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

^* 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:

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

A HorRat value between 0.5 and 2 is considered acceptable.

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

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.

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.