Correlation#
The strength and direction of a linear relationship between variables.
Important
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What it is#
Correlation measures the strength and direction of the relationship between two variables. The Pearson coefficient — r in a sample, ρ in the population — runs from −1 to +1: −1 a perfect negative line, +1 a perfect positive line, and 0 no linear relationship.
How to read it#
The sign gives direction, the magnitude gives strength; squaring it yields r², the share of one variable’s variance explained by the other. Rough effect-size guides call 0.1 small, 0.3 medium, 0.5 large — but a statistically significant r can still be trivially small in a large sample.
Its limits#
Correlation captures only linear association, so it can miss strong nonlinear patterns; it is not robust to outliers, which can inflate or hide it; and, crucially, correlation is not causation — two variables can move together because a third drives both. Use rank correlation (Spearman) for monotonic, non-linear ties.
Theme: Probability & Statistics Foundations · All terminology
Hint
Mind map — connected ideas
R² (R-squared) · Statistical Power · Statistical Tests · Confidence Intervals (CIs) · Population Proportion · Outlier
Hint
More in Probability & Statistics Foundations
Beta Distribution · Confidence Level · Critical Value · Cumulative Distribution Function (CDF) · Frequentist · IID (Independent and Identically Distributed) · Likelihood · Margin of Error (MoE) · Mean · Median · Normal Distribution · Outlier · Population Proportion · Probability
See also
Source article Adapted (context, re-expressed) in our own words from: Correlation (insightful-data-lab.com).