On the special application of Thompson–Howarth error analysis to geochemical variables exhibiting a nugget effect
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Bibliographic record
Abstract
Thompson–Howarth error analysis is based on the assumption that measurement error is normally distributed. As a result, geochemical variables that are not normally distributed, such as those containing rare nuggets, cannot be statistically evaluated using Thompson–Howarth error analysis unless a modification to the procedure, involving use of the group root mean square (RMS) standard deviations, is implemented that makes it independent of the normality assumption. This modification prevents samples exhibiting a positively skewed error distribution, such as that produced by a ‘nugget effect’, from having their measurement errors underestimated (biased) using conventional Thompson–Howarth error analysis. A consequence of the duplicate error analysis of ‘nuggety’ samples is that the maximum feasible relative error (of 141.2%; one standard deviation divided by the mean) may be observed in some samples. Maximum feasible relative errors for n replicates are equal to √ n . Maximum relative errors may be observed because Poisson probabilities of obtaining zero nuggets in one duplicate and one or several nuggets in another are not negligible, and thus very large grade disparities can be obtained in duplicate samples simply due to natural sampling variability. As a result, an abundance of samples exhibiting this maximum relative error is not necessarily an analytical or sample numbering error, but rather an expected consequence of sampling geological materials exhibiting large nugget effects, and may reflect relative measurement error that is larger than the maximum exhibited by duplicate samples. Consequently, if a large number of duplicate samples exhibit relative errors close to the maximum, it is likely that Thompson–Howarth error analysis of duplicate samples will underestimate the actual relative error in the data. As a result, replicate samples (where n >2) that have higher maximum relative error limits should be used to ensure that relative error estimates derived from such a Thompson–Howarth error analysis are not biased low (underestimated).
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it