The distribution of composite measurements: How to be certain of the uncertainties in what we measure

American Journal of Physics

Volumn 72, Issue 8, 2004, Pages 1068-1081

  Silverman, M P ^a   Strange, W ^a   Lipscombe, T C ^b  

^a TRINITY COLLEGE   (United States)

^b JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4344614575     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1738426     Document Type: Article

References (26)

1. Particle Data Group, "Review of particle physics," Euro. Phys. J. C. 17 (2002), Sec. 28.
2. K. Hagiwara et al., "Review of particle properties: Statistics," Phys. Rev. D 66, 010001 (2002).
3. B. R. Martin, Statistics for Physicists (Academic, London, 1971).
4. ISO Standards Handbook 3: Statistical Methods (ISO, Geneva, 1979).
5. 2 and X=U(0,a) is a random variable uniformly distributed over the range from 0 to a. Z itself is not uniformly distributed, and therein lies the reason for the inequality. Because the author cites earlier print references and numerous personal discussions as the basis for his knowledge of error analysis, we believe that this example illustrates how little known to physicists and physics students are the relations that we present here for rigorously handling the statistics of composite measurements.
6. J. R. Taylor, Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd ed. (University Science Books, Mill Valley, 2001), p. 126.
7. See, for example, H. J. Larson, Introduction to Probability Theory and Statistical Inference (Wiley, New York, 1974), pp. 215-223.
8. E. C. Fieller, "The distribution of index in a normal bivariate population," Biometrika 24, 428-440 (1932).
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13. x(x) must be changed so that the unit-area condition is still met.
14. 2+w) appearing in the denominator of the integrand.
15. -u2 du. See G. Arfken, Mathematical Methods For Physicists, 2nd ed. (Academic, New York, 1970), p. 474.
16. It is a well-known statistical result that the variance V(X̄) of the mean of n measurements of a quantity X is a fraction 1/n of the variance V(X). See, for example, Taylor, Ref. 6.
17. 2
18. M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, "Tests of alpha-, beta-, and electron capture decays for randomness," Phys. Lett. A 262, 265-273 (1999); M. P. Silverman and W. Strange, "Experimental tests for randomness of quantum decay examined as a Markov process," ibid. 272, 1-9 (2000).
19. M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, "Tests of alpha-, beta-, and electron capture decays for randomness," Phys. Lett. A 262, 265-273 (1999); M. P. Silverman and W. Strange, "Experimental tests for randomness of quantum decay examined as a Markov process," ibid. 272, 1-9 (2000).
20. M. P. Silverman, W. Strange, C. Silverman, and T. C. Lipscombe, "Tests for randomness of spontaneous quantum decay," Phys. Rev. A 61, 042106 (2000).
21. b-1 du. See Arfken, op. cit., p. 467.
22. M. P. Pignone, C. J. Phillips, D. Atkins, S. M. Teutsch, C. D. Mulrow, and K. N. Lohr, "Screening and treating adults for lipid disorders,"' Am. J. Prev. Med. 3S (4), 53-69 (2001).
23. Cholestech Corporation Technical Brief: Clinical Performance of the Bio-Scanner 2000™ and the Cholestech LDX System Compared to a Clinical Diagnostic Laboratory Reference Method for the Determination of Lipid Profiles (Cholestech Corporation, Haywood, CA, 2001).
24. Personal communication from Bradford Sherbume, MD. Medical Director of the Clinical Diagnostic Laboratory of Hartford Hospital, Hartford, Connecticut.
25. Clinical Laboratory Partners, Hartford Hospital, Hartford Connecticut.
26. Mark P. Silverman, Probing The Atom: Interactions of Coupled States, Fast Beams, and Loose Electrons (Princeton U.P., Princeton, NJ, 2000), Chap. 3.