Evaluation of four different standard addition approaches with respect to trueness and precision

Abstract

This work provides a statistical analysis of four different approaches suggested in the literature for the estimation of an unknown concentration based on data collected using the standard addition method. These approaches are the conventional extrapolation approach, the interpolation approach, inverse regression, and the normalization approach. These methods are compared under the assumption that the measurement errors are normally distributed and homoscedastic. Comparison is done with respect to the two most important characteristics of every estimator, namely trueness (bias) and precision (variability). In addition, the authors supply, if not already available, mathematical formulas to approximate both quantities. Also, a real-world data set is used to illustrate the performance of all four methods. It turns out, that, given that all assumptions underlying the use of the standard addition method apply, the common extrapolation method is still the most recommendable method with respect to bias and variability. Nonetheless, if additional concerns come into play, other methods like, for example, the normalization approach in the case of increased problems with outliers might also be of interest for the practitioner.

Keywords: Approximation formulas; Bias and variability; Extrapolation; Interpolation; Inverse regression; Normalization; Standard addition; Trueness and precision.