Full Range Testing of the Small Size Effect Bias for Benford Screening: A Note
Bibliographic record
Abstract
Bao, Lee, Heilig, and Lusk (2018) have documented and illustrated the Small Sample Size bias in Benford Screening of datasets for Non-Conformity. However, their sampling plan tested only a few random sample-bundles from a core set of data that were clearly Conforming to the Benford first digit profile. We extended their study using the same core datasets and DSS, called the Newcomb Benford Decision Support Systems Profiler [NBDSSP], to create an expanded set of random samples from their core sample. Specifically, we took repeated random samples in blocks of 10 down to 5% from their core-set of data in increments of 5% and finished with a random sample of 1%, 0.5% & 20 thus creating 221 sample-bundles. This arm focuses on the False Positive Signaling Error [FPSE]—i.e., believing that the sampled dataset is Non-Conforming when it, in fact, comes from a Conforming set of data. The second arm used the Hill Lottery dataset, argued and tested as Non-Conforming; we will use the same iteration model noted above to create a test of the False Negative Signaling Error [FNSE]—i.e., if for the sampled datasets the NBDSSP fails to detect Non-Conformity—to wit believing incorrectly that the dataset is Conforming. We find that there is a dramatic point in the sliding sampling scale at about 120 sampled points where the FPSE first appears—i.e., where the state of nature: Conforming incorrectly is flagged as Non-Conforming. Further, we find it is very unlikely that the FNSE manifests itself for the Hill dataset. This demonstrated clearly that small datasets are indeed likely to create the FPSE, and there should be little concern that Hill-type of datasets will not be indicated as Non-Conforming. We offer a discussion of these results with implications for audits in the Big-Data context where the audit In-charge may find it necessary to partition the datasets of the client.
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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 | 0.329 | 0.743 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.005 | 0.008 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.006 | 0.017 |
| Scholarly communication | 0.006 | 0.015 |
| Open science | 0.008 | 0.009 |
| Research integrity | 0.006 | 0.013 |
| Insufficient payload (model declined to judge) | 0.023 | 0.005 |
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".