Gössler Gerhard, Hofer Vera, Goessler Walter
Institute of Chemistry, Analytical Chemistry, University of Graz, Graz, Austria.
Institute of Operations and Information Systems, University of Graz, Graz, Austria.
Anal Bioanal Chem. 2025 Mar;417(6):1187-1197. doi: 10.1007/s00216-024-05725-8. Epub 2025 Jan 10.
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.
这项工作对文献中提出的四种基于标准加入法收集的数据估计未知浓度的不同方法进行了统计分析。这些方法是传统外推法、内插法、逆回归法和归一化法。在测量误差呈正态分布且同方差的假设下对这些方法进行了比较。比较是针对每个估计量的两个最重要特征进行的，即准确性（偏差）和精密度（变异性）。此外，如果尚无相关公式，作者还提供了用于近似这两个量的数学公式。此外，还使用了一个实际数据集来说明所有四种方法的性能。结果表明，假设标准加入法使用的所有假设都适用，就偏差和变异性而言，常用的外推法仍然是最值得推荐的方法。尽管如此，如果出现其他问题，例如在异常值问题增加的情况下，像归一化法这样的其他方法可能也会引起从业者的兴趣。
