# Pearson-Matthews correlation coefficients for binary and multinary classification and hypothesis testing

arXiv: https://arxiv.org/abs/2305.05974 · HTML: https://mlsanity.com/paper/2305.05974/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 26 references that are in the map.
- First posted on arXiv 10 May 2023.

## Builds on (most cited first, 2 of 2)

- [Metrics for Multi-Class Classification: an Overview](https://mlsanity.com/paper/2008.05756/) (2020)
- [Understanding metric-related pitfalls in image analysis validation](https://mlsanity.com/paper/2302.01790/) (2023)

## Built on by (most cited first, 4 of 4)

- [An end-to-end attention-based approach for learning on graphs](https://mlsanity.com/paper/2402.10793/) (2024)
- [Rethinking Suicidal Ideation Detection: A Trustworthy Annotation Framework and Cross-Lingual Model Evaluation](https://mlsanity.com/paper/2507.14693/) (2025)
- [Weighted MCC: A Robust Measure of Multiclass Classifier Performance for Observations with Individual Weights](https://mlsanity.com/paper/2512.20811/) (2025)
- [Atelier: Learning Local Self-Supervised Features for CryoEM Volumes via Hypernetworks](https://mlsanity.com/paper/2609.30569/) (2026)

## Abstract (arXiv)

The Pearson-Matthews correlation coefficient (usually abbreviated MCC) is considered to be one of the most useful metrics for the performance of a binary classification or hypothesis testing method (for the sake of conciseness we will use the classification terminology throughout, but the concepts and methods discussed in the paper apply verbatim to hypothesis testing as well). For multinary classification tasks (with more than two classes) the existing extension of MCC, commonly called the RK metric, has also been successfully used in many applications. The present paper begins with an introductory discussion on certain aspects of MCC. Then we go on to discuss the topic of multinary classification that is the main focus of this paper and which, despite its practical and theoretical importance, appears to be less developed than the topic of binary classification. Our discussion of the RK is followed by the introduction of two other metrics for multinary classification derived from the multivariate Pearson correlation (MPC) coefficients. We show that both RK and the MPC metrics suffer from the problem of not decisively indicating poor classification results when they should, and introduce three new enhanced metrics that do not suffer from this problem. We also present an additional new metric for multinary classification which can be viewed as a direct extension of MCC.