Pearson Correlation Coefficient Calculator
Calculate the Pearson correlation coefficient to measure the strength and direction of linear association between two variables. Includes significance testing.
Correlation Coefficient Guide
Pearson r Values
The Pearson correlation coefficient r ranges from −1 to +1. r = +1: perfect positive linear correlation — as X increases, Y increases proportionally. r = −1: perfect negative linear correlation — as X increases, Y decreases proportionally. r = 0: no linear correlation. Guidelines for interpretation: |r| 0.0–0.2: negligible. 0.2–0.4: weak. 0.4–0.6: moderate. 0.6–0.8: strong. 0.8–1.0: very strong. These thresholds are context-dependent — a correlation of 0.3 may be very meaningful in social scienc
R-squared and Explained Variance
R² (coefficient of determination) = r². It represents the proportion of variance in Y that is explained by X. R² = 0.64 means 64% of the variation in Y is explained by its linear relationship with X. The remaining 36% is due to other factors or random variation. Example: r = 0.8 (strong positive correlation) → R² = 0.64. If Y is exam score and X is hours studied: 64% of the variation in exam scores is explained by study time. The other 36% is explained by other factors (prior knowledge, sleep, a
Correlation vs Causation
Correlation does not imply causation — one of the most important statistical principles. Examples of spurious correlations: ice cream sales and drowning rates correlate strongly (both driven by summer/hot weather). Number of Nicolas Cage films and swimming pool drownings correlate (coincidence in a finite dataset). Shoe size and reading ability in primary school (both caused by age). Before concluding causation: check temporal order (cause must precede effect), consider confounding variables, te
When NOT to Use Pearson r
Pearson r measures linear association only. For non-linear relationships (curved, U-shaped), r may be near zero even with a strong non-linear pattern. Check by plotting a scatterplot first. For non-normal data or ordinal data (ranks), use Spearman's rank correlation (rₛ) instead. Outliers heavily influence Pearson r — a single extreme point can change r from near 0 to 0.8. Always check scatterplots before interpreting correlation coefficients. Restricted range: if data is sampled from a narrow r
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