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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]

The relationship between reproducibility standard deviation and mass fraction in food analysis has been studied in compilations of statistics from collaborative trials and from proficiency tests. There was a broad tendency for both categories of statistics to follow the Horwitz function although systematic deviations from it were easily detected at both extremes of the mass fraction range (below 10−7 and above 10−2). The two compilations were found to have very similar properties over the whole range of mass fractions, that is from about 10−10 (0.1 ppb) upwards. This similarity has implications for the determination of detection limit. [ABSTRACT FROM AUTHOR]

This work forms a background to the recent discussion about normal and log-normal distributions in the results of proficiency tests for GMO analysis. In order to clear up some common confusions, the paper first covers some basic principles, viz., a comparison of normally and log-normally distributed samples of results at various precisions, and a background to the determination of assigned values and scoring in proficiency tests. Then follows brief discussions on the identification of outliers and the use of 'tests for normality'. In conclusion, there is a broad outline of the steps that may assist a proficiency testing scheme in deciding on a suitable model of dispersion. [ABSTRACT FROM AUTHOR]