A method of analysis of covariance structure proposed by A. P. Dempster complements, in some respects, a recently suggested procedure by the author. The method is based on the comparison of ratios of generalized statistical distances and distancelike quantities. An analysis of septivariate data on the foraminiferTextilina mexicana (Cushman) shows general differences in covariance structure in which the sample rest linear discriminators also differ. This difference in covariance structure is thought to be genetic in origin. Two species of Middle Devonian brachiopods,Martinia inflata (Schnur) andUncites gryphus von Schlotheim), also show differences in covariance structure—the former slightly, the latter strongly. This is further analyzed forUncites by the author's methods and good agreement between the two approaches obtained.