1. What is the Matthews Correlation Coefficient?

Definition: The MCC is a measure of the quality of binary classifications that returns a value between -1 and +1.

Purpose: It provides a balanced evaluation metric even when the classes are of very different sizes, unlike simpler metrics like accuracy.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TP \) — True positives (correct positive predictions)
• \( TN \) — True negatives (correct negative predictions)
• \( FP \) — False positives (incorrect positive predictions)
• \( FN \) — False negatives (incorrect negative predictions)

Explanation: The MCC is essentially a correlation coefficient between the observed and predicted binary classifications.

3. Interpretation of MCC Values

Details:

• +1 indicates a perfect prediction
• 0 indicates no better than random prediction
• -1 indicates total disagreement between prediction and observation

4. Using the Calculator

Tips: Enter the counts from your confusion matrix (TP, TN, FP, FN). All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: Why use MCC instead of accuracy?
A: MCC is more informative than accuracy when classes are imbalanced, as it considers all four confusion matrix categories.

Q2: What's considered a "good" MCC value?
A: Generally, MCC > 0.5 is good, > 0.7 is strong, and > 0.9 is excellent, but this depends on your field.

Q3: Can MCC be used for multi-class problems?
A: Yes, through generalizations like the Rₖ statistic, but this calculator handles binary classification only.

Q4: How does MCC compare to F1 score?
A: MCC considers all four confusion matrix categories, while F1 score focuses only on the positive class (TP, FP, FN).

Q5: What if my denominator is zero?
A: The calculator returns 0 in this case, which occurs when any term in the denominator is zero (perfect or worst possible predictions).