Matthews Correlation Coefficient Calculator

1. What is the Matthews Correlation Coefficient Calculator?

Definition: The Matthews Correlation Coefficient (MCC) Calculator computes the MCC, a measure of the quality of binary classifications, based on a 2x2 confusion matrix.

Purpose: This tool is used in machine learning, medicine, and biological sciences to evaluate the performance of binary classification models, such as diagnostic tests or predictive algorithms.

2. How Does the Calculator Work?

The calculator uses the following formula:

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

Where:

\( TP \): True positives;
\( TN \): True negatives;
\( FP \): False positives;
\( FN \): False negatives;
\( MCC \): Matthews correlation coefficient.

Steps:

Enter the values for true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN).
Compute the numerator: \( (TP \times TN) - (FP \times FN) \).
Compute the denominator: \( \sqrt{(TP + FP)(TP + FN)(TN + FP)(TN + FN)} \).
Calculate MCC by dividing the numerator by the denominator.
Interpret the result: +1 (perfect prediction), 0 (no information), -1 (complete inconsistency).
Display the MCC and interpretation, formatted to four decimal places or scientific notation.

3. Importance of the Matthews Correlation Coefficient

The MCC is essential for:

Classification Evaluation: Provides a balanced measure of binary classification performance, even with imbalanced datasets.
Medical and Biological Applications: Evaluates diagnostic tests or drug efficacy in medicine and biology.
Machine Learning: Assesses the quality of predictive models in machine learning tasks.

4. Using the Calculator

Example: Calculate the MCC for a confusion matrix with TP=50, TN=40, FP=5, FN=5.

Input: TP: 50, TN: 40, FP: 5, FN: 5
Numerator: \( (50 \times 40) - (5 \times 5) = 2000 - 25 = 1975 \)
Denominator: \( \sqrt{(50 + 5)(50 + 5)(40 + 5)(40 + 5)} = \sqrt{55 \times 55 \times 45 \times 45} \approx 2475 \)
MCC: \( \frac{1975}{2475} \approx 0.7980 \)
Interpretation: Strong positive prediction (since \( 0.7980 > 0.5 \))
Result: Matthews Correlation Coefficient: 0.7980, Interpretation: Strong positive prediction

5. Frequently Asked Questions (FAQ)

Q: What is the Matthews Correlation Coefficient?
A: MCC is a measure of binary classification quality, ranging from -1 (complete inconsistency) to +1 (perfect prediction), based on a confusion matrix.

Q: How is MCC interpreted?
A: +1 indicates perfect prediction, 0 indicates no information, and -1 indicates complete inconsistency. Values above 0.5 suggest strong positive predictions.

Q: Why is MCC useful?
A: It provides a robust evaluation of binary classification performance, especially for imbalanced datasets, in fields like machine learning and medical diagnostics.