Beware of spurious self‐correlations!

Abstract

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.