Correlation Coefficient Calculator
Calculate Pearson, Spearman, Kendall tau, and Matthews correlation coefficients with detailed analysis
Calculate Correlation Coefficient
Data Points
Correlation Results
Interpretation: Very weak or no linear correlation
Description: Pearson correlation measures linear relationship between variables
Formula: r = Σ[(x-x̄)(y-ȳ)] / √[Σ(x-x̄)²Σ(y-ȳ)²]
Evans' Correlation Strength Guide
Example Calculation
Pearson Correlation Example
Data points:
X: [2, 7.5, 33, 34.2, 26]
Y: [21, 12.5, 3, 11, 17]
X mean: 20.54
Y mean: 12.90
Calculation Steps
1. Calculate deviations from means
2. Multiply deviations: Σ(x-x̄)(y-ȳ) = 25.12
3. Sum of squared deviations: Σ(x-x̄)² = 857.83, Σ(y-ȳ)² = 184.20
4. r = 25.12 / √(857.83 × 184.20) = 0.0632
Correlation Methods
Pearson
Linear relationships
Parametric, assumes normality
Spearman
Monotonic relationships
Non-parametric, rank-based
Kendall
Ordinal associations
Non-parametric, robust
Matthews
Binary classification
Balanced accuracy measure
Correlation Tips
Correlation does not imply causation
Use Pearson for linear relationships
Use Spearman for monotonic data
Check for outliers before analysis
Consider sample size for reliability
Understanding Correlation Coefficients
What is Correlation?
Correlation measures the strength and direction of the relationship between two variables. It indicates how changes in one variable are associated with changes in another variable.
Key Properties
- •Range: -1 to +1 for most correlation coefficients
- •+1: Perfect positive correlation
- •0: No linear relationship
- •-1: Perfect negative correlation
When to Use Each Method
Pearson Correlation
Use when both variables are continuous and normally distributed, and you want to measure linear relationships.
Spearman Correlation
Use for ordinal data or when the relationship is monotonic but not necessarily linear.
Kendall Tau
Use for small sample sizes or when you need a robust measure less affected by outliers.
Matthews Correlation
Use for evaluating binary classification performance, especially with imbalanced datasets.