The Matthews Correlation Coefficient (MCC) is More Informative Than Cohen’s Kappa and Brier Score in Binary Classification Assessment
Bibliographic record
Abstract
Even if measuring the outcome of binary classifications is a pivotal task in machine learning and statistics, no consensus has been reached yet about which statistical rate to employ to this end. In the last century, the computer science and statistics communities have introduced several scores summing up the correctness of the predictions with respect to the ground truth values. Among these scores, the Matthews correlation coefficient (MCC) was shown to have several advantages over confusion entropy, accuracy, F1score, balanced accuracy, bookmaker informedness, markedness, and diagnostic odds ratio: MCC, in fact, produces a high score only if the majority of the predicted negative data instances and the majority of the positive data instances are correct, and therefore it results being very trustworthy on imbalanced datasets. In this study, we compare MCC with two other popular scores: Cohen's Kappa, a metric that originated in social sciences, and the Brier score, a strictly proper scoring function which emerged in weather forecasting studies. After explaining the mathematical properties and the relationships between MCC and each of these two rates, we report some use cases where these scores generate different values, which lead to discordant outcomes, where MCC provides a more truthful and informative result. We highlight the reasons why it is more advisable to use MCC rather that Cohen's Kappa and the Brier score to evaluate binary classifications.
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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 | 0.047 | 0.231 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.019 | 0.015 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".