Correlation
Correlation describes an association between variables. A correlation coefficient summarises the strength and direction of a specified kind of relationship. Different coefficients measure different patterns, so the meaning of the number depends on the measure used.[1]
Direction and strength
The Pearson correlation coefficient measures linear association. It ranges from −1 to +1. A positive value means that higher values of one variable tend to accompany higher values of the other; a negative value indicates the opposite tendency. Values closer to either endpoint indicate a stronger linear relationship. A value of zero indicates no linear association, but does not rule out a curved relationship.[2]
A scatter plot shows the paired observations directly. Inspecting the pattern helps distinguish a roughly straight-line relationship from other shapes and reveals extreme observations that may strongly affect Pearson's coefficient. Spearman's rank correlation coefficient uses the ranks of observations rather than their original values.[2]
Interpretation
Terms such as weak, moderate and strong are used differently across research fields. Reporting the coefficient itself makes the result clearer than relying on a label alone. Statistical significance and the size of an association are separate matters: a statistically significant result need not represent a strong relationship.[1]
Correlation alone does not establish causation. An observed relationship may have either direction of influence, or arise because another factor affects both variables. Correlational research measures relationships without deliberately changing the conditions as an experiment does.[3]
References
- ↑ 1.0 1.1 Akoglu, Haldun (2018-08-07). "User's guide to correlation coefficients". Turkish Journal of Emergency Medicine. 18 (3): 91–93. doi:10.1016/j.tjem.2018.08.001. Retrieved 2026-10-18.
There are no absolute rules for the interpretation of their strength.
- ↑ 2.0 2.1 Mukaka, M. M. (2012). "A guide to appropriate use of Correlation coefficient in medical research". Malawi Medical Journal. 24 (3): 69–71. Retrieved 2026-10-18.
A correlation coefficient of zero indicates that no linear relationship exists between two continuous variables
- ↑ Scollon, Christie Napa. "Research Designs". Noba textbook series: Psychology. Diener Education Fund. Retrieved 2026-10-18.
This is why correlation does not mean causation
Attribution
Adapted from English Wikipedia's Correlation, revision 1379810158 (contributors and history), under the Creative Commons Attribution-ShareAlike 4.0 licence. Rewritten as an introductory overview using independently checked secondary sources; detailed derivations and advanced methods are outside its scope.