Baroni-Urbani, C. (Natural History Museum, Augustinergasse 2, CH-4051 Basel, Switzerland), and Buser, M. W. (Department of Nuclear Physics,2 Klingelbergstrasse 82, and Computing Center, Klingelbergstrasse 70, University of Basle, CH-4000 Basel, Switzerland) 1976. Similarity of binary data. Syst. Zool. 25:251-259.-A set of intuitively obvious properties of a coefficient of similarity for binary data is established. Critical examination of the coefficients available from the literature shows that none of them satisfies all these properties, and a new coefficient is proposed to obviate this inconvenience. The distribution of the new coefficient is studied on very large, perfectly random samples of OTU's, and a table is constructed to show its critical values at different significance levels. A mathematical appendix is given to demonstrate the procedure used to construct perfectly random samples of different size. [Numerical taxonomy; biogeography; ecology; similarity coefficients.] In the literature we find a variety of different coefficients proposed to measure the similarity between OTU's described by binaiy data, and each coefficient often gives results different from the others (BaroniUrbani and Collingwood, 1975). It is surprising how numerical taxonomy has undergone a fast process of growth in some complicated aspects of its procedure, such as clustering, apparently leaving aside the problem of a logical measure of similarity, which is the basis on which the quality of all the remaining work depends. This situation of uncertainty has sometimes led to the paradoxical situation of students using two differelnt coefficients in the same paper, and for the Q and R analysis of the same data matrix, in order to find a result better fitting their ideas of the phenomenon studied. Although our interest in the subject stems from an attempt to solve biogeographical problems, we firmly believe that there is just one type of similarity which is really useful both in Q and R analysis and in the whole of biology as well as in the humanities. Unfortunately, similarity in itself is not a mathematical concept, even if the data on which we measure it are expressed by numbers. Despite this inconvenience, 1 The execution of drawings for this paper has been made by Miss Eva Weber through a grant of the National Science Foundation of Switzerland, request Nr.3.785.-72. 2 Present address. which precludes a rigorously formalized approach to the problem, there are undoubtedly some properties which should be satisfied by a good coefficient of similarity and on which a general agreement should easily be found.