Tests for Hierarchical Structure in Random Data Sets

Abstract

The degree of fit of phenograms (constructed using UPGMA cluster analysis) to similarity matrices based on random data was examined using the cophenetic correlation coefficient. Approximate critical bounds were established for testing for the presence of hierarchic structure in one's data. Sokal's taxonomic distance coefficient was shown to be more sensitive than the product-moment correlation coefficient to differences in the multivariate structure of the sampled distributions. The purpose of this study was to investigate the degree of fit of phenograms to similarity matrices based on random data (both multivariate normal and uniform distributions were used). The degree of fit was measured using the cophenetic correlation coefficient (Sokal and Rohlf, 1962). It is of interest to develop a standard for comparsion with actual numerical taxonomic results in order to formulate a test criterion to indicate whether one has sufficient evidence to indicate that the phenetic relationships present in one's data are hierarchic (rather than simply what could be expected from a random sample of a single homogeneous population).