Pearson r Formula
Range: −1 ≤ r ≤ +1
r² = coefficient of determination
Interpreting the Correlation Coefficient
| r value | Strength | Direction |
|---|---|---|
| 0.90 to 1.00 | Very strong | Positive |
| 0.70 to 0.89 | Strong | Positive |
| 0.40 to 0.69 | Moderate | Positive |
| 0.10 to 0.39 | Weak | Positive |
| 0.00 to 0.09 | Negligible | — |
| −0.09 to 0.00 | Negligible | — |
| −0.39 to −0.10 | Weak | Negative |
| −0.69 to −0.40 | Moderate | Negative |
| −0.89 to −0.70 | Strong | Negative |
| −1.00 to −0.90 | Very strong | Negative |
Frequently Asked Questions
Does correlation imply causation?
No — correlation only measures the strength of a linear association, not whether one variable causes the other. Classic examples: ice cream sales and drowning rates are positively correlated (both driven by summer heat, not each other). Always consider confounding variables before inferring causation.
What is r² (coefficient of determination)?
r² tells you the proportion of variance in Y explained by X. If r = 0.8, then r² = 0.64, meaning 64% of the variation in Y is explained by the linear relationship with X. The remaining 36% is unexplained by this model.
What is Spearman's rank correlation?
Spearman's ρ (rho) is a non-parametric alternative to Pearson's r. It measures monotonic (not necessarily linear) relationships and is more robust to outliers. It works by ranking the data and computing Pearson r on the ranks. Use Spearman when data is ordinal or not normally distributed.