Extending Gower's general coefficient of similarity to ordinal characters

The possibilities of calculating similarity based on ordinal characters are evaluated by distinguishing subtypes of the ordinal scale. Multivariate analysis is most problematic when ordinal variables appear together with other scale types in the data. This difficulty is solved by extending Gower's general coefficient of similarity to ordinal data types, facilitating cluster analysis and multidimensional scaling. Two alternatives, a non-metric and a metric version, are offered. The modified formula implies that ordinal variables are equally weighted with the others, and that partially and fully ranked data are both applicable, due to the inherent standardisation procedure. A morphological data set derived for the moss genus Tortula illustrates the new approach.