Calculate the Pearson and Spearman correlation coefficients between two variables. Paste your data, get r, r², and an interpretation of the strength and direction of the relationship.
Pearson r measures the linear relationship between two variables. It ranges from -1 (perfect negative) through 0 (no correlation) to +1 (perfect positive). It assumes both variables are normally distributed and the relationship is linear.
|r| < 0.3: very weak. |r| 0.3-0.5: weak. |r| 0.5-0.7: moderate. |r| 0.7-0.9: strong. |r| > 0.9: very strong. The sign indicates direction: positive means both variables increase together, negative means one rises as the other falls.
R-squared (coefficient of determination) shows the proportion of variance in Y explained by X. r = 0.8 gives r² = 0.64, meaning 64% of the variation in Y is explained by its linear relationship with X.
Pearson measures linear correlation between actual values and requires normality. Spearman measures monotonic correlation between ranks — it works for non-linear relationships and non-normal data, and is more robust to outliers.
No. A high correlation between X and Y means they change together, but not that one causes the other. Both could be caused by a third variable (confound). Causation requires controlled experiments, not just correlation analysis.
At least 5-10 pairs for a meaningful result. With fewer points, the correlation is statistically unreliable — even random data can show r = ±1 with just 2 points. For hypothesis testing, use at least 25-30 pairs.
A spurious correlation is a high r value between two variables that have no causal or logical relationship. Famous examples: ice cream sales correlating with drowning rates (both caused by summer heat). Always consider the mechanism behind the numbers.