Correlation Coefficient Calculator

Pearson r is computed as covariance divided by the product of standard deviations. A t-test approximation provides a two-tailed p-value when sample size is sufficient (at least three observations) and assumptions hold.

Spearman rho is computed by converting values to ranks then applying the Pearson formula to ranks; p-values use standard approximations suitable for moderate to large samples or exact methods for small samples.

Kendall Tau is computed by counting concordant and discordant pairs; exact or asymptotic p-values are reported depending on sample size and ties.

Matthews correlation coefficient (MCC) is computed from confusion-matrix counts using the standard formula and is appropriate for evaluating binary classifiers especially when class sizes are imbalanced.

Select Pearson for linear associations, Spearman or Kendall when data are ordinal or assumptions are violated, and Matthews for binary classification evaluation.

Always inspect scatterplots or contingency tables and check assumptions before interpreting correlation coefficients. Correlation does not imply causation.

Example 1: Pearson — X: 1,2,3,4,5 and Y: 2,4,6,8,10 returns r = 1.0 and p ≈ 0 (perfect linear relationship).

Example 2: Spearman — X and Y with monotonic but non-linear relationship will show high rho even if Pearson r is lower.

Example 3: Matthews — For TP=50, FP=10, FN=5, TN=35, MCC summarizes classifier quality in a single value between -1 and 1.