Matthews Correlation Coefficient Calculator
Evaluate binary classification quality using the Matthews Correlation Coefficient with comprehensive metrics
Binary Classification Confusion Matrix
Enter Confusion Matrix Values
Correctly predicted positive cases
Incorrectly predicted as positive
Incorrectly predicted as negative
Correctly predicted negative cases
Confusion Matrix
Matthews Correlation Coefficient Results
Interpretation: No data provided
Formula: MCC = (TP×TN - FP×FN) / √[(TP+FP)(TP+FN)(TN+FP)(TN+FN)]
MCC Quality Scale
Example: Ceramic Factory Quality Control
Scenario
Problem: Quality control check of 100 ceramic plates
Prediction: 15 plates identified as defective
Reality: 25 plates were actually defective
Correct identifications: 10 out of 15 predictions
Confusion Matrix
Calculation
MCC = [(10×70) - (5×15)] / √[(10+5)(10+15)(70+5)(70+15)]
MCC = [700 - 75] / √[15×25×75×85]
MCC = 625 / √2,390,625
MCC = 0.4042 (Fair quality)
Sensitivity: 40% (only 40% of defects caught)
Classification Metrics
MCC
Overall classification quality
Best for imbalanced datasets
Sensitivity
True positive rate
How many positives caught
Specificity
True negative rate
How many negatives correct
Precision
Positive predictive value
Accuracy of positive predictions
MCC Tips
MCC considers all four confusion matrix quadrants
Best metric for imbalanced datasets
Range: -1 (worst) to +1 (perfect)
0 indicates random performance
Used in machine learning evaluation
Understanding Matthews Correlation Coefficient
What is MCC?
The Matthews Correlation Coefficient (MCC) is a balanced measure for evaluating binary classification quality, even with imbalanced datasets. Unlike accuracy, MCC considers all four quadrants of the confusion matrix and provides a more reliable assessment.
Why Use MCC?
- •Robust to class imbalance
- •Considers all classification outcomes
- •Interpretable scale (-1 to +1)
- •Widely used in bioinformatics and ML
Applications
Medical Diagnosis
Evaluating diagnostic test accuracy for diseases with different prevalence rates.
Machine Learning
Comparing classifier performance across different algorithms and datasets.
Quality Control
Assessing inspection systems in manufacturing and production environments.
Bioinformatics
Evaluating protein structure prediction and gene expression analysis.
Formula Components
MCC = (TP×TN - FP×FN) / √[(TP+FP)(TP+FN)(TN+FP)(TN+FN)]