A Contemporary Look at the Precision of Modern Analytical Methods in Food Analysis and the Relevance of the Horwitz Equation
Bibliographic record
Abstract
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 and 2017 for trends in analytical method precision and the applicability and relevance of the Horwitz model. METHODS: 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. CONCLUSION: 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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".