Mathematical Geology, Vol. t0, No. 2, 1978 An Empirical Assessment and Illustration of Some Multivariate Morphometric Techniques 1 Barry G. Fordham 2 and Geoffrey D. Bell ~ An artificial data set is used to illustrate the morphologic properties of some common multi- variate techniques and consideration of three common situations. The first concerns a sample showing no obvious groupings. In this situation principal components (or coordinates) and factor analyses give a logical ordination of form variation; cluster analysis produces size- dominated groups. The second situation considers an homogeneous sample where size and shape have important implications. Principal components are tested for association with size and shape, both of which can be isolated if isometry exists; if allometry is present, isolation of shape is possible only by size elimination, e.g., conversion to ratios. The third situation examines a sample of unknown groupings in which shape variation is the only interest. Aside from ratios, two other methods which produce shape-dominant clusters are assessed. Some of the options available in cluster analysis are also examined. KEY WORDS: classification, cluster analysis, principal components, morphometrics. INTRODUCTION The numerical study of form, morphometrics, frequently requires the pro- cessing of many measurements by mathematical techniques outside the researcher's field. Thus the user often does not fully appreciate the relation- ship between the matrix manipulations involved and the morphologic inter- pretation sought. With this in mind, a few of the more common multivariate techniques are applied to an artificial data set with an emphasis on a graphical display of the results. The methods considered fall into two categories: (a) ordination pro- cedures (principal components, principal coordinates, and factor analyses) which reduce the data set to smaller, more manageable subsets retaining most of the original information; and (b) classificatory methods, typified by cluster analysis, which attempt to simplify interpretation by seeking group- ings within the data. The latter techniques were evolved in other fields as an ordering device and therefore are unlikely to be appropriate for the analysis 1 Manuscript received 1 October 1977. 2 Department of Geology and Mineralogy, University of Queensland, St. Lucia, Australia 4067. 111 0020-5958178/0400-0111 $05.00/0 © 1978 Plenum Publishing Corporation