Numerical bias in correlation: carbonate modal data, stratigraphic thickness data, and geochemical data

Numerical techniques commonly used by geologists to quantitatively ferret out relationships among variables include scattergrams, dendrograms, and principal components analysis. These and other analytical methods are based on a measure of similarity, such as the Pearson product-moment correlation coefficient, r. The r matrix, however, may be subject to numerical bias depending on the type of data from which the matrix is calculated. Consequently, inferences about the geologic significance of the between-variable relationships may be unsound and may reflect nothing more than numerical inevitabilities. R-mode analyses of a set of carbonate modal data, a set of sedimentary thickness data, and a set of geochemical data show that the interpreter of quantitative analysis must bear in mind not only the constraints of the analytical method but also those of the data treatment. Among other results, this investigation has determined that closure can induce correlation of the rank type as well as of the product-moment type and that principal components analysis may not be any more efficient a reducer of data than a visual inspection of variances.