A contemporary look at the precision of modern analytical methods in food analysis and the relevance of the Horwitz equation.

Background: The Horwitz equation models an empirically observed relationship between inter-laboratory relative standard deviation RSDR and analyte concentration expressed as a mass fraction. The Horwitz ratio (HorRat) is the ratio of observed RSDR to the corresponding calculated RSDR from the Horwitz equation. The empirical acceptable range is 0.5 to 2.0 for a successful multi-laboratory method validation trial.

Objective: This work examines data from multi-laboratory trials on food analyses conducted between 2011-2017 for trends in analytical method precision and the applicability and relevance of the Horwitz model.

Method: Data on method precision from 20 multi-laboratory trials consisting of 961 data points were analyzed. The scope was limited to methods employing modern chromatographic and spectroscopic techniques and to well-defined small molecule analytes and elements. Within-laboratory and inter-laboratory precision and their ratio, HorRat, goodness of fit to the Horwitz model, and variation of precision across the analytical range were examined.

Results: The variance of inter-laboratory precision is largely (86%) independent of concentration and remains unexplained by the Horwitz equation. Only 52% of all data points fell within the Horwitz band (0.5-2.0), with 46% falling under 0.5, indicating substantially better inter-laboratory precision than predicted by the Horwitz equation at all concentration levels. Near-constant precision was confirmed across the analytical range of methods, even near the limit of quantitation.

Conclusions: The analysis of the data in scope demonstrates that the analytical method precision routinely achievable with modern chromatographic and spectroscopic techniques, proper laboratory controls, and training is much better than that predicted by the Horwitz equation. HorRat has lost its relevance as a method performance criterion for judging the success of a multi-laboratory trial.

Highlights: Recent data do not follow the Horwitz model. HorRat values <0.5 can be routinely achieved. Method precision is mostly independent of analyte concentration. Method-related factors have greater impact on precision.