The Benefits of the Matthews Correlation Coefficient (MCC) Over the Diagnostic Odds Ratio (DOR) in Binary Classification Assessment
Bibliographic record
Abstract
To assess the quality of a binary classification, researchers often take advantage of a four-entry contingency table calledconfusion matrix, containing true positives, true negatives, false positives, and false negatives. To recap the four values of a confusion matrix in a unique score, researchers and statisticians have developed several rates and metrics. In the past, several scientific studies already showed why the Matthews correlation coefficient (MCC) is more informative and trustworthy than confusion-entropy error, accuracy, F1score, bookmaker informedness, markedness, and balanced accuracy. In this study, we compare the MCC with the diagnostic odds ratio (DOR), a statistical rate employed sometimes in biomedical sciences. After examining the properties of the MCC and of the DOR, we describe the relationships between them, by also taking advantage of an innovative geometrical plot calledconfusion tetrahedron, presented here for the first time. We then report some use cases where the MCC and the DOR produce discordant outcomes, and explain why the Matthews correlation coefficient is more informative and reliable between the two. Our results can have a strong impact in computer science and statistics, because they clearly explain why the trustworthiness of the information provided by the Matthews correlation coefficient is higher than the one generated by the diagnostic odds ratio.
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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 | 0.076 | 0.337 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.020 | 0.014 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.006 | 0.006 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".