Relative Efficiency of Single‐Outlier Discordancy Tests for Processing Geochemical Data on Reference Materials and Application to Instrumental Calibrations by a Weighted Least‐Squares Linear Regression Model
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Bibliographic record
Abstract
Numerous studies report geochemical data on reference materials (RMs) processed by outlier‐based methods that use univariate discordancy tests. However, the relative efficiency of the discordancy tests is not precisely known. We used an extensive geochemical database for thirty‐five RMs from four countries (Canada, Japan, South Africa and USA) to empirically evaluate the performance of nine single‐outlier tests with thirteen test variants. It appears that the kurtosis test (N15) is the most powerful test for detecting discordant outliers in such geochemical RM databases and is closely followed by the Grubbs type tests (N1 and N4) and the skewness test (N14). The Dixon‐type tests (N7, N8, N9 and N10) as well as the Grubbs type test (N2) depicted smaller global relative efficiency criterion values for the detection of outlying observations in this extensive database. Upper discordant outliers were more common than the lower discordant outliers, implying that positively skewed inter‐laboratory geochemical datasets are more frequent than negatively skewed ones and that the median, a robust central tendency indicator, is likely to be biased especially for small‐sized samples. Our outlier‐based procedure should be useful for objectively identifying discordant outliers in many fields of science and engineering and for interpreting them accordingly. After processing these databases by single‐outlier discordancy tests and obtaining reliable estimates of central tendency and dispersion parameters of the geochemical data for the RMs in our database, we used these statistical data to apply a weighted least‐squares linear regression (WLR) model for the major element determinations by X‐ray fluorescence spectrometry and compared the WLR results with an ordinary least‐squares linear regression model. An advantage in using our outlier procedure and the new concentration values and uncertainty estimates for these RMs was clearly established.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.000 | 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 it