Metric and Euclidean properties of dissimilarity coefficients

We assemble here properties of certain dissimilarity coefficients and are specially concerned with their metric and Euclidean status. No attempt is made to be exhaustive as far as coefficients are concerned, but certain mathematical results that we have found useful are presented and should help establish similar properties for other coefficients. The response to different types of data is investigated, leading to guidance on the choice of an appropriate coefficient.The authors wish to thank the referees, one of whom did a magnificent job in painstakingly checking the detailed algebra and detecting several slips.