Matthews Correlation Coefficient Calculator with Steps

Matthews Correlation Coefficient Formula:

\[ MCC = \frac{TP \times TN - FP \times FN}{\sqrt{(TP + FP)(TP + FN)(TN + FP)(TN + FN)}} \]

True Positives (TP):

True Negatives (TN):

False Positives (FP):

False Negatives (FN):

Matthews Correlation Coefficient:

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1. What is Matthews Correlation Coefficient (MCC)?

Definition: MCC is a statistical measure that evaluates the quality of binary classifications, ranging from -1 (total disagreement) to +1 (perfect prediction).

Purpose: It provides a balanced evaluation metric even when classes are of very different sizes, unlike accuracy which can be misleading for imbalanced datasets.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ MCC = \frac{TP \times TN - FP \times FN}{\sqrt{(TP + FP)(TP + FN)(TN + FP)(TN + FN)}} \]

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: MCC considers all four confusion matrix categories to produce a value between -1 and 1, where 1 represents perfect prediction, 0 random prediction, and -1 inverse prediction.

3. Importance of MCC

Details: MCC is particularly valuable in machine learning and statistics because it:

Works well with imbalanced datasets
Considers all aspects of the confusion matrix
Provides a single informative metric for classification quality
Is symmetric (invariant to class label swapping)

4. Using the Calculator

Tips: Enter the counts from your confusion matrix:

True Positives (TP): Correctly predicted positive cases
True Negatives (TN): Correctly predicted negative cases
False Positives (FP): Negative cases incorrectly predicted as positive
False Negatives (FN): Positive cases incorrectly predicted as negative

All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What does an MCC value of 0 mean?
A: An MCC of 0 indicates that the classifier is no better than random prediction.

Q2: How does MCC compare to accuracy?
A: MCC is more informative than accuracy when classes are imbalanced, as it considers all four confusion matrix categories.

Q3: What's considered a "good" MCC value?
A: Generally, MCC > 0.3 is acceptable, > 0.7 is strong, and > 0.9 is excellent. However, this depends on your specific application.

Q4: Can MCC be negative?
A: Yes, MCC ranges from -1 to +1. Negative values indicate inverse prediction (worse than random).

Q5: When should I use MCC instead of F1 score?
A: MCC is generally preferred when you care about both classes equally, while F1 focuses more on the positive class.