Determination of a reference value and its uncertainty through a power-moderated mean

Abstract

A method is presented for calculating a key comparison reference value (KCRV) and its associated standard uncertainty. The method allows for technical scrutiny of data, correction or exclusion of extreme data, but above all uses a power-moderated mean that can calculate an efficient and robust mean from any data set. For mutually consistent data, the method approaches a weighted mean, the weights being the reciprocals of the variances (squared standard uncertainties) associated with the measured values. For data sets suspected of inconsistency, the weighting is moderated by increasing the laboratory variances by a common amount and/or decreasing the power of the weighting factors. By using computer simulations, it is shown that the PMM is a good compromise between efficiency and robustness, while also providing a realistic uncertainty. The method is of particular interest to data evaluators and organizers of proficiency tests.

Seeking excellence: An evaluation of 235 international laboratories conducting water isotope analyses by isotope‐ratio and laser‐absorption spectrometry

“…All samples were normalized to the VSMOW‐SLAP scale by using VSMOW/2 and SLAP (IAEA) or SLAP2 (GEOTOP, CIR, USGS) or USGS49 (USGS) reference waters measured along with the WICO samples. Following normality and outlier testing, the reference values were determined as the power‐moderated mean and robust standard deviation, which took into account the uncertainties reported by the reference laboratories . For the WICO5 sample, reference value measurements were conducted on an uncontaminated sub‐sample.…”

Absolute and relative measurement of the 243Am half-life

“…The uncertainties in this work are lower, mainly due to the more accurately performed alphaparticle counting and spectrometry measurements. A power-moderated mean (PMM) with α = 1 -where the number α denotes the power of the uncertainties in the weighting factors [53] -of the three most recent (and consistent) half-life ratio data in Table 5 results in 17.011 (28) a. This is compatible with, but less precise than the value 16.988 (24) measured in this work, or the slightly lower (24) derived from the mean half-life result 7345 (14) a from both methods.…”

60Co in cast steel matrix: A European interlaboratory comparison for the characterisation of new activity standards for calibration of gamma-ray spectrometers in metallurgy

“…In each case the consensus value was derived as the powermoderated mean (PMM) (Pommé and Keightley, 2015) of the reported activity concentrations, on the condition that they were not identified as outlier. The standard deviation of the PMM, u PMM , represented the uncertainty from characterisation, u char .…”