Horwitz equation/function

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... 

Calculated repeatability, intermediate precision, and reproducibility values can be compared with those of existing methods. If there are no methods with which to compare the precision parameters, theoretical relative reproducibility and repeatability standard deviations can be calculated from the Horwitz equation and the Horrat value (Table 5). Horwitz RSD values are reported in Table 6. Higher variability is expected as the analyte levels approach the detection limit (see below). Next to the Horwitz equation, the AOAC s Peer Verified Program proposes its own levels of acceptability of %RSD as a function of analyte concentration level [56,72]. 

Figure 4.6 Interlaboratory coefficient of variation as a function of concentration (note that the filled circles are values calculated by using equation (4.4), not experimental points) [10]. Reproduced by permission of AOAC International, from Horwitz, W., J. Assoc. Off. Anal. Chem., 66, 1295-1301 (1983).

If the original Horwitz function had been used, a larger value would have been obtained. If you check Figure 4.6, that predicts a value for the %CV of about 50%. Using the original function, equation (4.4), gives this value. 

The target value for the standard deviation, o, should be circulated in advance to the PT participants along with a summary of the method by which it has been established. It will vary with anal)4e concentration, and one approach to estimating it is to use a functional relationship between concentration and standard deviation. The best-known relationship is the Horwitz trumpet, dating from 1982, so called because of its shape. Using many results from collaborative trials, Horwitz showed that the relative standard deviation of a method varied with the concentration, c (e.g. mg g" ), according to the approximate and empirical equation ... 

The reliability of repeatability and reproducibility RSD estimates can be tested against values obtained by the Horwitz empirical equation." " " The equation allows an a priori estimation of the RSD as a function of the analyte concentration expressed as mass/mass units (e.g., as mass fraction 1 mg/kg=10" , 1 pg/ kg = 10" ) whatever analyte, matrix, and method of measurement ... 

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