On the evaluation of ordinal data with conventional multivariate procedures

In a recent Forum paper, it is argued that, in most studies, ordinal data such as the Braun-Blanquet abundance/dominance scale are not properly treated by multivariate methods. This is because conventional multivariate methods are generally adequate for ratio-scale variables only, while for ordinal variables differences between states and their ratios are not interpreted. Conversely, in this paper it is shown that using conventional multivariate procedures for evaluating ordinal data should imply a shift from a metric space to a topological data space; as such the use of ordinal data does not represent a serious methodological error, provided that results are interpreted accordingly.