Matthews Correlation Coefficient Calculator

Formula

The formula to calculate the Matthews Correlation Coefficient (MCC) is:

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

Where:

\(TP\) is the number of true positives
\(TN\) is the number of true negatives
\(FP\) is the number of false positives
\(FN\) is the number of false negatives

What is the Matthews Correlation Coefficient?

The Matthews Correlation Coefficient (MCC) is a measure of the quality of binary classifications. It takes into account true and false positives and negatives and is generally regarded as a balanced measure that can be used even if the classes are of very different sizes. The MCC is especially useful in the field of bioinformatics and machine learning for evaluating the performance of classification models.

Example Calculation

Let's assume the following values:

True Positives (TP) = 50
True Negatives (TN) = 40
False Positives (FP) = 10
False Negatives (FN) = 5

Using the formula to calculate the Matthews Correlation Coefficient (MCC):

\[ MCC = \frac{(TP \cdot TN) - (FP \cdot FN)}{\sqrt{(TP + FP) \cdot (TP + FN) \cdot (TN + FP) \cdot (TN + FN)}} = \frac{(50 \cdot 40) - (10 \cdot 5)}{\sqrt{(50 + 10) \cdot (50 + 5) \cdot (40 + 10) \cdot (40 + 5)}} = \frac{2000 - 50}{\sqrt{60 \cdot 55 \cdot 50 \cdot 45}} \approx 0.72 \]

The Matthews Correlation Coefficient (MCC) is approximately 0.72.