Correlation Coefficient Calculator (Matthews)

The Matthews Correlation Coefficient is computed using values from a binary confusion matrix: True Positives (TP), True Negatives (TN), False Positives (FP), and False Negatives (FN). The core formula for MCC is: MCC = (TP * TN - FP * FN) / sqrt((TP + FP) * (TP + FN) * (TN + FP) * (TN + FN)). This equation yields a value between -1 and +1. A coefficient of +1 represents a perfect prediction, 0 indicates random guessing, and -1 signifies total disagreement between predictions and actual observations. It also computes related performance metrics such as accuracy, precision, sensitivity, and specificity to give you a complete diagnostic overview of your model.

Imagine you are evaluating a medical screening model that tested 1,000 patients for a rare condition. Your confusion matrix yields the following counts: TP = 50, TN = 850, FP = 50, and FN = 50. First, calculate the numerator: (50 * 850) - (50 * 50) = 42,500 - 2,500 = 40,000. Next, calculate the four parts of the denominator product: (TP + FP) = 100, (TP + FN) = 100, (TN + FP) = 900, and (TN + FN) = 900. Multiplying these together gives 100 * 100 * 900 * 900 = 8,100,000,000. Taking the square root of this product results in 90,000. Finally, divide the numerator by the denominator: 40,000 / 90,000 = 0.444. This positive MCC score indicates a moderate, positive correlation between the test predictions and actual medical outcomes.

When working with binary classification metrics, always inspect your dataset balance before relying solely on standard accuracy. Standard accuracy can be misleadingly high if your negative class vastly outnumbers your positive class. Use the Matthews Correlation Coefficient as a primary validation metric for imbalanced classes because it heavily penalizes incorrect predictions across all categories. Additionally, cross-reference your MCC score with precision and sensitivity to pinpoint whether your model suffers from excessive false positives or false negatives.