Spurious or virtual correlation errors commonly encountered in reduction of scientific data

Abstract

Flawed analysis either intentional or though misunderstanding of commonly accepted data analysis methods can lead to erroneous results and presumption of correlation of cause and effect, when, in fact, there is little or none. Classical dimensional analysis combined with statistical regression of such scaled data may produce apparent correlation of information resulting in “virtual” or “spurious” correlation. Such inadvertent correlation errors can result in inappropriate conclusions and self-deception concerning the actual relationships between scaling variables and the associated reduction in variance found in tables and graphs. A number of dimensionless expressions used in meteorology and wind engineering induce large magnitudes of spurious correlation when plotted against other commonly accepted parameters. For example, when drag coefficients, CD, pressure coefficients, Cp, dimensionless shear, S*, or dimensionless concentrations, K, are regressed against Reynolds numbers, Re, dimensionless height, z/LMO, or stratified Jensen numbers, zo/LMO, then inherent virtual correlations can exist with values from 50% to 95% even when random numbers are used to generate the component parts of the dimensionless groups!