Precision of Trace Analyses

It is a well-known fact that the precision in trace analysis decreases with diminishing concentration in a similar way as it does with decreasing sample weight (Sect. 2.1). The dependency of the repeatability and reproducibility standard deviation on the concentration of analytes has been investigated systematically at first by Horwitz et al. [1980] on the basis of thousands of pieces of interlaboratory data (mostly from food analysis). The result of the study has been represented in form of the well-known Horwitz trumpet which is represented in Fig. 7.3. 

The Horwitz relationship agrees with the experience of analysts and has been confirmed in various fields of trace analysis, not only in its qualitative form but also quantitatively. Thompson et al. [2004] have estimated the mathematical form of the Horwitz functiontextscHorwitz function being sH = 0.02 x0,85, or linearized, logs = 0.85 log x. The agreement of this equation is usually good and, therefore, the Horwitz functiontextscHorwitz function is sometimes used as a bench-mark for the performance of analytical methods. For this purpose, the so-called Horrat (Horwitz ratio) has been defined, Horrat = sactuai/sHy by which the actual standard deviation is compared with the estimate of the Horwitz function. Serious deviations 

In general, in trace analysis concessions must be made with regard to precision and accuracy. However, accuracy has strictly to be distinguished from precision. 

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