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The Horwitz equation

In 1980, Horwitz et al.* suggested a relationship between the inter-laboratory reproducibility (expressed as relative standard deviation or RSDR) and the concentration (C expressed as a decimal fraction**) of the compound to be analyzed:

RSDR = 2(1 – 0.5 log C)

* Horwitz W., Kamps L.R., Boyer K.W. J. Assoc. Off. Anal. Chem. (1980) 63:1344.
** Example: 1 g/kg = 10-3 ; 1 mg/kg = 10-6

This is a purely empirical relationship that was based on a statistical treatment of the results of several inter-laboratory tests relating to mycotoxin analyses.

An estimate of repeatability was also given (expressed as relative standard deviation or RSDr) – this is referred to as the modified Horwitz equation:

RSDr = 0.67 x RSDR

To assess the quality of the accuracy of a method, the Horwitz Ratio is calculated (HorRat***):

HorRat = RSDr observed / RSDr theoretical

A HorRat value between 0.5 and 2 is considered acceptable.

Information pictogram
The HorRat is a useful performance criterion to assess the quality of a method in terms of precision.

Attention pictogram
The Horwitz equation should not be used directly to assess the precision of a method as it has no theoretical basis and does not take into account matrix effects.

Warning pictogram
The Horwitz equation has been shown to overestimate the value of the standard deviation at very low concentrations (c -7) as well as at high concentrations (c > 0.138) Therefore, modifications have been proposed for these concentrations.
cf. Thompson, Analyst (2000) 125:385-386.
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