Remark on the Quantification of Precision, Accuracy and Trueness

Precision, accuracy and trueness are important performance characteristics in analytical chemistry. Each of them is well-defined in a positive sense ( closeness of agreement... ). However, their quantifying is done by means of unfavourable measures, namely by error quantities like, e.g., standard deviation and bias, respectively, which indeed do quantify imprecision and 

It is difficult to comprehend why this measure has not been applied in analytical chemistry. Instead of this, in the last decades the signal-to-noise ratio has increasingly been used. Signal-to-noise ratio, see Eq. (7.1), is the measure that corresponds to r in the signal domain. In principle, quantities like S/N (Eq. (7.1)) and / (Eq. (7.7)) could represent measures of precision, but they have an unfavourable range of definition, namely range[r = range[S/N] = 0... oo. 

Useful measures of precision could be derived from relative dispersion measures, namely by their differences from 1, e.g., the precision of an analytical procedure 

The numerical value of this measure increases with decreasing error. The range is normally range[prec(x)] = 1. .. 0, i.e. for dispersion-free measurements (sx - 0) the precision becomes 1. On the other hand, if the dispersion amounts to 100% (sx — x) the precision becomes 0. Therefore, high precision is characterized by a high value of prec(x). The precision becomes negative if the error exceeds the measured value what corresponds to rsd(x) 100%. But such cases should appear very rarely in analytical chemistry. 

The precision of an analytical result can be quantified by means of the relative confidence interval A x 

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