http://www.bipm.org/utils/common/documents/jcgm/JCGM_104_2009_E.pdf.
  13. D.M. Kheiker, E.L. Lube, A.V. Mirenskii, N.I. Komyak, O.V. Maklakov, L.Z. Tatkin, E.N. Gurevich, V.S. Rogachev. A design of automatic diffractometer for studying single crystals. In Equipment and Methods of X-ray Analysis (Mashinostroenie, 1968), Vol. 3, p. 130 (in Russian).
  14. E.L. Lube, D.M. Kheiker. A control program for the automatic diffractometer DAR-1. In Equipment and Methods of X-ray Analysis (Mashinostroenie, 1968), Vol. 3, p. 145 (in Russian).