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Beware of spurious self‐correlations!
Author(s) -
Kenney Bernard C.
Publication year - 1982
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr018i004p01041
Subject(s) - spurious relationship , logarithm , mathematics , statistics , term (time) , correlation , magnitude (astronomy) , dispersion (optics) , linear regression , statistical physics , physics , mathematical analysis , optics , geometry , quantum mechanics , astronomy
Spurious self‐correlations arise when two parameters (sums, differences, ratios, products, or single variables) that are used in a linear regression analysis have a common term. Examples are presented to show that under certain conditions, perfect (but entirely spurious) correlation is obtained between two such parameters formed from random numbers. The magnitude of the spurious self‐correlation coefficient is greatest for data sets where there is much larger dispersion in the data for the common term relative to the unique term(s) in the parameters. Logarithmic transformations or log‐log plots enhance spurious self‐correlations of ratios and products. The misuse of spurious self‐correlation is illustrated with examples from the literature.