Horwitz curve

A fixed target value for a is preferable and can be arrived at in several ways. It could be fixed arbitrarily, with a value based on a perception of how laboratories should perform. It could be an estimate of the precision required for a specific task of data interpretation, a could be derived from a model of precision, such as the Horwitz Curve .15 However, while this model provides a general picture of reproducibility, substantial deviation from it may be experienced for particular methods. 

B. Selinger, A Statistical Justification Relating Interlaboratory Coefficients of Variation with Concentration Levels, Anal. Chem. 1989,61, 1465 and R. Albert and W. Horwitz, A Heuristic Derivation of the Horwitz Curve, ... 

Comparing these collaborative study results to the average expected from the Horwitz curve, a composite RSD, curve of more than 300 collaborative studies. For SFB the average Horwitz ratios were 0.8, 0.59 and 0.55 for the three spiking levels for PCD the ratios were 1.38, 0.33 and 0.96. Both SFB and PCD showed acceptable within and between laboratory precision. (The Horwitz ratio compares the RSD, at the various levels and in the various matrices of this method with those RSD, values predicted based historically on methods for a wide variety of analytes reported in AOAC collaborative studies a ratio <2 is considered to have acceptable and typical precision (12). 

The estimate of reproducibility may be compared with the expected value from the Horwitz curve. An analysis of 7500 method performance studies led to the proposal that the reproducibility expressed as a percentage of the concentration of the analyte (li%) was related to the concentration (c) by... 

Fig. 18.4 Horwitz curves RSD (-) RSDk = 2 x RSD (-y,RSDr = 0.65 xRSD (—). At 10 concentration levels (100 ppb level) RSD and RSDr values are about 22.63 and 14.7 %...

Albert R, Horwitz W (1997) A heuristic derivation of the Horwitz curve. Anal Chem 69 789-790... 

Figure 6.2. Horwitz horn curve of relative standard deviation as a function of mass fraction of analyte (x). The solid curve is log2(J ) = 1-0.5 log10(x) (Horwitz et al. 1980). Dotted lines at the extremes are modifications suggested after the original paper (Thompson 2004).

Figure 71-1 Relationship of Laboratory CV (as %) with analyte concentration as powers of 10 f. (For example, 6 on the abscissa represents a concentration of 10 or 1 ppm.) Note the shape of the curves has been referred to as Horwitz s trumpet.

Figure 3 shows the probability of accepting samples containing different concentrations of erucic acid. Two levels of variation are represented, both plausible in view of the Firestone and Horwitz (1979) results. The two curves, referred to as operational characteristic curves in quality control the-... 

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