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A statistic measuring the strength and direction of a linear relationship between two continuous variables.
DESCRIPTION
The Pearson correlation coefficient, typically denoted r, ranges from −1 to +1. Values near ±1 indicate strong linear relationships, while 0 indicates no linear correlation. It is sensitive to outliers and assumes approximate linearity and homoscedasticity. Pearson correlation is widely used in exploratory analysis, feature selection, and reporting associations. Alternatives like Spearman and Kendall handle monotonic but non-linear relationships or ties better. Proper interpretation requires scatter plots and domain context.
ALTERNATIVE DEFINITIONS
Wikipedia
In statistics, the Pearson correlation coefficient (PCC) is a measure of the linear correlation between two sets of data.
Defines scope as linear correlation between two datasets.
NIST/SEMATECH e-Handbook
The correlation coefficient r measures the strength and direction of a linear relationship between two variables.
Highlights strength and direction aspects for linear relationships.
Encyclopaedia Britannica
Correlation, in statistics, the degree of association between two random variables or two sets of data.
Broader correlation definition providing conceptual context.
RELATED TERMS
Covariance Linear Model R-squared Scatter Plot Feature Scaling Z-score Outliers Assumption of Linearity
COMPETING TERMS
Spearman’s Rank Correlation Coefficient Kendall Rank Correlation
RELATIONS
- Broader: Correlation Coefficient
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist Data Analyst BI Specialist
EXTERNAL SOURCES
- Wikipedia - Pearson correlation coefficient
- SciPy - pearsonr function documentation and usage
- NIST - Detailed explanation of correlation coefficient
- Statistics by Jim - Article explaining correlations with examples
TOP QUESTIONS
When should I use Pearson Correlation Coefficient?
Use it to assess linear relationships between continuous variables, after checking scatter plots and assumptions.
Category: Application
How do outliers affect Pearson Correlation?
Outliers can dramatically change r, inflating or deflating perceived relationships.
Category: Risks
What’s a common misunderstanding about Pearson Correlation?
High correlation does not imply causation; it only indicates association.
Category: Misunderstanding
How do I interpret r = 0?
It indicates no linear association, but non-linear relationships may still exist.
Category: Concept
How does Pearson compare to Spearman?
Pearson captures linear relationships; Spearman measures monotonic rank correlations and is more robust to outliers.
Category: Comparison
What sample size is needed for reliable r?
Larger samples provide more stable estimates and p-values; small samples can be misleading.
Category: Requirements
Can I compute Pearson on ordinal data?
No, Pearson assumes interval/ratio scales; use Spearman for ordinal data.
Category: Mistakes
How do I test significance of r?
Use a t-test for correlation or compute a p-value via statistical software.
Category: Testing
Where is Pearson Correlation used in ML?
Feature screening, multicollinearity checks, and exploratory analysis of relationships.
Category: Application