Correlation Analysis Calculator

Correlation analysis measures the strength and direction of the relationship between two or more variables. It helps you understand whether variables change together (positive correlation), change in opposite directions (negative correlation), or have no relationship at all. Unlike regression analysis which predicts one variable from another, correlation simply measures association. Importantly, correlation does not imply causation - just because two variables are correlated doesn't mean one causes the other. There may be confounding factors or the relationship could be coincidental. The correlation coefficient ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no linear relationship. This calculator computes three types of correlations: Pearson (for linear relationships), Spearman (for monotonic relationships), and Kendall (for robust association measures).

This calculator offers two analysis modes: **Pairwise Correlation:** Compare exactly two variables (X and Y) with detailed statistical analysis including confidence intervals, p-values, scatter plots, and rank plots. Perfect for exploring the relationship between two specific variables. **Correlation Matrix:** Analyze multiple variables (2 or more) simultaneously to see how each pair correlates. The results display as a heatmap and matrix tables showing all pairwise correlations. For data entry, simply type your values separated by commas, spaces, or line breaks. You can also use the advanced CSV upload feature for larger datasets. The calculator automatically handles missing values and validates your data.

The calculator provides comprehensive results for each correlation method: **Pearson r:** The standard correlation coefficient measuring linear relationships. Includes confidence intervals calculated using Fisher's z-transformation and p-values for significance testing. The scatter plot with regression line helps visualize the linear relationship. **Spearman ρ (rho):** Measures monotonic relationships by first ranking the data. More robust to outliers than Pearson. The rank plot shows the relationship between ranked values, revealing monotonic patterns that may not be linear. **Kendall τ-b (tau-b):** Measures ordinal association and handles tied values well. More conservative than Spearman but provides a more intuitive interpretation: it represents the probability of concordance minus discordance. The interpretation section categorizes correlation strength as weak (0.0-0.3), moderate (0.3-0.7), or strong (0.7-1.0), helping you understand practical significance beyond statistical significance.

Correlation analysis is widely used across many fields: **Research:** Test hypotheses about relationships between variables in psychology, education, medicine, and social sciences. For example, studying the relationship between study hours and exam scores, or between exercise frequency and health outcomes. **Finance:** Analyze relationships between stock prices, economic indicators, or portfolio diversification. Correlation matrices help identify which assets move together or independently. **Marketing:** Understand relationships between advertising spend and sales, customer satisfaction and retention, or price sensitivity and demand elasticity. **Quality Control:** Monitor relationships between process parameters and product quality in manufacturing. Identify which factors most strongly correlate with defect rates or product performance. **Healthcare:** Study associations between lifestyle factors and health outcomes, medication dosages and treatment effectiveness, or demographic variables and disease prevalence.