Thompson–Howarth error analysis: unbiased alternatives to the large-sample method for assessing non-normally distributed measurement error in geochemical samples
Bibliographic record
Abstract
The Thompson–Howarth error analysis procedures have become common in geochemical applications for assessing the magnitude of measurement error at any stage of determination (initial sampling, sample preparation, geochemical analysis). However, the large-sample method, as defined by Thompson and Howarth, which relies on an assumption that the measurement errors are normally distributed, produces significantly biased results when the errors are not normally distributed. Four examples of quality control data-sets from a variety of mineral deposit types illustrate that normally distributed errors are probably the exception rather than the rule in ore deposits, and non-normally distributed geochemical data-sets may exist in other geological materials. As a result, using Thompson and Howarth's large-sample error analysis approach, geoscientists may obtain a significantly inaccurate estimate of the quality of their geochemical concentration data. Two new methods, which are modifications to the Thompson–Howarth large-sample technique, eliminate this bias because they ensure that the results are independent of a normally distributed error assumption. Regression of group root mean square standard deviations produces accurate error estimates, at least provided that the concentrations are distributed relatively evenly across their range. Similarly, regression of duplicate variances against duplicate means using a quadratic model, and then taking the square root of this model, also results in an unbiased estimate of measurement error. Furthermore, if this quadratic model is a perfect square, then the square root of the quadratic model will be linear on a mean versus standard deviation scatterplot. This approach is further independent of the distribution of the error in the data. Using these modified approaches, geoscientists can now obtain unbiased Thompson–Howarth estimates of measurement error that is not normally distributed in quality control/quality assessment programmes.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.114 | 0.398 |
| Meta-epidemiology (narrow) | 0.005 | 0.003 |
| Meta-epidemiology (broad) | 0.008 | 0.008 |
| Bibliometrics | 0.013 | 0.011 |
| Science and technology studies | 0.004 | 0.009 |
| Scholarly communication | 0.007 | 0.008 |
| Open science | 0.006 | 0.010 |
| Research integrity | 0.006 | 0.009 |
| Insufficient payload (model declined to judge) | 0.009 | 0.003 |
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 source (direct Gemma or distilled Codex), 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".