Estimation of uncertainty from duplicate measurements: new quantification procedure in the case of concentration-dependent precision

Abstract

Abstract In many analytical measurements, the analyte concentration in the test samples varies over a wide range. In such cases, the standard deviation (SD) quantifying the imprecision of the measurement should be expressed as a function of the analyte concentration, c: \({s}_{c}=\sqrt{{\text{s}}_{0}^{2}+{ s}_{r}^{2}{c}^{2}}\), where s0 represents a nonzero SD at zero concentration and sr represents a near-constant relative SD at very high concentrations. These parameters can be estimated from the differences in the values measured in duplicate on test samples; datasets with a high number of duplicate results can be obtained within the internal quality control. The procedures recommended for parameter estimation published so far are based on statistically demanding weighted regression. This article proposes a statistically less demanding procedure that estimates s0 and sr separately by processing the differences between the duplicates from areas with lower and higher concentration levels, where the terms \({ s}_{r}^{2}{c}^{2}\) and \({\text{s}}_{0}^{2}\)do not represent the dominant components of \({ s}_{c}^{2}\), respectively. The parameter estimates are calculated by using the root mean square of the differences, with an addition correction for the interfering effect of second, less significant term. This procedure was verified on Monte Carlo simulated datasets. The variability of the parameter estimates obtained by this simpler procedure was similar to or slightly worse than that of the estimates obtained by the best but statistically demanding regression procedure, but better than the variability of the estimates obtained by the other tested regression procedures.