Assessment of quantitative techniques in paleobiogeography

A series of multivariate methods has been compared to assess their effectiveness in extracting essential information out of a complex micropaleontological data-set. The data-set used for this experiment consists of relative frequencies (percentages) of Miocene coccolith taxa or groups of taxa in cores of the Deep Sea Drilling Project (DSDP) from the Atlantic Ocean. All methods tested are varieties of principal components analysis in R- and Q-mode, and “true” factor analysis. Various secondary rotational procedures ancillary to some of these methods are also tested.A test, denoted Δ-Test, is developed, which assesses how well principal components or factors reproduce the data-set. Δ-Test may be used for determining the optimum number of principal components or factors, the most relevant rotational procedure, and thus the most suitable analytical technique. The Δ-Test does not rely on mathematical testing, but on simple inspection of the compositions of the principal components or factors, and their relations to correlations existing in the data-set.Our experiment reveals that the most efficient methods are the maximum-likelihood factor analysis and the R-mode principal components analysis, within which the varimax (orthogonal) rotations best reproduce correlations. Of these methods, maximum-likelihood factor analysis is considered the optimum method, because of the greater simplicity of compositions. In addition to these methods, Kaiser's second generation “Little Jiffy” factor analysis was also found to be efficient. Three methods provide less sensitive reduction of the data: the “true” R-mode principal components analysis (without secondary rotations), the Q-mode principal components analysis, and the correspondence analysis.