Nien Fan Zhang 2006 Metrologia 43 195 doi:10.1088/0026-1394/43/3/002
Nien Fan Zhang
Show affiliationsWeighted mean has been used to combine means from several sets of measurements, which are either from different laboratories or based on different measurement methods. It is also often used in key comparisons and other inter-laboratory comparisons. However, the traditional estimator of the variance of the weighted mean underestimates the variance. Two new variance estimators are proposed with smaller biases, smaller mean square errors and much better coverage probabilities for the correspondingly formed intervals. In metrology, the uncertainties based on Type B evaluation which are not based on statistical analysis of data cannot be ignored. In the later part of this paper, the results are extended to the general case with both Type A and Type B uncertainty components being presented.
06.20.Dk Measurement and error theory
02.50.-r Probability theory, stochastic processes, and statistics
Issue 3 (June 2006)
Received 23 August 2005
Published 28 February 2006
Nien Fan Zhang 2006 Metrologia 43 195
Yu S Sayasov 1982 Plasma Phys. 24 155
R. Fitzpatrick 1993 Nucl. Fusion 33 1049
Pun-hon Ng et al 2009 Phys. Educ. 44 639
N H March 1955 Proc. Phys. Soc. A 68 726
E G Kalnins and W Miller 1982 J. Phys. A: Math. Gen. 15 2003
J Hietarinta et al 1994 J. Phys. A: Math. Gen. 27 3149
Virginia Yong and H Thomas Hahn 2005 Nanotechnology 16 354
M Rozenfeld 1972 Phys. Med. Biol. 17 861
S Simons and I C Simpson 1974 J. Phys. C: Solid State Phys. 7 3692