Analytical Bias: the Neglected Component of Measurement Uncertainty†

Abstract

All analysts are accustomed to reporting measurement results accompanied by either the standard deviation of individual results from the mean or the standard error of the mean. These statements indicate repeatability of measurement under unchanged conditions, or reproducibility, where the time period over which measurements are taken is the source of changed conditions. Repeatability generally produces a smaller deviation between replicates than does reproducibility. However, most of the variability of measurements made by different laboratories, or using different methods in a single laboratory, is not accounted for by either repeatability or reproducibility attributable to time period. This is evident in all interlaboratory data sets; these frequently contain between-laboratory and between-method discrepancies that are very large in comparison with the uncertainty of measurements typically reported by individual laboratories. Recently issued ISO guidelines and related documents address these discrepancies as a legitimate component of measurement uncertainty, and recommend expanding the concept to include the deviation of a measurement from the true value of the measurand, so long as this deviation is small relative to fitness for purpose requirements. When the bias of measurement renders the result unsuitable for purpose, however, that bias is a significant effect and must be removed by use of a correction factor. To correct for significant bias, or to include smaller bias as an uncertainty component, laboratories must evaluate and quantify the bias in their measurements to the fullest extent possible. This paper presents uncertainty statements developed in accordance with the ISO guidelines for several reference sample measurements. Some are very complex, drawn from published work of metrology laboratories. Others, drawn from the author’s data for the Japanese Sedimentary rock reference materials, are more suitable for routine laboratory use.