An illustration of spurious correlation, this figure shows 500 observations of x/z plotted against y/z. The sample correlation is 0.53, even though x, y, and z are statistically independent of each other (i.e., the pairwise correlations between each of them are zero). The z-values are highlighted on a colour scale.
In statistics, spurious correlation of ratios is a form of spurious correlation that arises between ratios of absolute measurements which themselves are uncorrelated.[1][2]
The phenomenon of spurious correlation of ratios is one of the main motives for the field of compositional data analysis, which deals with the analysis of variables that carry only relative information, such as proportions, percentages and parts-per-million.[3][4]
Spurious correlation is distinct from misconceptions about correlation and causality.
^Pearson, Karl (1896). "Mathematical Contributions to the Theory of Evolution – On a Form of Spurious Correlation Which May Arise When Indices Are Used in the Measurement of Organs". Proceedings of the Royal Society of London. 60 (359–367): 489–498. doi:10.1098/rspl.1896.0076. JSTOR 115879.
^Aldrich, John (1995). "Correlations Genuine and Spurious in Pearson and Yule". Statistical Science. 10 (4): 364–376. doi:10.1214/ss/1177009870.
^Aitchison, John (1986). The statistical analysis of compositional data. Chapman & Hall. ISBN 978-0-412-28060-3.
^Pawlowsky-Glahn, Vera; Buccianti, Antonella, eds. (2011). Compositional Data Analysis: Theory and Applications. Wiley. doi:10.1002/9781119976462. ISBN 978-0470711354.
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