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Towards an explanation of the Horwitz function
1School of Biological and Chemical Sciences, Birkbeck University of London, Malet Street, London, WC1E 7HX, UK. m.thompson@bbk.ac.uk.
Analytical and Bioanalytical Chemistry
|November 25, 2021
Summary
The Horwitz function, used in analytical chemistry, describes reproducibility in collaborative trials. This study reconciles it with Zitter and God
Area of Science:
- Analytical Chemistry
- Chemometrics
- Food Analysis
Background:
- The Horwitz function empirically relates reproducibility (interlaboratory) standard deviations to analyte mass fraction.
- A theoretical explanation for the Horwitz function's power-law form and parameters is lacking.
- The Zitter and God equation, though theoretically sound, appears incompatible with the Horwitz function.
Purpose of the Study:
- To reconcile the empirically observed Horwitz function with the theoretically grounded Zitter and God equation.
- To explain the prevalence of the Horwitz function across a wide range of analyte concentrations.
Main Methods:
- Analysis of collaborative trial statistics across varying mass fractions.
- Comparison of empirical data with theoretical models.
Main Results:
- Collections of collaborative trial data exhibit the Horwitz function over a broad mass fraction range (10-7 to 10-1).
- The apparent incompatibility between the Horwitz function and the Zitter and God equation arises from the limited mass fraction range of single trials.
Conclusions:
- The Horwitz function can be understood as an emergent property of aggregated data from collaborative trials conducted over limited mass fraction ranges.
- The Zitter and God equation provides a theoretical framework that encompasses the observed Horwitz function behavior.
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