Revisiting the relationship between reproducibility and concentration: a new, data-driven statistical model
Stefan Ehling1, Paul Wehling2, Philip A Haselberger1
1Abbott, 3300 Stelzer Road, Columbus, OH, 43219 USA.
Journal of AOAC International
|June 4, 2026
Summary
A new model shows reproducibility relative standard deviation (RSDR) in nutritional analysis increases gradually with lower analyte concentration, outperforming the Horwitz equation for modern methods.
Area of Science:
- Analytical Chemistry
- Chemometrics
- Food Science
Background:
- The Horwitz equation historically models reproducibility relative standard deviation (RSDR) vs. analyte concentration.
- Modern analytical methods, especially for nutritional matrices, show better reproducibility than the Horwitz equation predicts.
- A data-driven model is needed to reflect current analytical performance.
Purpose of the Study:
- Develop and evaluate a new statistical model for the relationship between reproducibility standard deviation (sR) and analyte concentration (C).
- Utilize a large dataset of 961 analyte-matrix combinations across 62 analytes.
Main Methods:
- Reanalyzed published multi-laboratory study data.
- Performed ordinary least squares regression on log-transformed sR and log-transformed C (mass fractions).
- Employed an approach similar to previous dietary fiber data analysis.
Main Results:
- A strong linear relationship (R² = 0.98) was found between log(sR) and log(C) across eight orders of magnitude.
- RSDR increases gradually with decreasing concentration, generally below Horwitz equation predictions.
- Deviations were mainly linked to specific analytical methods (e.g., AOAC 2014.08) and analytes.
Conclusions:
- A linear relationship between log(sR) and log(C) effectively models reproducibility for modern analytical techniques in homogeneous nutritional matrices.
- This empirical model accurately captures current performance but is not a method performance criterion.
- The new model offers a more realistic representation of analytical precision compared to the Horwitz equation.
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