Variation of precision with concentration in an analytical system

Abstract

A data set consisting of the analyses of about 700 geochemical materials for 25 elements, duplicated within-batch, has been investigated in respect of the relationship between the standard deviation of the determination and the concentration of the analytes. The data were fitted to three models of this relationship. A simple linear model with a positive intercept was found to be a good fit with nearly all of the analytes when fitted by weighted regression, but not by simple regression. A more complex relationship based on the addition of variances was found to be equally good. A suggested relationship based on a linear fit between the logarithms of the standard deviation and concentration was less satisfactory statistically, and also raised some theoretical difficulties. The choice of an appropriate model is important both from the scientific viewpoint and for data quality control purposes.