Towards an explanation of the Horwitz function.

Analytical chemists in the food sector are well acquainted with the empirically observed Horwitz function. It relates reproducibility (interlaboratory) standard deviations estimated by collaborative trial with the mass fraction of the analyte. No compelling theory accounts for the power-law form of the function or its parameters. The equation of Zitter and God, ostensibly covering the same ground, is less well known but, in spite of its secure foundation in theory and practice, seems at first sight to be incompatible with the Horwitz function. In this paper, we see that because of the limited range of mass fractions in which a single collaborative trial is usually conducted, collections of statistics from collaborative trials exhibit the Horwitz function over the mass fraction range from about 10−7 (100 ppb) to about 10−1 (10%). [ABSTRACT FROM AUTHOR]