Modelling measurement uncertainty as a function of concentration: an example from a contaminated land investigation

Abstract

A new method has been developed to model the uncertainty of measured concentrations in test materials as a function of concentration. Previously, the measurement uncertainty which originates mainly from the primary sampling and analysis, has been estimated using robust ANOVA (RANOVA) with duplicated samples and analyses. However, the limitation of this method is that the estimated uncertainty value is only applicable close to the mean value of the sample’s concentration, and does not apply to either higher or lower analyte concentration ranges. The new method utilises a linear precision model that describes how the precision of a measurement method changes as a function of concentration. This model can be used to estimate the uncertainty arising from the chemical analysis, and in an analogous way, to that arising from the primary sampling. An investigation of contaminated land in Wolverhampton, UK, is used to demonstrate the technique, using a balanced design of duplicated sampling and analysis. Two linear models of sampling and analytical precision were combined to estimate the total measurement uncertainty for the range of analyte concentrations. Not all the elements showed statistically significant precision changes in this particular sampling and analytical system. This may originate from the rather narrow concentration range and/or insufficient data points for the regression. However, another factor controlling sampling uncertainty may be explained by the particular spatial distribution characteristics of the contaminants across this site. As a result, the refined estimates of uncertainty for each sample provide an improved means for the classification of the extent of contamination at such sites and for probabilistic risk assessment.