Correlation coefficients
| Coefficient | Range | Assumptions | Use |
|---|---|---|---|
| Pearson r | −1 to +1 | Linear relationship, roughly normal | Linear correlation on continuous vars |
| Spearman ρ | −1 to +1 | Monotonic relationship | Rank correlation; robust to outliers |
| Kendall τ | −1 to +1 | Concordant / discordant pairs | Small-sample rank correlation |
| Point-biserial | −1 to +1 | One binary + one continuous | Binary vs continuous correlation |
| Phi φ | −1 to +1 | Two binary variables | 2×2 table correlation |
Interpretation of |r|
| |r| | Strength |
|---|---|
| 0.00 – 0.10 | Negligible |
| 0.10 – 0.30 | Weak |
| 0.30 – 0.50 | Moderate |
| 0.50 – 0.70 | Strong |
| 0.70 – 1.00 | Very strong |
Caveats
- Correlation ≠ causation. Confounders, selection bias, and reverse causality can all create spurious correlations.
- Pearson r only measures linear association — a perfect parabola can have r = 0.
- Outliers can drive r artificially high or low — always plot the scatter.
- Statistical significance (p-value) of r depends on sample size — big n makes tiny correlations "significant" without practical meaning.
- R² (coefficient of determination) = r² — proportion of variance explained.
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