Correlation

Correlation measures the degree to which two variables move together. The standard measure is Pearson’s r: a single number from −1 to +1 where +1 means perfect positive linear relationship, 0 means no linear relationship, and −1 means perfect negative linear relationship.

Practical interpretation:

• |r| < 0.3 — weak
• 0.3 ≤ |r| < 0.7 — moderate
• |r| ≥ 0.7 — strong

Three things every reader of correlation numbers should know:

1. Pearson’s r only captures linear relationships. Two variables related by a perfect quadratic (y = x²) can have r ≈ 0 if x ranges over both positive and negative values. For non-linear relationships, Spearman’s rho is the more robust alternative.
2. Correlation is not causation. Two variables can correlate strongly because A causes B, B causes A, both are caused by a third variable, or pure coincidence (especially in small samples or comparing many pairs).
3. Outliers distort r dramatically. A single outlier in a small dataset can flip the sign of the correlation. Always plot the data before trusting the number.

For categorical or rank-ordered data, use Spearman’s rank correlation instead of Pearson. For binary outcomes, look up the phi coefficient. For nominal categorical data with more than two levels, Cramér’s V.