The Matthews correlation coefficient (MCC) should replace the ROC AUC as the standard metric for assessing binary classification
Bibliographic record
Abstract
Abstract Binary classification is a common task for which machine learning and computational statistics are used, and the area under the receiver operating characteristic curve (ROC AUC) has become the common standard metric to evaluate binary classifications in most scientific fields. The ROC curve has true positive rate (also called sensitivity or recall) on the y axis and false positive rate on the x axis, and the ROC AUC can range from 0 (worst result) to 1 (perfect result). The ROC AUC, however, has several flaws and drawbacks. This score is generated including predictions that obtained insufficient sensitivity and specificity, and moreover it does not say anything about positive predictive value (also known as precision) nor negative predictive value (NPV) obtained by the classifier, therefore potentially generating inflated overoptimistic results. Since it is common to include ROC AUC alone without precision and negative predictive value, a researcher might erroneously conclude that their classification was successful. Furthermore, a given point in the ROC space does not identify a single confusion matrix nor a group of matrices sharing the same MCC value. Indeed, a given (sensitivity, specificity) pair can cover a broad MCC range, which casts doubts on the reliability of ROC AUC as a performance measure. In contrast, the Matthews correlation coefficient (MCC) generates a high score in its $$[-1; +1]$$ [ - 1 ; + 1 ] interval only if the classifier scored a high value for all the four basic rates of the confusion matrix: sensitivity, specificity, precision, and negative predictive value. A high MCC (for example, MCC $$=$$ = 0.9), moreover, always corresponds to a high ROC AUC, and not vice versa. In this short study, we explain why the Matthews correlation coefficient should replace the ROC AUC as standard statistic in all the scientific studies involving a binary classification, in all scientific fields.
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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 | 0.024 | 0.168 |
| Meta-epidemiology (narrow) | 0.002 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.006 | 0.006 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.005 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".