Sub-species of Homopus Areolatus? Biplots and Small Class Inference with Analysis of Distance

A canonical variance analysis (CVA) biplot can visually portray a oneway MANOVA. Both techniques are subject to the assumption of equal class covariance matrices. In the application considered, very small sample sizes resulted in some singular class covariance matrix estimates and furthermore it seemed unlikely that the assumption of homogeneity of covariance matrices would hold. Analysis of distance (AOD) is employed as nonparametric inference tool. In particular, AOD biplots are introduced for a visual display of samples and variables, analogous to the CVA biplot.